Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration

NASA Astrophysics Data System (ADS)

Li, G. Q.; Zhu, Z. H.

2015-12-01

Dynamic modeling of tethered spacecraft with the consideration of elasticity of tether is prone to the numerical instability and error accumulation over long-term numerical integration. This paper addresses the challenges by proposing a globally stable numerical approach with the nodal position finite element method (NPFEM) and the implicit, symplectic, 2-stage and 4th order Gaussian-Legendre Runge-Kutta time integration. The NPFEM eliminates the numerical error accumulation by using the position instead of displacement of tether as the state variable, while the symplectic integration enforces the energy and momentum conservation of the discretized finite element model to ensure the global stability of numerical solution. The effectiveness and robustness of the proposed approach is assessed by an elastic pendulum problem, whose dynamic response resembles that of tethered spacecraft, in comparison with the commonly used time integrators such as the classical 4th order Runge-Kutta schemes and other families of non-symplectic Runge-Kutta schemes. Numerical results show that the proposed approach is accurate and the energy of the corresponding numerical model is conservative over the long-term numerical integration. Finally, the proposed approach is applied to the dynamic modeling of deorbiting process of tethered spacecraft over a long period.

Exponentially fitted symplectic Runge-Kutta-Nyström methods derived by partitioned Runge-Kutta methods

NASA Astrophysics Data System (ADS)

Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.

2013-10-01

In this work we derive symplectic EF/TF RKN methods by symplectic EF/TF PRK methods. Also EF/TF symplectic RKN methods are constructed directly from classical symplectic RKN methods. Several numerical examples will be given in order to decide which is the most favourable implementation.

Minimal models of compact symplectic semitoric manifolds

NASA Astrophysics Data System (ADS)

Kane, D. M.; Palmer, J.; Pelayo, Á.

2018-02-01

A symplectic semitoric manifold is a symplectic 4-manifold endowed with a Hamiltonian (S1 × R) -action satisfying certain conditions. The goal of this paper is to construct a new symplectic invariant of symplectic semitoric manifolds, the helix, and give applications. The helix is a symplectic analogue of the fan of a nonsingular complete toric variety in algebraic geometry, that takes into account the effects of the monodromy near focus-focus singularities. We give two applications of the helix: first, we use it to give a classification of the minimal models of symplectic semitoric manifolds, where "minimal" is in the sense of not admitting any blowdowns. The second application is an extension to the compact case of a well known result of Vũ Ngọc about the constraints posed on a symplectic semitoric manifold by the existence of focus-focus singularities. The helix permits to translate a symplectic geometric problem into an algebraic problem, and the paper describes a method to solve this type of algebraic problem.

Life on the Edge of Chaos: Orbital Mechanics and Symplectic Integration

NASA Astrophysics Data System (ADS)

Newman, William I.; Hyman, James M.

1998-09-01

Symplectic mapping techniques have become very popular among celestial mechanicians and molecular dynamicists. The word "symplectic" was coined by Hermann Weyl (1939), exploiting the Greek root for a word meaning "complex," to describe a Lie group with special geometric properties. A symplectic integration method is one whose time-derivative satisfies Hamilton's equations of motion (Goldstein, 1980). When due care is paid to the standard computational triad of consistency, accuracy, and stability, a numerical method that is also symplectic offers some potential advantages. Varadarajan (1974) at UCLA was the first to formally explore, for a very restrictive class of problems, the geometric implications of symplectic splittings through the use of Lie series and group representations. Over the years, however, a "mythology" has emerged regarding the nature of symplectic mappings and what features are preserved. Some of these myths have already been shattered by the computational mathematics community. These results, together with new ones we present here for the first time, show where important pitfalls and misconceptions reside. These misconceptions include that: (a) symplectic maps preserve conserved quantities like the energy; (b) symplectic maps are equivalent to the exact computation of the trajectory of a nearby, time-independent Hamiltonian; (c) complicated splitting methods (i.e., "maps in composition") are not symplectic; (d) symplectic maps preserve the geometry associated with separatrices and homoclinic points; and (e) symplectic maps possess artificial resonances at triple and quadruple frequencies. We verify, nevertheless, that using symplectic methods together with traditional safeguards, e.g. convergence and scaling checks using reduced step sizes for integration schemes of sufficient order, can provide an important exploratory and development tool for Solar System applications.

Symplecticity in Beam Dynamics: An Introduction

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

Rees, John R

2003-06-10

A particle in a particle accelerator can often be considered a Hamiltonian system, and when that is the case, its motion obeys the constraints of the Symplectic Condition. This tutorial monograph derives the condition from the requirement that a canonical transformation must yield a new Hamiltonian system from an old one. It then explains some of the consequences of symplecticity and discusses examples of its applications, touching on symplectic matrices, phase space and Liouville's Theorem, Lagrange and Poisson brackets, Lie algebra, Lie operators and Lie transformations, symplectic maps and symplectic integrators.

Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

2017-04-01

Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

Explicit symplectic algorithms based on generating functions for charged particle dynamics.

PubMed

Zhang, Ruili; Qin, Hong; Tang, Yifa; Liu, Jian; He, Yang; Xiao, Jianyuan

2016-07-01

Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity. For long-term simulations with high efficiency, explicit symplectic algorithms are desirable. However, it is generally believed that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and this restriction limits the application of explicit symplectic algorithms to charged particle dynamics. To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second- and third-order explicit symplectic algorithms for dynamics of charged particle. The generating function method is designed to generate explicit symplectic algorithms for product-separable Hamiltonian with form of H(x,p)=p_{i}f(x) or H(x,p)=x_{i}g(p). Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency.

Explicit symplectic algorithms based on generating functions for charged particle dynamics

NASA Astrophysics Data System (ADS)

Zhang, Ruili; Qin, Hong; Tang, Yifa; Liu, Jian; He, Yang; Xiao, Jianyuan

2016-07-01

Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity. For long-term simulations with high efficiency, explicit symplectic algorithms are desirable. However, it is generally believed that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and this restriction limits the application of explicit symplectic algorithms to charged particle dynamics. To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second- and third-order explicit symplectic algorithms for dynamics of charged particle. The generating function method is designed to generate explicit symplectic algorithms for product-separable Hamiltonian with form of H (x ,p ) =pif (x ) or H (x ,p ) =xig (p ) . Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency.

Relational symplectic groupoid quantization for constant poisson structures

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Moshayedi, Nima; Wernli, Konstantin

2017-09-01

As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the relational symplectic groupoid for a constant Poisson structure. The presence of mixed boundary conditions and the globalization of results are also addressed. In particular, the paper includes an extension to space-times with boundary of some formal geometry considerations in the BV-BFV formalism, and specifically introduces into the BV-BFV framework a "differential" version of the classical and quantum master equations. The quantization constructed in this paper induces Kontsevich's deformation quantization on the underlying Poisson manifold, i.e., the Moyal product, which is known in full details. This allows focussing on the BV-BFV technology and testing it. For the inexperienced reader, this is also a practical and reasonably simple way to learn it.

Poly-symplectic Groupoids and Poly-Poisson Structures

NASA Astrophysics Data System (ADS)

Martinez, Nicolas

2015-05-01

We introduce poly-symplectic groupoids, which are natural extensions of symplectic groupoids to the context of poly-symplectic geometry, and define poly-Poisson structures as their infinitesimal counterparts. We present equivalent descriptions of poly-Poisson structures, including one related with AV-Dirac structures. We also discuss symmetries and reduction in the setting of poly-symplectic groupoids and poly-Poisson structures, and use our viewpoint to revisit results and develop new aspects of the theory initiated in Iglesias et al. (Lett Math Phys 103:1103-1133, 2013).

Formal Symplectic Groupoid of a Deformation Quantization

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

2005-08-01

We give a self-contained algebraic description of a formal symplectic groupoid over a Poisson manifold M. To each natural star product on M we then associate a canonical formal symplectic groupoid over M. Finally, we construct a unique formal symplectic groupoid ‘with separation of variables’ over an arbitrary Kähler-Poisson manifold.

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

A modified symplectic PRK scheme for seismic wave modeling

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Ma, Jian

2017-02-01

A new scheme for the temporal discretization of the seismic wave equation is constructed based on symplectic geometric theory and a modified strategy. The ordinary differential equation in terms of time, which is obtained after spatial discretization via the spectral-element method, is transformed into a Hamiltonian system. A symplectic partitioned Runge-Kutta (PRK) scheme is used to solve the Hamiltonian system. A term related to the multiplication of the spatial discretization operator with the seismic wave velocity vector is added into the symplectic PRK scheme to create a modified symplectic PRK scheme. The symplectic coefficients of the new scheme are determined via Taylor series expansion. The positive coefficients of the scheme indicate that its long-term computational capability is more powerful than that of conventional symplectic schemes. An exhaustive theoretical analysis reveals that the new scheme is highly stable and has low numerical dispersion. The results of three numerical experiments demonstrate the high efficiency of this method for seismic wave modeling.

Mirror symmetry in emergent gravity

NASA Astrophysics Data System (ADS)

Yang, Hyun Seok

2017-09-01

Given a six-dimensional symplectic manifold (M , B), a nondegenerate, co-closed four-form C introduces a dual symplectic structure B ˜ = * C independent of B via the Hodge duality *. We show that the doubling of symplectic structures due to the Hodge duality results in two independent classes of noncommutative U (1) gauge fields by considering the Seiberg-Witten map for each symplectic structure. As a result, emergent gravity suggests a beautiful picture that the variety of six-dimensional manifolds emergent from noncommutative U (1) gauge fields is doubled. In particular, the doubling for the variety of emergent Calabi-Yau manifolds allows us to arrange a pair of Calabi-Yau manifolds such that they are mirror to each other. Therefore, we argue that the mirror symmetry of Calabi-Yau manifolds is the Hodge theory for the deformation of symplectic and dual symplectic structures.

Symmetries of the Space of Linear Symplectic Connections

NASA Astrophysics Data System (ADS)

Fox, Daniel J. F.

2017-01-01

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt moment map, the Ricci tensor, and a translational term. The critical points of a functional constructed from it interpolate between the equations for preferred symplectic connections and the equations for critical symplectic connections. The commutative algebra of formal sums of symmetric tensors on a symplectic manifold carries a pair of compatible Poisson structures, one induced from the canonical Poisson bracket on the space of functions on the cotangent bundle polynomial in the fibers, and the other induced from the algebraic fiberwise Schouten bracket on the symmetric algebra of each fiber of the cotangent bundle. These structures are shown to be compatible, and the required Lie algebras are constructed as central extensions of their! linear combinations restricted to formal sums of symmetric tensors whose first order term is a multiple of the differential of its zeroth order term.

Constant symplectic 2-groupoids

NASA Astrophysics Data System (ADS)

Mehta, Rajan Amit; Tang, Xiang

2018-05-01

We propose a definition of symplectic 2-groupoid which includes integrations of Courant algebroids that have been recently constructed. We study in detail the simple but illustrative case of constant symplectic 2-groupoids. We show that the constant symplectic 2-groupoids are, up to equivalence, in one-to-one correspondence with a simple class of Courant algebroids that we call constant Courant algebroids. Furthermore, we find a correspondence between certain Dirac structures and Lagrangian sub-2-groupoids.

Symplectic discretization for spectral element solution of Maxwell's equations

NASA Astrophysics Data System (ADS)

Zhao, Yanmin; Dai, Guidong; Tang, Yifa; Liu, Qinghuo

2009-08-01

Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.

Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

NASA Astrophysics Data System (ADS)

Minesaki, Yukitaka

2018-04-01

We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems

NASA Astrophysics Data System (ADS)

Mei, Lijie; Wu, Xinyuan

2017-06-01

Symplecticity is also an important property for exponential Runge-Kutta (ERK) methods in the sense of structure preservation once the underlying problem is a Hamiltonian system, though ERK methods provide a good performance of higher accuracy and better efficiency than classical Runge-Kutta (RK) methods in dealing with stiff problems: y‧ (t) = My + f (y). On account of this observation, the main theme of this paper is to derive and analyze the symplectic conditions for ERK methods. Using the fundamental analysis of geometric integrators, we first establish one class of sufficient conditions for symplectic ERK methods. It is shown that these conditions will reduce to the conventional ones when M → 0, and this means that these conditions of symplecticity are extensions of the conventional ones in the literature. Furthermore, we also present a new class of structure-preserving ERK methods possessing the remarkable property of symplecticity. Meanwhile, the revised stiff order conditions are proposed and investigated in detail. Since the symplectic ERK methods are implicit and iterative solutions are required in practice, we also investigate the convergence of the corresponding fixed-point iterative procedure. Finally, the numerical experiments, including a nonlinear Schrödinger equation, a sine-Gordon equation, a nonlinear Klein-Gordon equation, and the well-known Fermi-Pasta-Ulam problem, are implemented in comparison with the corresponding symplectic RK methods and the prominent numerical results definitely coincide with the theories and conclusions made in this paper.

Explicit methods in extended phase space for inseparable Hamiltonian problems

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2015-03-01

We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator.

Variational and symplectic integrators for satellite relative orbit propagation including drag

NASA Astrophysics Data System (ADS)

Palacios, Leonel; Gurfil, Pini

2018-04-01

Orbit propagation algorithms for satellite relative motion relying on Runge-Kutta integrators are non-symplectic—a situation that leads to incorrect global behavior and degraded accuracy. Thus, attempts have been made to apply symplectic methods to integrate satellite relative motion. However, so far all these symplectic propagation schemes have not taken into account the effect of atmospheric drag. In this paper, drag-generalized symplectic and variational algorithms for satellite relative orbit propagation are developed in different reference frames, and numerical simulations with and without the effect of atmospheric drag are presented. It is also shown that high-order versions of the newly-developed variational and symplectic propagators are more accurate and are significantly faster than Runge-Kutta-based integrators, even in the presence of atmospheric drag.

Fedosov Deformation Quantization as a BRST Theory

NASA Astrophysics Data System (ADS)

Grigoriev, M. A.; Lyakhovich, S. L.

The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold M is presented as a second class constrained surface in the fibre bundle ?*ρM which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The second class system is converted into the first class one by continuation of the constraints into the extended manifold, being a direct sum of ?*ρM and the tangent bundle TM. This extended manifold is equipped with a nontrivial Poisson bracket which naturally involves two basic ingredients of Fedosov geometry: the symplectic structure and the symplectic connection. The constructed first class constrained theory, being equivalent to the original symplectic manifold, is quantized through the BFV-BRST procedure. The existence theorem is proven for the quantum BRST charge and the quantum BRST invariant observables. The adjoint action of the quantum BRST charge is identified with the Abelian Fedosov connection while any observable, being proven to be a unique BRST invariant continuation for the values defined in the original symplectic manifold, is identified with the Fedosov flat section of the Weyl bundle. The Fedosov fibrewise star multiplication is thus recognized as a conventional product of the quantum BRST invariant observables.

Supersymmetric symplectic quantum mechanics

NASA Astrophysics Data System (ADS)

de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.

2018-02-01

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

Normal forms for Poisson maps and symplectic groupoids around Poisson transversals

NASA Astrophysics Data System (ADS)

Frejlich, Pedro; Mărcuț, Ioan

2018-03-01

Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Our second result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all structure maps in normal form. We conclude by illustrating our results with examples arising from Lie algebras.

Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.

PubMed

Frejlich, Pedro; Mărcuț, Ioan

2018-01-01

Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Our second result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all structure maps in normal form. We conclude by illustrating our results with examples arising from Lie algebras.

Higher order temporal finite element methods through mixed formalisms.

PubMed

Kim, Jinkyu

2014-01-01

The extended framework of Hamilton's principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.

Symplectic multiparticle tracking model for self-consistent space-charge simulation

DOE PAGES

Qiang, Ji

2017-01-23

Symplectic tracking is important in accelerator beam dynamics simulation. So far, to the best of our knowledge, there is no self-consistent symplectic space-charge tracking model available in the accelerator community. In this paper, we present a two-dimensional and a three-dimensional symplectic multiparticle spectral model for space-charge tracking simulation. This model includes both the effect from external fields and the effect of self-consistent space-charge fields using a split-operator method. Such a model preserves the phase space structure and shows much less numerical emittance growth than the particle-in-cell model in the illustrative examples.

Symplectic multiparticle tracking model for self-consistent space-charge simulation

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

Qiang, Ji

Symplectic tracking is important in accelerator beam dynamics simulation. So far, to the best of our knowledge, there is no self-consistent symplectic space-charge tracking model available in the accelerator community. In this paper, we present a two-dimensional and a three-dimensional symplectic multiparticle spectral model for space-charge tracking simulation. This model includes both the effect from external fields and the effect of self-consistent space-charge fields using a split-operator method. Such a model preserves the phase space structure and shows much less numerical emittance growth than the particle-in-cell model in the illustrative examples.

A new multi-symplectic scheme for the generalized Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Li, Haochen; Sun, Jianqiang

2012-09-01

We propose a new scheme for the generalized Kadomtsev-Petviashvili (KP) equation. The multi-symplectic conservation property of the new scheme is proved. Back error analysis shows that the new multi-symplectic scheme has second order accuracy in space and time. Numerical application on studying the KPI equation and the KPII equation are presented in detail.

Dissipation-preserving spectral element method for damped seismic wave equations

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai; Wang, Yushun

2017-12-01

This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating homogeneous and heterogeneous media.

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.

Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field

NASA Astrophysics Data System (ADS)

Zhang, Ruili; Wang, Yulei; He, Yang; Xiao, Jianyuan; Liu, Jian; Qin, Hong; Tang, Yifa

2018-02-01

Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. The numerical simulation of relativistic dynamics is often multi-scale and requires accurate long-term numerical simulations. Therefore, explicit symplectic algorithms are much more preferable than non-symplectic methods and implicit symplectic algorithms. In this paper, we employ the proper time and express the Hamiltonian as the sum of exactly solvable terms and product-separable terms in space-time coordinates. Then, we give the explicit symplectic algorithms based on the generating functions of orders 2 and 3 for relativistic dynamics of a charged particle. The methodology is not new, which has been applied to non-relativistic dynamics of charged particles, but the algorithm for relativistic dynamics has much significance in practical simulations, such as the secular simulation of runaway electrons in tokamaks.

Fermi Blobs and the Symplectic Camel: A Geometric Picture of Quantum States

NASA Astrophysics Data System (ADS)

Gossona, Maurice A. De

We have explained in previous work the correspondence between the standard squeezed coherent states of quantum mechanics, and quantum blobs, which are the smallest phase space units compatible with the uncertainty principle of quantum mechanics and having the symplectic group as a group of symmetries. In this work, we discuss the relation between quantum blobs and a certain level set (which we call "Fermi blob") introduced by Enrico Fermi in 1930. Fermi blobs allows us to extend our previous results not only to the excited states of the generalized harmonic oscillator in n dimensions, but also to arbitrary quadratic Hamiltonians. As is the case for quantum blobs, we can evaluate Fermi blobs using a topological notion, related to the uncertainty principle, the symplectic capacity of a phase space set. The definition of this notion is made possible by Gromov's symplectic non-squeezing theorem, nicknamed the "principle of the symplectic camel".

SYMPLECTIC INVARIANTS AND FLOWERS' CLASSIFICATION OF SHELL MODEL STATES

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

Helmers, K.

1961-01-01

Flowers has given a classification of shell model states in j-j coupling for a fixed number of nucleons in a shell with respect to a symplectic group. The relation between these classifications for the various nucleon numbers is studied and is found to be governed by another symplectic group, the transformations of which in general change the nucleon number. (auth)

Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods

NASA Astrophysics Data System (ADS)

Monovasilis, Theodore; Kalogiratou, Zacharoula; Simos, T. E.

2014-10-01

In this work we derive exponentially fitted symplectic Runge-Kutta-Nyström (RKN) methods from symplectic exponentially fitted partitioned Runge-Kutta (PRK) methods methods (for the approximate solution of general problems of this category see [18] - [40] and references therein). We construct RKN methods from PRK methods with up to five stages and fourth algebraic order.

On the n-symplectic structure of faithful irreducible representations

NASA Astrophysics Data System (ADS)

Norris, L. K.

2017-04-01

Each faithful irreducible representation of an N-dimensional vector space V1 on an n-dimensional vector space V2 is shown to define a unique irreducible n-symplectic structure on the product manifold V1×V2 . The basic details of the associated Poisson algebra are developed for the special case N = n2, and 2n-dimensional symplectic submanifolds are shown to exist.

A Symplectic Instanton Homology via Traceless Character Varieties

NASA Astrophysics Data System (ADS)

Horton, Henry T.

Since its inception, Floer homology has been an important tool in low-dimensional topology. Floer theoretic invariants of 3-manifolds tend to be either gauge theoretic or symplecto-geometric in nature, and there is a general philosophy that each gauge theoretic Floer homology should have a corresponding symplectic Floer homology and vice-versa. In this thesis, we construct a Lagrangian Floer invariant for any closed, oriented 3-manifold Y (called the symplectic instanton homology of Y and denoted SI(Y)) which is conjecturally equivalent to a Floer homology defined using a certain variant of Yang-Mills gauge theory. The crucial ingredient for defining SI( Y) is the use of traceless character varieties in the symplectic setting, which allow us to avoid the debilitating technical hurdles present when one attempts to define a symplectic version of instanton Floer homologies. Floer theories are also expected to roughly satisfy the axioms of a topological quantum field theory (TQFT), and furthermore Dehn surgeries on knots should induce exact triangles of Floer homologies. Following a strategy used by Ozsvath and Szabo in the context of Heegaard Floer homology, we prove that our theory is functorial with respect to connected 4-dimensional cobordisms, so that cobordisms induce homomorphisms between symplectic instanton homologies. By studying the effect of Dehn surgeries on traceless character varieties, we establish a surgery exact triangle using work of Seidel that relates the geometry of Lefschetz fibrations with exact triangles in Lagrangian Floer theory. We further prove that Dehn surgeries on a link L in a 3-manifold Y induce a spectral sequence of symplectic instanton homologies - the E2-page is isomorphic to a direct sum of symplectic instanton homologies of all possible combinations of 0- and 1-surgeries on the components of L, and the spectral sequence converges to SI(Y). For the branched double cover Sigma(L) of a link L in S3, we show there is a link surgery spectral sequence whose E 2-page is isomorphic to the reduced Khovanov homology of L and which converges to the symplectic instanton homology of Sigma( L).

Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

NASA Astrophysics Data System (ADS)

Xin-Lei, Kong; Hui-Bin, Wu; Feng-Xiang, Mei

2016-01-01

In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities. Project supported by the National Natural Science Foundation of China (Grant No. 11272050), the Excellent Young Teachers Program of North China University of Technology (Grant No. XN132), and the Construction Plan for Innovative Research Team of North China University of Technology (Grant No. XN129).

On the Inverse Mapping of the Formal Symplectic Groupoid of a Deformation Quantization

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

2004-10-01

To each natural star product on a Poisson manifold $M$ we associate an antisymplectic involutive automorphism of the formal neighborhood of the zero section of the cotangent bundle of $M$. If $M$ is symplectic, this mapping is shown to be the inverse mapping of the formal symplectic groupoid of the star product. The construction of the inverse mapping involves modular automorphisms of the star product.

Structure-preserving spectral element method in attenuating seismic wave modeling

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai

2016-04-01

This work describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems which has superior behaviors in long-time stability and dissipation preservation. To construct the conformal symplectic method, we first reformulate the damped acoustic wave equation and the elastic wave equations in their equivalent conformal multi-symplectic structures, which naturally reveal the intrinsic properties of the original systems, especially, the dissipation laws. We thereafter separate each structures into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed numerical scheme, which is conformal symplectic and can therefore guarantee the numerical stability and dissipation preservation after a large time modeling. Additionally, a relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh-wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic method in both the attenuating homogeneous and heterogeneous mediums.

GENERAL: Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem

NASA Astrophysics Data System (ADS)

Lu, Wei-Tao; Zhang, Hua; Wang, Shun-Jin

2008-07-01

Symplectic algebraic dynamics algorithm (SADA) for ordinary differential equations is applied to solve numerically the circular restricted three-body problem (CR3BP) in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge-Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term calculations of the CR3BP.

Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

NASA Astrophysics Data System (ADS)

Huang, Zhi-Xiang; Wu, Xian-Liang

Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

Symplectic geometry spectrum regression for prediction of noisy time series

NASA Astrophysics Data System (ADS)

Xie, Hong-Bo; Dokos, Socrates; Sivakumar, Bellie; Mengersen, Kerrie

2016-05-01

We present the symplectic geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the symplectic geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order symplectic geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and Rössler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).

Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes

NASA Astrophysics Data System (ADS)

Harrington, James William

Quantum information theory is concerned with identifying how quantum mechanical resources (such as entangled quantum states) can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g. , factoring large numbers, securely communicating over a public channel, and simulating quantum mechanical systems) that appear to be very difficult with just classical resources. In addition to identifying the separation between classical and quantum computational power, much of the theoretical focus in this field over the last decade has been concerned with finding novel ways of encoding quantum information that are robust against errors, which is an important step toward building practical quantum information processing devices. In this thesis I present some results on the quantum error-correcting properties of oscillator codes (also described as symplectic lattice codes) and toric codes. Any harmonic oscillator system (such as a mode of light) can be encoded with quantum information via symplectic lattice codes that are robust against shifts in the system's continuous quantum variables. I show the existence of lattice codes whose achievable rates match the one-shot coherent information over the Gaussian quantum channel. Also, I construct a family of symplectic self-dual lattices and search for optimal encodings of quantum information distributed between several oscillators. Toric codes provide encodings of quantum information into two-dimensional spin lattices that are robust against local clusters of errors and which require only local quantum operations for error correction. Numerical simulations of this system under various error models provide a calculation of the accuracy threshold for quantum memory using toric codes, which can be related to phase transitions in certain condensed matter models. I also present a local classical processing scheme for correcting errors on toric codes, which demonstrates that quantum information can be maintained in two dimensions by purely local (quantum and classical) resources.

Pedagogical introduction to the entropy of entanglement for Gaussian states

NASA Astrophysics Data System (ADS)

Demarie, Tommaso F.

2018-05-01

In quantum information theory, the entropy of entanglement is a standard measure of bipartite entanglement between two partitions of a composite system. For a particular class of continuous variable quantum states, the Gaussian states, the entropy of entanglement can be expressed elegantly in terms of symplectic eigenvalues, elements that characterise a Gaussian state and depend on the correlations of the canonical variables. We give a rigorous step-by-step derivation of this result and provide physical insights, together with an example that can be useful in practice for calculations.

A Fifth-order Symplectic Trigonometrically Fitted Partitioned Runge-Kutta Method

NASA Astrophysics Data System (ADS)

Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.

2007-09-01

Trigonometrically fitted symplectic Partitioned Runge Kutta (EFSPRK) methods for the numerical integration of Hamoltonian systems with oscillatory solutions are derived. These methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions sin(wx),cos(wx), w∈R. We modify a fifth order symplectic PRK method with six stages so to derive an exponentially fitted SPRK method. The methods are tested on the numerical integration of the two body problem.

Yangians and Yang-Baxter R-operators for ortho-symplectic superalgebras

NASA Astrophysics Data System (ADS)

Fuksa, J.; Isaev, A. P.; Karakhanyan, D.; Kirschner, R.

2017-04-01

Yang-Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start with the formulation of graded algebras and the linear superspace carrying the vector (fundamental) representation of the ortho-symplectic supergroup. On this basis we study the analogy of the Yang-Baxter operators considered earlier for the cases of orthogonal and symplectic symmetries: the vector (fundamental) R-matrix, the L-operator defining the Yangian algebra and its first and second order evaluations. We investigate the condition for L (u) in the case of the truncated expansion in inverse powers of u and give examples of Lie algebra representations obeying these conditions. We construct the R-operator intertwining two superspinor representations and study the fusion of L-operators involving the tensor product of such representations.

Characterization and solvability of quasipolynomial symplectic mappings

NASA Astrophysics Data System (ADS)

Hernández-Bermejo, Benito; Brenig, Léon

2004-02-01

Quasipolynomial (or QP) mappings constitute a wide generalization of the well-known Lotka-Volterra mappings, of importance in different fields such as population dynamics, physics, chemistry or economy. In addition, QP mappings are a natural discrete-time analogue of the continuous QP systems, which have been extensively used in different pure and applied domains. After presenting the basic definitions and properties of QP mappings in a previous paper [1], the purpose of this work is to focus on their characterization by considering the existence of symplectic QP mappings. In what follows such QP symplectic maps are completely characterized. Moreover, use of the QP formalism can be made in order to demonstrate that all QP symplectic mappings have an analytical solution that is explicitly and generally constructed. Examples are given.

Symplectic semiclassical wave packet dynamics II: non-Gaussian states

NASA Astrophysics Data System (ADS)

Ohsawa, Tomoki

2018-05-01

We generalize our earlier work on the symplectic/Hamiltonian formulation of the dynamics of the Gaussian wave packet to non-Gaussian semiclassical wave packets. We find the symplectic forms and asymptotic expansions of the Hamiltonians associated with these semiclassical wave packets, and obtain Hamiltonian systems governing their dynamics. Numerical experiments demonstrate that the dynamics give a very good approximation to the short-time dynamics of the expectation values computed by a method based on Egorov’s theorem or the initial value representation.

On the geometry of mixed states and the Fisher information tensor

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

Contreras, I., E-mail: icontrer@illinois.edu; Ercolessi, E., E-mail: ercolessi@bo.infn.it; Schiavina, M., E-mail: michele.schiavina@math.uzh.ch

2016-06-15

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant–Kirillov–Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjointmore » orbits, seen as spaces of mixed states, is also discussed.« less

On the Restricted Toda and c-KdV Flows of Neumann Type

NASA Astrophysics Data System (ADS)

Zhou, RuGuang; Qiao, ZhiJun

2000-09-01

It is proven that on a symplectic submanifold the restricted c-KdV flow is just the interpolating Hamiltonian flow of invariant for the restricted Toda flow, which is an integrable symplectic map of Neumann type. They share the common Lax matrix, dynamical r-matrix and system of involutive conserved integrals. Furthermore, the procedure of separation of variables is considered for the restricted c-KdV flow of Neumann type. The project supported by the Chinese National Basic Research Project "Nonlinear Science" and the Doctoral Programme Foundation of Institution of High Education of China. The first author also thanks the National Natural Science Foundation of China (19801031) and "Qinglan Project" of Jiangsu Province of China; and the second author also thanks the Alexander von Humboldt Fellowships, Deutschland, the Special Grant of Excellent Ph. D Thesis of China, the Science & Technology Foundation (Youth Talent Foundation) and the Science Research Foundation of Education Committee of Liaoning Province of China.

On the symplectic structure of harmonic superspace

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

Kachkachi, M.; Saidi, E.H.

In this paper, the symplectic properties of harmonic superspace are studied. It is shown that Diff(S[sup 2]) is isomorphic to Diff[sub 0](S[sup 3])/Ab(Diff[sub 0](S[sup 3])), where Diff[sub 0](S[sup 3]) is the group of the diffeomorphisms of S[sup 3] preserving the Cartan charge operator D[sup 0] and Ab(Diff[sub 0](S[sup 3])) is its Abelian subgroup generated by the Cartan vectors L[sub 0] = w[sup 0]D[sup 0]. The authors show also that the eigenvalue equation D[sup 0] [lambda](z) = 0 defines a symplectic structure in harmonic superspace, and the authors calculate the corresponding algebra. The general symplectic invariant coupling of the Maxwell prepotentialmore » is constructed in both flat and curved harmonic superspace. Other features are discussed.« less

Symplectic test particle encounters: a comparison of methods

NASA Astrophysics Data System (ADS)

Wisdom, Jack

2017-01-01

A new symplectic method for handling encounters of test particles with massive bodies is presented. The new method is compared with several popular methods (RMVS3, SYMBA, and MERCURY). The new method compares favourably.

Complete characterization of fourth-order symplectic integrators with extended-linear coefficients.

PubMed

Chin, Siu A

2006-02-01

The structure of symplectic integrators up to fourth order can be completely and analytically understood when the factorization (split) coefficients are related linearly but with a uniform nonlinear proportional factor. The analytic form of these extended-linear symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and nonforward fourth-order algorithms with an arbitrary number of operators. Most fourth-order forward integrators can now be derived analytically from this extended-linear formulation without the use of symbolic algebra.

SimTrack: A compact c++ code for particle orbit and spin tracking in accelerators

DOE PAGES

Luo, Yun

2015-08-29

SimTrack is a compact c++ code of 6-d symplectic element-by-element particle tracking in accelerators originally designed for head-on beam–beam compensation simulation studies in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory. It provides a 6-d symplectic orbit tracking with the 4th order symplectic integration for magnet elements and the 6-d symplectic synchro-beam map for beam–beam interaction. Since its inception in 2009, SimTrack has been intensively used for dynamic aperture calculations with beam–beam interaction for RHIC. Recently, proton spin tracking and electron energy loss due to synchrotron radiation were added. In this article, I will present the code architecture,more » physics models, and some selected examples of its applications to RHIC and a future electron-ion collider design eRHIC.« less

SimTrack: A compact c++ library for particle orbit and spin tracking in accelerators

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

Luo, Yun

2015-06-24

SimTrack is a compact c++ library of 6-d symplectic element-by-element particle tracking in accelerators originally designed for head-on beam-beam compensation simulation studies in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory. It provides a 6-d symplectic orbit tracking with the 4th order symplectic integration for magnet elements and the 6-d symplectic synchro-beam map for beam-beam interaction. Since its inception in 2009, SimTrack has been intensively used for dynamic aperture calculations with beam-beam interaction for RHIC. Recently, proton spin tracking and electron energy loss due to synchrotron radiation were added. In this article, I will present the code architecture,more » physics models, and some selected examples of its applications to RHIC and a future electron-ion collider design eRHIC.« less

Canonical and symplectic analysis for three dimensional gravity without dynamics

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

Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx; Osmart Ochoa-Gutiérrez, H.

2017-03-15

In this paper a detailed Hamiltonian analysis of three-dimensional gravity without dynamics proposed by V. Hussain is performed. We report the complete structure of the constraints and the Dirac brackets are explicitly computed. In addition, the Faddeev–Jackiw symplectic approach is developed; we report the complete set of Faddeev–Jackiw constraints and the generalized brackets, then we show that the Dirac and the generalized Faddeev–Jackiw brackets coincide to each other. Finally, the similarities and advantages between Faddeev–Jackiw and Dirac’s formalism are briefly discussed. - Highlights: • We report the symplectic analysis for three dimensional gravity without dynamics. • We report the Faddeev–Jackiwmore » constraints. • A pure Dirac’s analysis is performed. • The complete structure of Dirac’s constraints is reported. • We show that symplectic and Dirac’s brackets coincide to each other.« less

Unity of quark and lepton interactions with symplectic gauge symmetry

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

Rajpoot, S.

1982-07-01

Properties of symplectic groups are reviewed and the gauge structure of Sp(2n) derived. The electroweak unification of leptons within Sp(8) gauge symmetry and grand unification of quarks and leptons within Sp(10) gauge symmetry are discussed.

Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger–Maxwell systems

DOE PAGES

Chen, Qiang; Qin, Hong; Liu, Jian; ...

2017-08-24

An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon–matter interactions described by the Schrödinger–Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. Here, this new numerical capability enables us to carry out first-principle based simulation study of important photon–matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.

Parametric symplectic partitioned Runge-Kutta methods with energy-preserving properties for Hamiltonian systems

NASA Astrophysics Data System (ADS)

Wang, Dongling; Xiao, Aiguo; Li, Xueyang

2013-02-01

Based on W-transformation, some parametric symplectic partitioned Runge-Kutta (PRK) methods depending on a real parameter α are developed. For α=0, the corresponding methods become the usual PRK methods, including Radau IA-IA¯ and Lobatto IIIA-IIIB methods as examples. For any α≠0, the corresponding methods are symplectic and there exists a value α∗ such that energy is preserved in the numerical solution at each step. The existence of the parameter and the order of the numerical methods are discussed. Some numerical examples are presented to illustrate these results.

Rotation number of integrable symplectic mappings of the plane

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

Zolkin, Timofey; Nagaitsev, Sergei; Danilov, Viatcheslav

2017-04-11

Symplectic mappings are discrete-time analogs of Hamiltonian systems. They appear in many areas of physics, including, for example, accelerators, plasma, and fluids. Integrable mappings, a subclass of symplectic mappings, are equivalent to a Twist map, with a rotation number, constant along the phase trajectory. In this letter, we propose a succinct expression to determine the rotation number and present two examples. Similar to the period of the bounded motion in Hamiltonian systems, the rotation number is the most fundamental property of integrable maps and it provides a way to analyze the phase-space dynamics.

Symplectic approach to calculation of magnetic field line trajectories in physical space with realistic magnetic geometry in divertor tokamaks

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

Punjabi, Alkesh; Ali, Halima

A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates ({psi},{theta}) from experimental data from a Grad-Shafranov equilibrium solver for a tokamak. {psi} is the toroidal magnetic flux and {theta} is the poloidal angle. Natural canonical coordinates ({psi},{theta},{phi}) can be transformed to physical position (R,Z,{phi}) using a canonical transformation. (R,Z,{phi}) are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonicalmore » coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates (x,y) or (R,Z), the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.« less

Symplectic approach to calculation of magnetic field line trajectories in physical space with realistic magnetic geometry in divertor tokamaks

NASA Astrophysics Data System (ADS)

Punjabi, Alkesh; Ali, Halima

2008-12-01

A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates (ψ,θ) from experimental data from a Grad-Shafranov equilibrium solver for a tokamak. ψ is the toroidal magnetic flux and θ is the poloidal angle. Natural canonical coordinates (ψ,θ,φ) can be transformed to physical position (R,Z,φ) using a canonical transformation. (R,Z,φ) are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonical coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates (x,y) or (R,Z), the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.

Obstructions for twist star products

NASA Astrophysics Data System (ADS)

Bieliavsky, Pierre; Esposito, Chiara; Waldmann, Stefan; Weber, Thomas

2018-05-01

In this short note, we point out that not every star product is induced by a Drinfel'd twist by showing that not every Poisson structure is induced by a classical r-matrix. Examples include the higher genus symplectic Pretzel surfaces and the symplectic sphere S^2.

Symplectic multi-particle tracking on GPUs

NASA Astrophysics Data System (ADS)

Liu, Zhicong; Qiang, Ji

2018-05-01

A symplectic multi-particle tracking model is implemented on the Graphic Processing Units (GPUs) using the Compute Unified Device Architecture (CUDA) language. The symplectic tracking model can preserve phase space structure and reduce non-physical effects in long term simulation, which is important for beam property evaluation in particle accelerators. Though this model is computationally expensive, it is very suitable for parallelization and can be accelerated significantly by using GPUs. In this paper, we optimized the implementation of the symplectic tracking model on both single GPU and multiple GPUs. Using a single GPU processor, the code achieves a factor of 2-10 speedup for a range of problem sizes compared with the time on a single state-of-the-art Central Processing Unit (CPU) node with similar power consumption and semiconductor technology. It also shows good scalability on a multi-GPU cluster at Oak Ridge Leadership Computing Facility. In an application to beam dynamics simulation, the GPU implementation helps save more than a factor of two total computing time in comparison to the CPU implementation.

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches

NASA Astrophysics Data System (ADS)

Antonowicz, Marek; Szczyrba, Wiktor

1985-06-01

We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.

Symplectic Quantization of a Reducible Theory

NASA Astrophysics Data System (ADS)

Barcelos-Neto, J.; Silva, M. B. D.

We use the symplectic formalism to quantize the Abelian antisymmetric tensor gauge field. It is related to a reducible theory in the sense that all of its constraints are not independent. A procedure like ghost-of-ghost of the BFV method has to be used, but in terms of Lagrange multipliers.

Identification of single-input-single-output quantum linear systems

NASA Astrophysics Data System (ADS)

Levitt, Matthew; GuÅ£ǎ, Mǎdǎlin

2017-03-01

The purpose of this paper is to investigate system identification for single-input-single-output general (active or passive) quantum linear systems. For a given input we address the following questions: (1) Which parameters can be identified by measuring the output? (2) How can we construct a system realization from sufficient input-output data? We show that for time-dependent inputs, the systems which cannot be distinguished are related by symplectic transformations acting on the space of system modes. This complements a previous result of Guţă and Yamamoto [IEEE Trans. Autom. Control 61, 921 (2016), 10.1109/TAC.2015.2448491] for passive linear systems. In the regime of stationary quantum noise input, the output is completely determined by the power spectrum. We define the notion of global minimality for a given power spectrum, and characterize globally minimal systems as those with a fully mixed stationary state. We show that in the case of systems with a cascade realization, the power spectrum completely fixes the transfer function, so the system can be identified up to a symplectic transformation. We give a method for constructing a globally minimal subsystem direct from the power spectrum. Restricting to passive systems the analysis simplifies so that identifiability may be completely understood from the eigenvalues of a particular system matrix.

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

Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx; Cruz, Hans, E-mail: hans@ciencias.unam.mx; Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx

In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.

Symplectic potentials and resolved Ricci-flat ACG metrics

NASA Astrophysics Data System (ADS)

Balasubramanian, Aswin K.; Govindarajan, Suresh; Gowdigere, Chethan N.

2007-12-01

We pursue the symplectic description of toric Kähler manifolds. There exists a general local classification of metrics on toric Kähler manifolds equipped with Hamiltonian 2-forms due to Apostolov, Calderbank and Gauduchon (ACG). We derive the symplectic potential for these metrics. Using a method due to Abreu, we relate the symplectic potential to the canonical potential written by Guillemin. This enables us to recover the moment polytope associated with metrics and we thus obtain global information about the metric. We illustrate these general considerations by focusing on six-dimensional Ricci-flat metrics and obtain Ricci-flat metrics associated with real cones over Lpqr and Ypq manifolds. The metrics associated with cones over Ypq manifolds turn out to be partially resolved with two blow-up parameters taking special (non-zero) values. For a fixed Ypq manifold, we find explicit metrics for several inequivalent blow-ups parametrized by a natural number k in the range 0 < k < p. We also show that all known examples of resolved metrics such as the resolved conifold and the resolution of {\\bb C}^3/{\\bb Z}_3 also fit the ACG classification.

Symplectic homoclinic tangles of the ideal separatrix of the DIII-D from type I ELMs

NASA Astrophysics Data System (ADS)

Punjabi, Alkesh; Ali, Halima

2012-10-01

The ideal separatrix of the divertor tokamaks is a degenerate manifold where both the stable and unstable manifolds coincide. Non-axisymmetric magnetic perturbations remove the degeneracy; and split the separatrix manifold. This creates an extremely complex topological structure, called homoclinic tangles. The unstable manifold intersects the stable manifold and creates alternating inner and outer lobes at successive homoclinic points. The Hamiltonian system must preserve the symplectic topological invariance, and this controls the size and radial extent of the lobes. Very recently, lobes near the X-point have been experimentally observed in MAST [A. Kirk et al, PRL 108, 255003 (2012)]. We have used the DIII-D map [A. Punjabi, NF 49, 115020 (2009)] to calculate symplectic homoclinic tangles of the ideal separatrix of the DIII-D from the type I ELMs represented by the peeling-ballooning modes (m,n)=(30,10)+(40,10). The DIII-D map is symplectic, accurate, and is in natural canonical coordinates which are invertible to physical coordinates [A. Punjabi and H. Ali, POP 15, 122502 (2008)]. To our knowledge, we are the first to symplectically calculate these tangles in physical space. Homoclinic tangles of separatrix can cause radial displacement of mobile passing electrons and create sheared radial electric fields and currents, resulting in radial flows, drifts, differential spinning, and reduction in turbulence, and other effects. This work is supported by the grants DE-FG02-01ER54624 and DE-FG02-04ER54793.

An accurate symplectic calculation of the inboard magnetic footprint from statistical topological noise and field errors in the DIII-D

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

Punjabi, Alkesh; Ali, Halima

2011-02-15

Any canonical transformation of Hamiltonian equations is symplectic, and any area-preserving transformation in 2D is a symplectomorphism. Based on these, a discrete symplectic map and its continuous symplectic analog are derived for forward magnetic field line trajectories in natural canonical coordinates. The unperturbed axisymmetric Hamiltonian for magnetic field lines is constructed from the experimental data in the DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The equilibrium Hamiltonian is a highly accurate, analytic, and realistic representation of the magnetic geometry of the DIII-D. These symplectic mathematical maps are used to calculate the magnetic footprint onmore » the inboard collector plate in the DIII-D. Internal statistical topological noise and field errors are irreducible and ubiquitous in magnetic confinement schemes for fusion. It is important to know the stochasticity and magnetic footprint from noise and error fields. The estimates of the spectrum and mode amplitudes of the spatial topological noise and magnetic errors in the DIII-D are used as magnetic perturbation. The discrete and continuous symplectic maps are used to calculate the magnetic footprint on the inboard collector plate of the DIII-D by inverting the natural coordinates to physical coordinates. The combination of highly accurate equilibrium generating function, natural canonical coordinates, symplecticity, and small step-size together gives a very accurate calculation of magnetic footprint. Radial variation of magnetic perturbation and the response of plasma to perturbation are not included. The inboard footprint from noise and errors are dominated by m=3, n=1 mode. The footprint is in the form of a toroidally winding helical strip. The width of stochastic layer scales as (1/2) power of amplitude. The area of footprint scales as first power of amplitude. The physical parameters such as toroidal angle, length, and poloidal angle covered before striking, and the safety factor all have fractal structure. The average field diffusion near the X-point for lines that strike and that do not strike differs by about three to four orders of magnitude. The magnetic footprint gives the maximal bounds on size and heat flux density on collector plate.« less

Quasi-hamiltonian quotients as disjoint unions of symplectic manifolds

NASA Astrophysics Data System (ADS)

Schaffhauser, Florent

2007-08-01

The main result of this paper is Theorem 2.12 which says that the quotient μ-1({1})/U associated to a quasi-hamiltonian space (M, ω, μ: M → U) has a symplectic structure even when 1 is not a regular value of the momentum map μ. Namely, it is a disjoint union of symplectic manifolds of possibly different dimensions, which generalizes the result of Alekseev, Malkin and Meinrenken in [AMM98]. We illustrate this theorem with the example of representation spaces of surface groups. As an intermediary step, we give a new class of examples of quasi-hamiltonian spaces: the isotropy submanifold MK whose points are the points of M with isotropy group K ⊂ U. The notion of quasi-hamiltonian space was introduced by Alekseev, Malkin and Meinrenken in their paper [AMM98]. The main motivation for it was the existence, under some regularity assumptions, of a symplectic structure on the associated quasi-hamiltonian quotient. Throughout their paper, the analogy with usual hamiltonian spaces is often used as a guiding principle, replacing Lie-algebra-valued momentum maps with Lie-group-valued momentum maps. In the hamiltonian setting, when the usual regularity assumptions on the group action or the momentum map are dropped, Lerman and Sjamaar showed in [LS91] that the quotient associated to a hamiltonian space carries a stratified symplectic structure. In particular, this quotient space is a disjoint union of symplectic manifolds. In this paper, we prove an analogous result for quasi-hamiltonian quotients. More precisely, we show that for any quasi-hamiltonian space (M, ω, μ: M → U), the associated quotient M//U := μ-1({1})/U is a disjoint union of symplectic manifolds (Theorem 2.12): [ mu^{-1}(\\{1\\})/U = bigsqcup_{jin J} (mu^{-1}(\\{1\\})\\cap M_{K_j})/L_{K_j} . ] Here Kj denotes a closed subgroup of U and MKj denotes the isotropy submanifold of type Kj: MKj = {x ∈ M | Ux = Kj}. Finally, LKj is the quotient group LKj = { N}(Kj)/K_j, where { N}(Kj) is the normalizer of Kj in U. As an intermediary step in our study, we show that MKj is a quasi-hamiltonian space when endowed with the (free) action of LKj.

cuSwift --- a suite of numerical integration methods for modelling planetary systems implemented in C/CUDA

NASA Astrophysics Data System (ADS)

Hellmich, S.; Mottola, S.; Hahn, G.; Kührt, E.; Hlawitschka, M.

2014-07-01

Simulations of dynamical processes in planetary systems represent an important tool for studying the orbital evolution of the systems [1--3]. Using modern numerical integration methods, it is possible to model systems containing many thousands of objects over timescales of several hundred million years. However, in general, supercomputers are needed to get reasonable simulation results in acceptable execution times [3]. To exploit the ever-growing computation power of Graphics Processing Units (GPUs) in modern desktop computers, we implemented cuSwift, a library of numerical integration methods for studying long-term dynamical processes in planetary systems. cuSwift can be seen as a re-implementation of the famous SWIFT integrator package written by Hal Levison and Martin Duncan. cuSwift is written in C/CUDA and contains different integration methods for various purposes. So far, we have implemented three algorithms: a 15th-order Radau integrator [4], the Wisdom-Holman Mapping (WHM) integrator [5], and the Regularized Mixed Variable Symplectic (RMVS) Method [6]. These algorithms treat only the planets as mutually gravitationally interacting bodies whereas asteroids and comets (or other minor bodies of interest) are treated as massless test particles which are gravitationally influenced by the massive bodies but do not affect each other or the massive bodies. The main focus of this work is on the symplectic methods (WHM and RMVS) which use a larger time step and thus are capable of integrating many particles over a large time span. As an additional feature, we implemented the non-gravitational Yarkovsky effect as described by M. Brož [7]. With cuSwift, we show that the use of modern GPUs makes it possible to speed up these methods by more than one order of magnitude compared to the single-core CPU implementation, thereby enabling modest workstation computers to perform long-term dynamical simulations. We use these methods to study the influence of the Yarkovsky effect on resonant asteroids. We present first results and compare them with integrations done with the original algorithms implemented in SWIFT in order to assess the numerical precision of cuSwift and to demonstrate the speed-up we achieved using the GPU.

Second-order evaluations of orthogonal and symplectic Yangians

NASA Astrophysics Data System (ADS)

Karakhanyan, D. R.; Kirschner, R.

2017-08-01

Orthogonal or symplectic Yangians are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with the corresponding so( n) or sp(2 m) symmetry. We investigate the second-order solution conditions, where the expansion of L( u) in u -1 is truncated at the second power, and we derive the relations for the two nontrivial terms in L( u).

Special Bohr-Sommerfeld Lagrangian submanifolds

NASA Astrophysics Data System (ADS)

Tyurin, N. A.

2016-12-01

We introduce a new notion in symplectic geometry, that of speciality for Lagrangian submanifolds satisfying the Bohr- Sommerfeld condition. We show that it enables one to construct finite-dimensional moduli spaces of special Bohr- Sommerfeld Lagrangian submanifolds with respect to any ample line bundle on an algebraic variety with a Hodge metric regarded as the symplectic form. This construction can be used to study mirror symmetry.

Dirichlet to Neumann operator for Abelian Yang-Mills gauge fields

NASA Astrophysics Data System (ADS)

Díaz-Marín, Homero G.

We consider the Dirichlet to Neumann operator for Abelian Yang-Mills boundary conditions. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler-Lagrange solutions modulo gauge for space-time manifolds with smooth boundary. Thus we prepare a suitable scenario for geometric quantization within the reduced symplectic space of boundary conditions of Abelian gauge fields.

Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems

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

Xiao, Jianyuan; Qin, Hong; Liu, Jian

2015-11-01

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint arXiv: 1505.06076 (2015)], which produces fivemore » exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. (C) 2015 AIP Publishing LLC.« less

Efficient high-order structure-preserving methods for the generalized Rosenau-type equation with power law nonlinearity

NASA Astrophysics Data System (ADS)

Cai, Jiaxiang; Liang, Hua; Zhang, Chun

2018-06-01

Based on the multi-symplectic Hamiltonian formula of the generalized Rosenau-type equation, a multi-symplectic scheme and an energy-preserving scheme are proposed. To improve the accuracy of the solution, we apply the composition technique to the obtained schemes to develop high-order schemes which are also multi-symplectic and energy-preserving respectively. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results verify that all the proposed schemes have satisfactory performance in providing accurate solution and preserving the discrete mass and energy invariants. Numerical results also show that although each basic time step is divided into several composition steps, the computational efficiency of the composition schemes is much higher than that of the non-composite schemes.

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

NASA Astrophysics Data System (ADS)

Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

2018-05-01

A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

Geometric integration in Born-Oppenheimer molecular dynamics.

PubMed

Odell, Anders; Delin, Anna; Johansson, Börje; Cawkwell, Marc J; Niklasson, Anders M N

2011-12-14

Geometric integration schemes for extended Lagrangian self-consistent Born-Oppenheimer molecular dynamics, including a weak dissipation to remove numerical noise, are developed and analyzed. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. We investigate three different geometric integration schemes: (1) regular time reversible Verlet, (2) second order optimal symplectic, and (3) third order optimal symplectic. We look at energy conservation, accuracy, and stability as a function of dissipation, integration time step, and SCF convergence. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. © 2011 American Institute of Physics

Symplectic Quantization of a Vector-Tensor Gauge Theory with Topological Coupling

NASA Astrophysics Data System (ADS)

Barcelos-Neto, J.; Silva, M. B. D.

We use the symplectic formalism to quantize a gauge theory where vectors and tensors fields are coupled in a topological way. This is an example of reducible theory and a procedure like of ghosts-of-ghosts of the BFV method is applied but in terms of Lagrange multipliers. Our final results are in agreement with the ones found in the literature by using the Dirac method.

Time irreversibility from symplectic non-squeezing

NASA Astrophysics Data System (ADS)

Kalogeropoulos, Nikolaos

2018-04-01

The issue of how time reversible microscopic dynamics gives rise to macroscopic irreversible processes has been a recurrent issue in Physics since the time of Boltzmann whose ideas shaped, and essentially resolved, such an apparent contradiction. Following Boltzmann's spirit and ideas, but employing Gibbs's approach, we advance the view that macroscopic irreversibility of Hamiltonian systems of many degrees of freedom can be also seen as a result of the symplectic non-squeezing theorem.

Multidimensional entropic uncertainty relation based on a commutator matrix in position and momentum spaces

NASA Astrophysics Data System (ADS)

Hertz, Anaelle; Vanbever, Luc; Cerf, Nicolas J.

2018-01-01

The uncertainty relation for continuous variables due to Byałinicki-Birula and Mycielski [I. Białynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975), 10.1007/BF01608825] expresses the complementarity between two n -tuples of canonically conjugate variables (x1,x2,...,xn) and (p1,p2,...,pn) in terms of Shannon differential entropy. Here we consider the generalization to variables that are not canonically conjugate and derive an entropic uncertainty relation expressing the balance between any two n -variable Gaussian projective measurements. The bound on entropies is expressed in terms of the determinant of a matrix of commutators between the measured variables. This uncertainty relation also captures the complementarity between any two incompatible linear canonical transforms, the bound being written in terms of the corresponding symplectic matrices in phase space. Finally, we extend this uncertainty relation to Rényi entropies and also prove a covariance-based uncertainty relation which generalizes the Robertson relation.

Aubry-Mather Theory for Conformally Symplectic Systems

NASA Astrophysics Data System (ADS)

Marò, Stefano; Sorrentino, Alfonso

2017-09-01

In this article we develop an analogue of Aubry-Mather theory for a class of dissipative systems, namely conformally symplectic systems, and prove the existence of interesting invariant sets, which, in analogy to the conservative case, will be called the Aubry and the Mather sets. Besides describing their structure and their dynamical significance, we shall analyze their attracting/repelling properties, as well as their noteworthy role in driving the asymptotic dynamics of the system.

Symplectic no-core configuration interaction framework for ab initio nuclear structure. II. Structure of rotational states

NASA Astrophysics Data System (ADS)

Caprio, Mark A.; McCoy, Anna E.; Dytrych, Tomas

2017-09-01

Rotational band structure is readily apparent as an emergent phenomenon in ab initio nuclear many-body calculations of light nuclei, despite the incompletely converged nature of most such calculations at present. Nuclear rotation in light nuclei can be analyzed in terms of approximate dynamical symmetries of the nuclear many-body problem: in particular, Elliott's SU (3) symmetry of the three-dimensional harmonic oscillator and the symplectic Sp (3 , R) symmetry of three-dimensional phase space. Calculations for rotational band members in the ab initio symplectic no-core configuration interaction (SpNCCI) framework allow us to directly examine the SU (3) and Sp (3 , R) nature of rotational states. We present results for rotational bands in p-shell nuclei. Supported by the US DOE under Award No. DE-FG02-95ER-40934 and the Czech Science Foundation under Grant No. 16-16772S.

Regularization of the Perturbed Spatial Restricted Three-Body Problem by L-Transformations

NASA Astrophysics Data System (ADS)

Poleshchikov, S. M.

2018-03-01

Equations of motion for the perturbed circular restricted three-body problem have been regularized in canonical variables in a moving coordinate system. Two different L-matrices of the fourth order are used in the regularization. Conditions for generalized symplecticity of the constructed transform have been checked. In the unperturbed case, the regular equations have a polynomial structure. The regular equations have been numerically integrated using the Runge-Kutta-Fehlberg method. The results of numerical experiments are given for the Earth-Moon system parameters taking into account the perturbation of the Sun for different L-matrices.

Superspace models for S-3

NASA Astrophysics Data System (ADS)

McKeon, D. G. C.

2003-11-01

The simplest supersymmetric extension of the group SO(4) is discussed. The superalgebra is realized in a superspace whose Bosonic subspace is the surface of a sphere S-3 embedded in four-dimensional Euclidean space. By using Fermionic coordinates in this superspace, which are chiral symplectic Majorana spinors, it proves possible to devise superfield models involving a complex scalar, a pair of chiral symplectic Majorana spinors, and a complex auxiliary scalar. Kinetic terms involve operators that are isometry generators on S-3.

Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs

NASA Astrophysics Data System (ADS)

Tang, Wensheng; Sun, Yajuan; Cai, Wenjun

2017-02-01

In this article, we present a unified framework of discontinuous Galerkin (DG) discretizations for Hamiltonian ODEs and PDEs. We show that with appropriate numerical fluxes the numerical algorithms deduced from DG discretizations can be combined with the symplectic methods in time to derive the multi-symplectic PRK schemes. The resulting numerical discretizations are applied to the linear and nonlinear Schrödinger equations. Some conservative properties of the numerical schemes are investigated and confirmed in the numerical experiments.

Trees, B-series and G-symplectic methods

NASA Astrophysics Data System (ADS)

Butcher, J. C.

2017-07-01

The order conditions for Runge-Kutta methods are intimately connected with the graphs known as rooted trees. The conditions can be expressed in terms of Taylor expansions written as weighted sums of elementary differentials, that is as B-series. Polish notation provides a unifying structure for representing many of the quantities appearing in this theory. Applications include the analysis of general linear methods with special reference to G-symplectic methods. A new order 6 method has recently been constructed.

Inverse scattering method and soliton double solution family for the general symplectic gravity model

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

Gao Yajun

A previously established Hauser-Ernst-type extended double-complex linear system is slightly modified and used to develop an inverse scattering method for the stationary axisymmetric general symplectic gravity model. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method applied fine and effective. As an application, a concrete family of soliton double solutions for the considered theory is obtained.

A Gauge Invariant Description for the General Conic Constrained Particle from the FJBW Iteration Algorithm

NASA Astrophysics Data System (ADS)

Barbosa, Gabriel D.; Thibes, Ronaldo

2018-06-01

We consider a second-degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting concerning its quantum counterpart with subtleties in its symplectic structure and symmetries. We start with a second-class version of the general conic constrained particle, which encompasses previous versions of circular and elliptical paths discussed in the literature. By applying the symplectic FJBW iteration program, we proceed on to show how a gauge invariant version for the model can be achieved from the originally second-class system. We pursue the complete constraint analysis in phase space and perform the Faddeev-Jackiw symplectic quantization following the Barcelos-Wotzasek iteration program to unravel the essential aspects of the constraint structure. While in the standard Dirac-Bergmann approach there are four second-class constraints, in the FJBW they reduce to two. By using the symplectic potential obtained in the last step of the FJBW iteration process, we construct a gauge invariant model exhibiting explicitly its BRST symmetry. We obtain the quantum BRST charge and write the Green functions generator for the gauge invariant version. Our results reproduce and neatly generalize the known BRST symmetry of the rigid rotor, clearly showing that this last one constitutes a particular case of a broader class of theories.

Time-symmetric integration in astrophysics

NASA Astrophysics Data System (ADS)

Hernandez, David M.; Bertschinger, Edmund

2018-04-01

Calculating the long-term solution of ordinary differential equations, such as those of the N-body problem, is central to understanding a wide range of dynamics in astrophysics, from galaxy formation to planetary chaos. Because generally no analytic solution exists to these equations, researchers rely on numerical methods that are prone to various errors. In an effort to mitigate these errors, powerful symplectic integrators have been employed. But symplectic integrators can be severely limited because they are not compatible with adaptive stepping and thus they have difficulty in accommodating changing time and length scales. A promising alternative is time-reversible integration, which can handle adaptive time-stepping, but the errors due to time-reversible integration in astrophysics are less understood. The goal of this work is to study analytically and numerically the errors caused by time-reversible integration, with and without adaptive stepping. We derive the modified differential equations of these integrators to perform the error analysis. As an example, we consider the trapezoidal rule, a reversible non-symplectic integrator, and show that it gives secular energy error increase for a pendulum problem and for a Hénon-Heiles orbit. We conclude that using reversible integration does not guarantee good energy conservation and that, when possible, use of symplectic integrators is favoured. We also show that time-symmetry and time-reversibility are properties that are distinct for an integrator.

Reading off the nongeometric scalar potentials via the topological data of the compactifying Calabi-Yau manifolds

NASA Astrophysics Data System (ADS)

Shukla, Pramod

2016-10-01

In the context of studying the 4D-effective potentials of type IIB nongeometric flux compactifications, this article has a twofold goal. First, we present a modular invariant symplectic rearrangement of the tree level nongeometric scalar potential arising from a flux superpotential which includes the S-dual pairs of nongeometric fluxes (Q , P ), the standard NS-NS and RR three-form fluxes (F3 , H3 ), and the geometric flux (ω ). This "symplectic formulation" is valid for arbitrary numbers of Kähler moduli, and the complex structure moduli which are implicitly encoded in a set of symplectic matrices. In the second part, we further explicitly rewrite all the symplectic ingredients in terms of saxionic and axionic components of the complex structure moduli. The same leads to a compact form of the generic scalar potential being explicitly written out in terms of all the real moduli/axions. Moreover, the final form of the scalar potential needs only the knowledge of some topological data (such as Hodge numbers and the triple-intersection numbers) of the compactifying threefolds and their respective mirrors. Finally, we demonstrate how the same is equivalent to say that, for a given concrete example, various pieces of the scalar potential can be directly read off from our generic proposal, without the need of starting from the Kähler and superpotentials.

The Riccati equation, imprimitive actions and symplectic forms. [with application to decentralized optimal control problem

NASA Technical Reports Server (NTRS)

Garzia, M. R.; Loparo, K. A.; Martin, C. F.

1982-01-01

This paper looks at the structure of the solution of a matrix Riccati differential equation under a predefined group of transformations. The group of transformations used is an expanded form of the feedback group. It is shown that this group of transformations is a subgroup of the symplectic group. The orbits of the Riccati differential equation under the action of this group are studied and it is seen how these techniques apply to a decentralized optimal control problem.

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

Chen, Qiang; Qin, Hong; Liu, Jian

An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon–matter interactions described by the Schrödinger–Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. Here, this new numerical capability enables us to carry out first-principle based simulation study of important photon–matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.

Realization of Uq(sp(2n)) within the Differential Algebra on Quantum Symplectic Space

NASA Astrophysics Data System (ADS)

Zhang, Jiao; Hu, Naihong

2017-10-01

We realize the Hopf algebra U_q({sp}_{2n}) as an algebra of quantum differential operators on the quantum symplectic space X(f_s;R) and prove that X(f_s;R) is a U_q({sp}_{2n})-module algebra whose irreducible summands are just its homogeneous subspaces. We give a coherence realization for all the positive root vectors under the actions of Lusztig's braid automorphisms of U_q({sp}_{2n}).

An hp symplectic pseudospectral method for nonlinear optimal control

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

Fast and reliable symplectic integration for planetary system N-body problems

NASA Astrophysics Data System (ADS)

Hernandez, David M.

2016-06-01

We apply one of the exactly symplectic integrators, which we call HB15, of Hernandez & Bertschinger, along with the Kepler problem solver of Wisdom & Hernandez, to solve planetary system N-body problems. We compare the method to Wisdom-Holman (WH) methods in the MERCURY software package, the MERCURY switching integrator, and others and find HB15 to be the most efficient method or tied for the most efficient method in many cases. Unlike WH, HB15 solved N-body problems exhibiting close encounters with small, acceptable error, although frequent encounters slowed the code. Switching maps like MERCURY change between two methods and are not exactly symplectic. We carry out careful tests on their properties and suggest that they must be used with caution. We then use different integrators to solve a three-body problem consisting of a binary planet orbiting a star. For all tested tolerances and time steps, MERCURY unbinds the binary after 0 to 25 years. However, in the solutions of HB15, a time-symmetric HERMITE code, and a symplectic Yoshida method, the binary remains bound for >1000 years. The methods' solutions are qualitatively different, despite small errors in the first integrals in most cases. Several checks suggest that the qualitative binary behaviour of HB15's solution is correct. The Bulirsch-Stoer and Radau methods in the MERCURY package also unbind the binary before a time of 50 years, suggesting that this dynamical error is due to a MERCURY bug.

A hybrid symplectic principal component analysis and central tendency measure method for detection of determinism in noisy time series with application to mechanomyography

NASA Astrophysics Data System (ADS)

Xie, Hong-Bo; Dokos, Socrates

2013-06-01

We present a hybrid symplectic geometry and central tendency measure (CTM) method for detection of determinism in noisy time series. CTM is effective for detecting determinism in short time series and has been applied in many areas of nonlinear analysis. However, its performance significantly degrades in the presence of strong noise. In order to circumvent this difficulty, we propose to use symplectic principal component analysis (SPCA), a new chaotic signal de-noising method, as the first step to recover the system dynamics. CTM is then applied to determine whether the time series arises from a stochastic process or has a deterministic component. Results from numerical experiments, ranging from six benchmark deterministic models to 1/f noise, suggest that the hybrid method can significantly improve detection of determinism in noisy time series by about 20 dB when the data are contaminated by Gaussian noise. Furthermore, we apply our algorithm to study the mechanomyographic (MMG) signals arising from contraction of human skeletal muscle. Results obtained from the hybrid symplectic principal component analysis and central tendency measure demonstrate that the skeletal muscle motor unit dynamics can indeed be deterministic, in agreement with previous studies. However, the conventional CTM method was not able to definitely detect the underlying deterministic dynamics. This result on MMG signal analysis is helpful in understanding neuromuscular control mechanisms and developing MMG-based engineering control applications.

Gauge properties of the guiding center variational symplectic integrator

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

Squire, J.; Tang, W. M.; Qin, H.

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008); H. Qin, X. Guan, and W. Tang, Phys. Plasmas (2009); J. Li, H. Qin, Z. Pu, L. Xie, and S. Fu, Phys. Plasmas 18, 052902 (2011)]. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed formore » this type of system. It is found that for explicit algorithms, an instability arises because the discrete symplectic structure does not become the continuous structure in the t{yields}0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the 'antisymmetric discretization gauge,' in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and {phi} are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law [J. Squire, H. Qin, and W. Tang (to be published)].« less

A hybrid symplectic principal component analysis and central tendency measure method for detection of determinism in noisy time series with application to mechanomyography.

PubMed

Xie, Hong-Bo; Dokos, Socrates

2013-06-01

We present a hybrid symplectic geometry and central tendency measure (CTM) method for detection of determinism in noisy time series. CTM is effective for detecting determinism in short time series and has been applied in many areas of nonlinear analysis. However, its performance significantly degrades in the presence of strong noise. In order to circumvent this difficulty, we propose to use symplectic principal component analysis (SPCA), a new chaotic signal de-noising method, as the first step to recover the system dynamics. CTM is then applied to determine whether the time series arises from a stochastic process or has a deterministic component. Results from numerical experiments, ranging from six benchmark deterministic models to 1/f noise, suggest that the hybrid method can significantly improve detection of determinism in noisy time series by about 20 dB when the data are contaminated by Gaussian noise. Furthermore, we apply our algorithm to study the mechanomyographic (MMG) signals arising from contraction of human skeletal muscle. Results obtained from the hybrid symplectic principal component analysis and central tendency measure demonstrate that the skeletal muscle motor unit dynamics can indeed be deterministic, in agreement with previous studies. However, the conventional CTM method was not able to definitely detect the underlying deterministic dynamics. This result on MMG signal analysis is helpful in understanding neuromuscular control mechanisms and developing MMG-based engineering control applications.

Surface charges for gravity and electromagnetism in the first order formalism

NASA Astrophysics Data System (ADS)

Frodden, Ernesto; Hidalgo, Diego

2018-02-01

A new derivation of surface charges for 3  +  1 gravity coupled to electromagnetism is obtained. Gravity theory is written in the tetrad-connection variables. The general derivation starts from the Lagrangian, and uses the covariant symplectic formalism in the language of forms. For gauge theories, surface charges disentangle physical from gauge symmetries through the use of Noether identities and the exactness symmetry condition. The surface charges are quasilocal, explicitly coordinate independent, gauge invariant and background independent. For a black hole family solution, the surface charge conservation implies the first law of black hole mechanics. As a check, we show the first law for an electrically charged, rotating black hole with an asymptotically constant curvature (the Kerr–Newman (anti-)de Sitter family). The charges, including the would-be mass term appearing in the first law, are quasilocal. No reference to the asymptotic structure of the spacetime nor the boundary conditions is required and therefore topological terms do not play a rôle. Finally, surface charge formulae for Lovelock gravity coupled to electromagnetism are exhibited, generalizing the one derived in a recent work by Barnich et al Proc. Workshop ‘ About Various Kinds of Interactions’ in honour of Philippe Spindel (4–5 June 2015, Mons, Belgium) C15-06-04 (2016 (arXiv:1611.01777 [gr-qc])). The two different symplectic methods to define surface charges are compared and shown equivalent.

On the Cohomology of Almost Complex Manifolds

NASA Astrophysics Data System (ADS)

Fino, Anna; Tomassini, Adriano

2010-07-01

We review some properties of two special types of almost complex structures, introduced by T.-J. Li and W. Zhang in [11], in relation to the existence of compatible symplectic structures and to the Hard Lefschetz condition. The two types of almost complex structures are defined respectively in terms of differential forms and currents. The paper is based on the results obtained in [9]. We give a new example of an 8-dimensional compact solvmanifold endowed with a C∞ pure and full almost complex structure calibrated by a symplectic form satisfying the Hard Lefschetz condition.

Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes

NASA Astrophysics Data System (ADS)

Escalante, Alberto; Medel-Portugal, C.

2018-04-01

The symplectic analysis for the four dimensional Pontryagin and Euler invariants is performed within the Faddeev-Jackiw context. The Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw brackets are reported; we show that in spite of the Pontryagin and Euler classes give rise the same equations of motion, its respective symplectic structures are different to each other. In addition, a quantum state that solves the Faddeev-Jackiw constraints is found, and we show that the quantum states for these invariants are different to each other. Finally, we present some remarks and conclusions.

A classification of open Gaussian dynamics

NASA Astrophysics Data System (ADS)

Grimmer, Daniel; Brown, Eric; Kempf, Achim; Mann, Robert B.; Martín-Martínez, Eduardo

2018-06-01

We introduce a classification scheme for the generators of bosonic open Gaussian dynamics, providing instructive diagrams description for each type of dynamics. Using this classification, we discuss the consequences of imposing complete positivity on Gaussian dynamics. In particular, we show that non-symplectic operations must be active to allow for complete positivity. In addition, non-symplectic operations can, in fact, conserve the volume of phase space only if the restriction of complete positivity is lifted. We then discuss the implications for the relationship between information and energy flows in open quantum mechanics.

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

NASA Technical Reports Server (NTRS)

Jones, Brandon A.; Anderson, Rodney L.

2012-01-01

Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.

Symplectic Propagation of the Map, Tangent Map and Tangent Map Derivative through Quadrupole and Combined-Function Dipole Magnets without Truncation

NASA Astrophysics Data System (ADS)

Bruhwiler, D. L.; Cary, J. R.; Shasharina, S.

1998-04-01

The MAPA accelerator modeling code symplectically advances the full nonlinear map, tangent map and tangent map derivative through all accelerator elements. The tangent map and its derivative are nonlinear generalizations of Browns first- and second-order matrices(K. Brown, SLAC-75, Rev. 4 (1982), pp. 107-118.), and they are valid even near the edges of the dynamic aperture, which may be beyond the radius of convergence for a truncated Taylor series. In order to avoid truncation of the map and its derivatives, the Hamiltonian is split into pieces for which the map can be obtained analytically. Yoshidas method(H. Yoshida, Phys. Lett. A 150 (1990), pp. 262-268.) is then used to obtain a symplectic approximation to the map, while the tangent map and its derivative are appropriately composed at each step to obtain them with equal accuracy. We discuss our splitting of the quadrupole and combined-function dipole Hamiltonians and show that typically few steps are required for a high-energy accelerator.

Structure of the low-lying positive parity states in the proton-neutron symplectic model

NASA Astrophysics Data System (ADS)

Ganev, H. G.

2018-05-01

The proton-neutron symplectic model with Sp(12, R) dynamical symmetry is applied for the simultaneous description of the microscopic structure of the low-lying states of the ground state, γ and β bands in 166 Er. For this purpose, the model Hamiltonian is diagonalized in the space of stretched states by exploiting the SUp (3) ⊗ SUn (3) symmetry-adapted basis. The theoretical predictions are compared with experiment and some other microscopic collective models, like the one-component Sp(6, R) symplectic and pseudo-SU(3) models. A good description of the energy levels of the three bands under consideration, as well as the enhanced intraband B(E2) transition strengths between the states of the ground and γ bands is obtained without the use of effective charges. The results show the presence of a good SU(3) dynamical symmetry. It is also shown that, in contrast to the Sp(6, R) case, the lowest excited bands, e.g., the β and γ bands, naturally appear together with the ground state band within a single Sp(12, R) irreducible representation.

Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory

DOE PAGES

Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; ...

2016-10-20

We introduce several families of N = (2, 2) UV boundary conditions in 3d N=4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studyingmore » two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality $-$ an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.« less

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

Xiao, Jianyuan; Liu, Jian; He, Yang

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactlymore » soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave.« less

Explicit symplectic orbit and spin tracking method for electric storage ring

DOE PAGES

Hwang, Kilean; Lee, S. Y.

2016-08-18

We develop a symplectic charged particle tracking method for phase space coordinates and polarization in all electric storage rings. Near the magic energy, the spin precession tune is proportional to the fractional momentum deviation δ m from the magic energy, and the amplitude of the radial and longitudinal spin precession is proportional to η/δ m, where η is the electric dipole moment for an initially vertically polarized beam. As a result, the method can be used to extract the electron electric dipole moment of a charged particle by employing narrow band frequency analysis of polarization around the magic energy.

Symplectic no-core shell-model approach to intermediate-mass nuclei

NASA Astrophysics Data System (ADS)

Tobin, G. K.; Ferriss, M. C.; Launey, K. D.; Dytrych, T.; Draayer, J. P.; Dreyfuss, A. C.; Bahri, C.

2014-03-01

We present a microscopic description of nuclei in the intermediate-mass region, including the proximity to the proton drip line, based on a no-core shell model with a schematic many-nucleon long-range interaction with no parameter adjustments. The outcome confirms the essential role played by the symplectic symmetry to inform the interaction and the winnowing of shell-model spaces. We show that it is imperative that model spaces be expanded well beyond the current limits up through 15 major shells to accommodate particle excitations, which appear critical to highly deformed spatial structures and the convergence of associated observables.

Isometry group orbit quantization of spinning strings in AdS3 × S3

NASA Astrophysics Data System (ADS)

Heinze, Martin; Jorjadze, George; Megrelidze, Luka

2015-03-01

Describing the bosonic AdS3 × S3 particle and string in SU(1,1) × SU(2) group variables, we provide a Hamiltonian treatment of the isometry group orbits of solutions via analysis of the pre-symplectic form. For the particle we obtain a one-parameter family of orbits parameterized by creation-annihilation variables, which leads to the Holstein-Primakoff realization of the isometry group generators. The scheme is then applied to spinning string solutions characterized by one winding number in AdS3 and two winding numbers in S3. We find a two-parameter family of orbits, where quantization again provides the Holstein-Primakoff realization of the symmetry generators with an oscillator-type energy spectrum. Analyzing the minimal energy at strong coupling, we verify the spectrum of short strings at special values of winding numbers.

Entropy generation in Gaussian quantum transformations: applying the replica method to continuous-variable quantum information theory

NASA Astrophysics Data System (ADS)

Gagatsos, Christos N.; Karanikas, Alexandros I.; Kordas, Georgios; Cerf, Nicolas J.

2016-02-01

In spite of their simple description in terms of rotations or symplectic transformations in phase space, quadratic Hamiltonians such as those modelling the most common Gaussian operations on bosonic modes remain poorly understood in terms of entropy production. For instance, determining the quantum entropy generated by a Bogoliubov transformation is notably a hard problem, with generally no known analytical solution, while it is vital to the characterisation of quantum communication via bosonic channels. Here we overcome this difficulty by adapting the replica method, a tool borrowed from statistical physics and quantum field theory. We exhibit a first application of this method to continuous-variable quantum information theory, where it enables accessing entropies in an optical parametric amplifier. As an illustration, we determine the entropy generated by amplifying a binary superposition of the vacuum and a Fock state, which yields a surprisingly simple, yet unknown analytical expression.

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.

Structure and structure-preserving algorithms for plasma physics

NASA Astrophysics Data System (ADS)

Morrison, P. J.

2016-10-01

Conventional simulation studies of plasma physics are based on numerically solving the underpinning differential (or integro-differential) equations. Usual algorithms in general do not preserve known geometric structure of the physical systems, such as the local energy-momentum conservation law, Casimir invariants, and the symplectic structure (Poincaré invariants). As a consequence, numerical errors may accumulate coherently with time and long-term simulation results may be unreliable. Recently, a series of geometric algorithms that preserve the geometric structures resulting from the Hamiltonian and action principle (HAP) form of theoretical models in plasma physics have been developed by several authors. The superiority of these geometric algorithms has been demonstrated with many test cases. For example, symplectic integrators for guiding-center dynamics have been constructed to preserve the noncanonical symplectic structures and bound the energy-momentum errors for all simulation time-steps; variational and symplectic algorithms have been discovered and successfully applied to the Vlasov-Maxwell system, MHD, and other magnetofluid equations as well. Hamiltonian truncations of the full Vlasov-Maxwell system have opened the field of discrete gyrokinetics and led to the GEMPIC algorithm. The vision that future numerical capabilities in plasma physics should be based on structure-preserving geometric algorithms will be presented. It will be argued that the geometric consequences of HAP form and resulting geometric algorithms suitable for plasma physics studies cannot be adapted from existing mathematical literature but, rather, need to be discovered and worked out by theoretical plasma physicists. The talk will review existing HAP structures of plasma physics for a variety of models, and how they have been adapted for numerical implementation. Supported by DOE DE-FG02-04ER-54742.

Mathematics of Quantization and Quantum Fields

NASA Astrophysics Data System (ADS)

Dereziński, Jan; Gérard, Christian

2013-03-01

Preface; 1. Vector spaces; 2. Operators in Hilbert spaces; 3. Tensor algebras; 4. Analysis in L2(Rd); 5. Measures; 6. Algebras; 7. Anti-symmetric calculus; 8. Canonical commutation relations; 9. CCR on Fock spaces; 10. Symplectic invariance of CCR in finite dimensions; 11. Symplectic invariance of the CCR on Fock spaces; 12. Canonical anti-commutation relations; 13. CAR on Fock spaces; 14. Orthogonal invariance of CAR algebras; 15. Clifford relations; 16. Orthogonal invariance of the CAR on Fock spaces; 17. Quasi-free states; 18. Dynamics of quantum fields; 19. Quantum fields on space-time; 20. Diagrammatics; 21. Euclidean approach for bosons; 22. Interacting bosonic fields; Subject index; Symbols index.

Invariant measures on multimode quantum Gaussian states

NASA Astrophysics Data System (ADS)

Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.

2012-12-01

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Two Virasoro symmetries in stringy warped AdS 3

DOE PAGES

Compere, Geoffrey; Guica, Monica; Rodriguez, Maria J.

2014-12-02

We study three-dimensional consistent truncations of type IIB supergravity which admit warped AdS 3 solutions. These theories contain subsectors that have no bulk dynamics. We show that the symplectic form for these theories, when restricted to the non-dynamical subsectors, equals the symplectic form for pure Einstein gravity in AdS 3. Consequently, for each consistent choice of boundary conditions in AdS 3, we can define a consistent phase space in warped AdS 3 with identical conserved charges. This way, we easily obtain a Virasoro × Virasoro asymptotic symmetry algebra in warped AdS 3; two different types of Virasoro × Kač-Moody symmetriesmore » are also consistent alternatives. Next, we study the phase space of these theories when propagating modes are included. We show that, as long as one can define a conserved symplectic form without introducing instabilities, the Virasoro × Virasoro asymptotic symmetries can be extended to the entire (linearised) phase space. In conclusion, this implies that, at least at semi-classical level, consistent theories of gravity in warped AdS 3 are described by a two-dimensional conformal field theory, as long as stability is not an issue.« less

Degenerate variational integrators for magnetic field line flow and guiding center trajectories

NASA Astrophysics Data System (ADS)

Ellison, C. L.; Finn, J. M.; Burby, J. W.; Kraus, M.; Qin, H.; Tang, W. M.

2018-05-01

Symplectic integrators offer many benefits for numerically approximating solutions to Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two important Hamiltonian systems encountered in plasma physics—the flow of magnetic field lines and the guiding center motion of magnetized charged particles—resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates. New algorithms were recently developed using the variational integration formalism; however, those integrators were found to admit parasitic mode instabilities due to their multistep character. This work eliminates the multistep character, and therefore the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem "degenerate variational integration." Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that the resultant Euler-Lagrange equations are systems of first-order ordinary differential equations. We show that retaining the same degree of degeneracy when constructing discrete Lagrangians yields one-step variational integrators preserving a non-canonical symplectic structure. Numerical examples demonstrate the benefits of the new algorithms, including superior stability relative to the existing variational integrators for these systems and superior qualitative behavior relative to non-conservative algorithms.

Two Virasoro symmetries in stringy warped AdS 3

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

Compere, Geoffrey; Guica, Monica; Rodriguez, Maria J.

We study three-dimensional consistent truncations of type IIB supergravity which admit warped AdS 3 solutions. These theories contain subsectors that have no bulk dynamics. We show that the symplectic form for these theories, when restricted to the non-dynamical subsectors, equals the symplectic form for pure Einstein gravity in AdS 3. Consequently, for each consistent choice of boundary conditions in AdS 3, we can define a consistent phase space in warped AdS 3 with identical conserved charges. This way, we easily obtain a Virasoro × Virasoro asymptotic symmetry algebra in warped AdS 3; two different types of Virasoro × Kač-Moody symmetriesmore » are also consistent alternatives. Next, we study the phase space of these theories when propagating modes are included. We show that, as long as one can define a conserved symplectic form without introducing instabilities, the Virasoro × Virasoro asymptotic symmetries can be extended to the entire (linearised) phase space. In conclusion, this implies that, at least at semi-classical level, consistent theories of gravity in warped AdS 3 are described by a two-dimensional conformal field theory, as long as stability is not an issue.« less

Extremal entanglement and mixedness in continuous variable systems

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

Adesso, Gerardo; Serafini, Alessio; Illuminati, Fabrizio

2004-08-01

We investigate the relationship between mixedness and entanglement for Gaussian states of continuous variable systems. We introduce generalized entropies based on Schatten p norms to quantify the mixedness of a state and derive their explicit expressions in terms of symplectic spectra. We compare the hierarchies of mixedness provided by such measures with the one provided by the purity (defined as tr {rho}{sup 2} for the state {rho}) for generic n-mode states. We then review the analysis proving the existence of both maximally and minimally entangled states at given global and marginal purities, with the entanglement quantified by the logarithmic negativity.more » Based on these results, we extend such an analysis to generalized entropies, introducing and fully characterizing maximally and minimally entangled states for given global and local generalized entropies. We compare the different roles played by the purity and by the generalized p entropies in quantifying the entanglement and the mixedness of continuous variable systems. We introduce the concept of average logarithmic negativity, showing that it allows a reliable quantitative estimate of continuous variable entanglement by direct measurements of global and marginal generalized p entropies.« less

The canonical Lagrangian approach to three-space general relativity

NASA Astrophysics Data System (ADS)

Shyam, Vasudev; Venkatesh, Madhavan

2013-07-01

We study the action for the three-space formalism of general relativity, better known as the Barbour-Foster-Ó Murchadha action, which is a square-root Baierlein-Sharp-Wheeler action. In particular, we explore the (pre)symplectic structure by pulling it back via a Legendre map to the tangent bundle of the configuration space of this action. With it we attain the canonical Lagrangian vector field which generates the gauge transformations (3-diffeomorphisms) and the true physical evolution of the system. This vector field encapsulates all the dynamics of the system. We also discuss briefly the observables and perennials for this theory. We then present a symplectic reduction of the constrained phase space.

Symmetry and conservation laws in semiclassical wave packet dynamics

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

Ohsawa, Tomoki, E-mail: tomoki@utdallas.edu

2015-03-15

We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether’s theorem. We consider two slightly different formulations of Gaussian wave packet dynamics; one is based on earlier works of Heller and Hagedorn and the other based on the symplectic-geometric approach by Lubich and others. In either case, we reveal the symplectic and Hamiltonian nature of the dynamics and formulate natural symmetry group actions in the setting to derive the corresponding conserved quantities (momentum maps). The semiclassical angular momentum inherits the essential properties of the classical angular momentum asmore » well as naturally corresponds to the quantum picture.« less

Localization in a quantum spin Hall system.

PubMed

Onoda, Masaru; Avishai, Yshai; Nagaosa, Naoto

2007-02-16

The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.

Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere

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

Li Jinxing; Pu Zuyin; Xie Lun

Charged particle dynamics in magnetosphere has temporal and spatial multiscale; therefore, numerical accuracy over a long integration time is required. A variational symplectic integrator (VSI) [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008) and H. Qin, X. Guan, and W. M. Tang, Phys. Plasmas 16, 042510 (2009)] for the guiding-center motion of charged particles in general magnetic field is applied to study the dynamics of charged particles in magnetosphere. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing themore » dynamics. The VSI conserves exactly a discrete Lagrangian symplectic structure and has better numerical properties over a long integration time, compared with standard integrators, such as the standard and adaptive fourth order Runge-Kutta (RK4) methods. Applying the VSI method to guiding-center dynamics in the inner magnetosphere, we can accurately calculate the particles'orbits for an arbitrary long simulating time with good conservation property. When a time-independent convection and corotation electric field is considered, the VSI method can give the accurate single particle orbit, while the RK4 method gives an incorrect orbit due to its intrinsic error accumulation over a long integrating time.« less

Symplectic analysis of vertical random vibration for coupled vehicle track systems

NASA Astrophysics Data System (ADS)

Lu, F.; Kennedy, D.; Williams, F. W.; Lin, J. H.

2008-10-01

A computational model for random vibration analysis of vehicle-track systems is proposed and solutions use the pseudo excitation method (PEM) and the symplectic method. The vehicle is modelled as a mass, spring and damping system with 10 degrees of freedom (dofs) which consist of vertical and pitching motion for the vehicle body and its two bogies and vertical motion for the four wheelsets. The track is treated as an infinite Bernoulli-Euler beam connected to sleepers and hence to ballast and is regarded as a periodic structure. Linear springs couple the vehicle and the track. Hence, the coupled vehicle-track system has only 26 dofs. A fixed excitation model is used, i.e. the vehicle does not move along the track but instead the track irregularity profile moves backwards at the vehicle velocity. This irregularity is assumed to be a stationary random process. Random vibration theory is used to obtain the response power spectral densities (PSDs), by using PEM to transform this random multiexcitation problem into a deterministic harmonic excitation one and then applying symplectic solution methodology. Numerical results for an example include verification of the proposed method by comparing with finite element method (FEM) results; comparison between the present model and the traditional rigid track model and; discussion of the influences of track damping and vehicle velocity.

Efficient adaptive pseudo-symplectic numerical integration techniques for Landau-Lifshitz dynamics

NASA Astrophysics Data System (ADS)

d'Aquino, M.; Capuano, F.; Coppola, G.; Serpico, C.; Mayergoyz, I. D.

2018-05-01

Numerical time integration schemes for Landau-Lifshitz magnetization dynamics are considered. Such dynamics preserves the magnetization amplitude and, in the absence of dissipation, also implies the conservation of the free energy. This property is generally lost when time discretization is performed for the numerical solution. In this work, explicit numerical schemes based on Runge-Kutta methods are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order p, but preserve magnetization amplitude and free energy to order q > p. An effective strategy for adaptive time-stepping control is discussed for schemes of this class. Numerical tests against analytical solutions for the simulation of fast precessional dynamics are performed in order to point out the effectiveness of the proposed methods.

Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform.

PubMed

Hausel, Tamás

2006-04-18

A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski-Dancer and Hausel-Sturmfels), Poincaré polynomials of Hilbert schemes of points and twisted Atiyah-Drinfeld-Hitchin-Manin (ADHM) spaces of instantons on C2 (recovering results of Nakajima-Yoshioka), and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced.

Efficient Generation and Use of Power Series for Broad Application.

NASA Astrophysics Data System (ADS)

Rudmin, Joseph; Sochacki, James

2017-01-01

A brief history and overview of the Parker-Sockacki Method of Power Series generation is presented. This method generates power series to order n in time n2 for any system of differential equations that has a power series solution. The method is simple enough that novices to differential equations can easily learn it and immediately apply it. Maximal absolute error estimates allow one to determine the number of terms needed to reach desired accuracy. Ratios of coefficients in a solution with global convergence differ signficantly from that for a solution with only local convergence. Divergence of the series prevents one from overlooking poles. The method can always be cast in polynomial form, which allows separation of variables in almost all physical systems, facilitating exploration of hidden symmetries, and is implicitly symplectic.

Mercury - A New Software Package for Orbital Integrations

NASA Astrophysics Data System (ADS)

Chambers, J. E.; Migliorini, F.

1997-07-01

We present Mercury: a new general-purpose software package for carrying out orbital integrations for problems in solar-system dynamics. Suitable applications include studying the long-term stability of the planetary system, investigating the orbital evolution of comets, asteroids or meteoroids, and simulating planetary accretion. Mercury is designed to be versatile and easy to use, accepting initial conditions in either Cartesian coordinates or Keplerian elements in ``cometary'' or ``asteroidal'' format, with different epochs of osculation for different objects. Output from an integration consists of either osculating or averaged (``proper'') elements, written in a machine-independent compressed format, which allows the results of a calculation performed on one platform to be transferred (e.g. via FTP) and decoded on another. Mercury itself is platform independent, and can be run on machines using DEC Unix, Open VMS, HP Unix, Solaris, Linux or DOS. During an integration, Mercury monitors and records details of close encounters, sungrazing events, ejections and collisions between objects. The effects of non-gravitational forces on comets can also be modelled. Additional effects such as Poynting-Robertson drag, post-Newtonian corrections, oblateness of the primary, and the galactic potential will be incorporated in future. The package currently supports integrations using a mixed-variable symplectic routine, the Bulirsch-Stoer method, and a hybrid code for planetary accretion calculations; with Everhart's popular RADAU algorithm and a symmetric multistep routine to be added shortly. Our presentation will include a demonstration of the latest version of Mercury, with the explicit aim of getting feedback from potential users and incorporating these suggestions into a final version that will be made available to everybody.

Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps

NASA Astrophysics Data System (ADS)

Goto, Shin-itiro; Umeno, Ken

2018-03-01

Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps, where it is defined on a subset of the real line and its probability distribution function is the Cauchy distribution with some parameters. With this reduction, some relations between the statistical picture and the orbital one are shown. From the viewpoint of information geometry, the parameter space can be identified with a statistical manifold, and then it is shown that the derived maps can be characterized. Also, with an induced symplectic structure from a statistical structure, symplectic and information geometric aspects of the derived maps are discussed.

JANUS: a bit-wise reversible integrator for N-body dynamics

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2018-01-01

Hamiltonian systems such as the gravitational N-body problem have time-reversal symmetry. However, all numerical N-body integration schemes, including symplectic ones, respect this property only approximately. In this paper, we present the new N-body integrator JANUS , for which we achieve exact time-reversal symmetry by combining integer and floating point arithmetic. JANUS is explicit, formally symplectic and satisfies Liouville's theorem exactly. Its order is even and can be adjusted between two and ten. We discuss the implementation of JANUS and present tests of its accuracy and speed by performing and analysing long-term integrations of the Solar system. We show that JANUS is fast and accurate enough to tackle a broad class of dynamical problems. We also discuss the practical and philosophical implications of running exactly time-reversible simulations.

Symplectic maps and chromatic optics in particle accelerators

DOE PAGES

Cai, Yunhai

2015-07-06

Here, we have applied the nonlinear map method to comprehensively characterize the chromatic optics in particle accelerators. Our approach is built on the foundation of symplectic transfer maps of magnetic elements. The chromatic lattice parameters can be transported from one element to another by the maps. We also introduce a Jacobian operator that provides an intrinsic linkage between the maps and the matrix with parameter dependence. The link allows us to directly apply the formulation of the linear optics to compute the chromatic lattice parameters. As an illustration, we analyze an alternating-gradient cell with nonlinear sextupoles, octupoles, and decapoles andmore » derive analytically their settings for the local chromatic compensation. Finally, the cell becomes nearly perfect up to the third-order of the momentum deviation.« less

Actions, topological terms and boundaries in first-order gravity: A review

NASA Astrophysics Data System (ADS)

Corichi, Alejandro; Rubalcava-García, Irais; Vukašinac, Tatjana

2016-03-01

In this review, we consider first-order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad eaI and a SO(3, 1) connection ωaIJ. We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein-Hilbert-Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space Γ is given by solutions to the equations of motion. For each of the possible terms contributing to the action, we consider the well-posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges. The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way, we point out and clarify some issues that have not been clearly understood in the literature.

Gyro-gauge-independent formulation of the guiding-center reduction to arbitrary order in the Larmor radius

NASA Astrophysics Data System (ADS)

de Guillebon, L.; Vittot, M.

2013-10-01

Guiding-center reduction is studied using gyro-gauge-independent coordinates. The Lagrangian 1-form of charged particle dynamics is Lie transformed without introducing a gyro-gauge, but using directly the unit vector of the component of the velocity perpendicular to the magnetic field as the coordinate corresponding to Larmor gyration. The reduction is shown to provide a maximal reduction for the Lagrangian and to work for all orders in the Larmor radius, following exactly the same procedure as when working with the standard gauge-dependent coordinate. The gauge-dependence is removed from the coordinate system by using a constrained variable for the gyro-angle. The closed 1-form dθ is replaced by a more general non-closed 1-form, which is equal to dθ in the gauge-dependent case. The gauge vector is replaced by a more general connection in the definition of the gradient, which behaves as a covariant derivative, in perfect agreement with the circle-bundle picture. This explains some results of previous works, whose gauge-independent expressions did not correspond to gauge fixing but did indeed correspond to connection fixing. In addition, some general results are obtained for the guiding-center reduction. The expansion is polynomial in the cotangent of the pitch-angle as an effect of the structure of the Lagrangian, preserved by Lie derivatives. The induction for the reduction is shown to rely on the inversion of a matrix, which is the same for all orders higher than three. It is inverted and explicit induction relations are obtained to go to an arbitrary order in the perturbation expansion. The Hamiltonian and symplectic representations of the guiding-center reduction are recovered, but conditions for the symplectic representation at each order are emphasized.

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

NASA Astrophysics Data System (ADS)

Nejad, Salman Abarghouei; Dehghani, Mehdi; Monemzadeh, Majid

2018-01-01

We study the effect of the simplest geometry which is imposed via the topology of the universe by gauging non-relativistic particle model on torus and 3-torus with the help of symplectic formalism of constrained systems. Also, we obtain generators of gauge transformations for gauged models. Extracting corresponding Poisson structure of existed constraints, we show the effect of the shape of the universe on canonical structure of phase-spaces of models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space. In addition, we show that the number of extra dimensions in the phase-spaces of gauged embedded models are exactly two. Moreover, in classical form, we talk over modification of Newton's second law in order to study the origin of the terms appeared in the gauged theory.

Quantum mechanics on phase space: The hydrogen atom and its Wigner functions

NASA Astrophysics Data System (ADS)

Campos, P.; Martins, M. G. R.; Fernandes, M. C. B.; Vianna, J. D. M.

2018-03-01

Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo-Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.

ALARIC: An algorithm for constructing arbitrarily complex initial density distributions with low particle noise for SPH/SPMHD applications

NASA Astrophysics Data System (ADS)

Vela Vela, Luis; Sanchez, Raul; Geiger, Joachim

2018-03-01

A method is presented to obtain initial conditions for Smoothed Particle Hydrodynamic (SPH) scenarios where arbitrarily complex density distributions and low particle noise are needed. Our method, named ALARIC, tampers with the evolution of the internal variables to obtain a fast and efficient profile evolution towards the desired goal. The result has very low levels of particle noise and constitutes a perfect candidate to study the equilibrium and stability properties of SPH/SPMHD systems. The method uses the iso-thermal SPH equations to calculate hydrodynamical forces under the presence of an external fictitious potential and evolves them in time with a 2nd-order symplectic integrator. The proposed method generates tailored initial conditions that perform better in many cases than those based on purely crystalline lattices, since it prevents the appearance of anisotropies.

Extended Riemannian geometry II: local heterotic double field theory

NASA Astrophysics Data System (ADS)

Deser, Andreas; Heller, Marc Andre; Sämann, Christian

2018-04-01

We continue our exploration of local Double Field Theory (DFT) in terms of symplectic graded manifolds carrying compatible derivations and study the case of heterotic DFT. We start by developing in detail the differential graded manifold that captures heterotic Generalized Geometry which leads to new observations on the generalized metric and its twists. We then give a symplectic pre-N Q-manifold that captures the symmetries and the geometry of local heterotic DFT. We derive a weakened form of the section condition, which arises algebraically from consistency of the symmetry Lie 2-algebra and its action on extended tensors. We also give appropriate notions of twists — which are required for global formulations — and of the torsion and Riemann tensors. Finally, we show how the observed α'-corrections are interpreted naturally in our framework.

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

Qin, Hong; Liu, Jian; Xiao, Jianyuan

Particle-in-cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretising its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g. 10(9), degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinearmore » Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.« less

Quantum gravity from noncommutative spacetime

NASA Astrophysics Data System (ADS)

Lee, Jungjai; Yang, Hyun Seok

2014-12-01

We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative ★-algebra) of quantum gravity.

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

DOE PAGES

Su, Hongling; Li, Shengtai

2016-02-03

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

K-decompositions and 3d gauge theories

NASA Astrophysics Data System (ADS)

Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.

2016-11-01

This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL( K, ℂ)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli space ℒ K ( M) of framed flat connections on the boundary ∂ M that extend to M. Our goal is to understand an open part of ℒ K ( M) as a Lagrangian subvariety in the symplectic moduli space {{X}}_K^{un}(partial M) of framed flat connections on the boundary — and more so, as a "K2-Lagrangian," meaning that the K2-avatar of the symplectic form restricts to zero. We construct an open part of ℒ K ( M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston's gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL( K, ℂ)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of ℒ K ( M) is K2-isotropic as long as ∂ M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that ℒ K ( M) is K2-Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K2-Lagrangian property to a combinatorial statement.

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

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

Su, Hongling; Li, Shengtai

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

An Innovative Sensing Approach Using Carbon Nanotube-Based Composites for Structural Health Monitoring of Concrete Structures

NASA Astrophysics Data System (ADS)

Dwivedi, Vatsal

This thesis presents some work on two quite disparate kinds of dynamical systems described by Hamiltonian dynamics. The first part describes a computation of gauge anomalies and their macroscopic effects in a semiclassical picture. The geometric (symplectic) formulation of classical mechanics is used to describe the dynamics of Weyl fermions in even spacetime dimensions, the only quantum input to the symplectic form being the Berry curvature that encodes the spin-momentum locking. The (semi-)classical equations of motion are used in a kinetic theory setup to compute the gauge and singlet currents, whose conservation laws reproduce the nonabelian gauge and singlet anomalies. Anomalous contributions to the hydrodynamic currents for a gas of Weyl fermions at a finite temperature and chemical potential are also calculated, and are in agreement with similar results in literature which were obtained using thermodynamic and/or quantum field theoretical arguments. The second part describes a generalized transfer matrix formalism for noninteracting tight-binding models. The formalism is used to study the bulk and edge spectra, both of which are encoded in the spectrum of the transfer matrices, for some of the common tight-binding models for noninteracting electronic topological phases of matter. The topological invariants associated with the boundary states are interpreted as winding numbers for windings around noncontractible loops on a Riemann sheet constructed using the algebraic structure of the transfer matrices, as well as with a Maslov index on a symplectic group manifold, which is the space of transfer matrices.

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

Koenig, Robert

We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications for entanglement-assisted classical communication over additive bosonic noise channels.

Diff-invariant kinetic terms in arbitrary dimensions

NASA Astrophysics Data System (ADS)

Barbero G., J. Fernando; Villaseñor, Eduardo J.

2002-06-01

We study the physical content of quadratic diff-invariant Lagrangians in arbitrary dimensions by using covariant symplectic techniques. This paper extends previous results in dimension four. We discuss the difference between the even and odd dimensional cases.

A Hamiltonian approach to Thermodynamics

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

Baldiotti, M.C., E-mail: baldiotti@uel.br; Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br; Molina, C., E-mail: cmolina@usp.br

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensivelymore » used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.« less

Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics

NASA Astrophysics Data System (ADS)

Manno, Gianni; Moreno, Giovanni

2016-03-01

This paper is a natural companion of [Alekseevsky D.V., Alonso Blanco R., Manno G., Pugliese F., Ann. Inst. Fourier (Grenoble) 62 (2012), 497-524, arXiv:1003.5177], generalising its perspectives and results to the context of third-order (2D) Monge-Ampère equations, by using the so-called ''meta-symplectic structure'' associated with the 8D prolongation M^{(1)} of a 5D contact manifold M. We write down a geometric definition of a third-order Monge-Ampère equation in terms of a (class of) differential two-form on M^{(1)}. In particular, the equations corresponding to decomposable forms admit a simple description in terms of certain three-dimensional distributions, which are made from the characteristics of the original equations. We conclude the paper with a study of the intermediate integrals of these special Monge-Ampère equations, herewith called of Goursat type.

Natural differential operations on manifolds: an algebraic approach

NASA Astrophysics Data System (ADS)

Katsylo, P. I.; Timashev, D. A.

2008-10-01

Natural algebraic differential operations on geometric quantities on smooth manifolds are considered. A method for the investigation and classification of such operations is described, the method of IT-reduction. With it the investigation of natural operations reduces to the analysis of rational maps between k-jet spaces, which are equivariant with respect to certain algebraic groups. On the basis of the method of IT-reduction a finite generation theorem is proved: for tensor bundles \\mathscr{V},\\mathscr{W}\\to M all the natural differential operations D\\colon\\Gamma(\\mathscr{V})\\to\\Gamma(\\mathscr{W}) of degree at most d can be algebraically constructed from some finite set of such operations. Conceptual proofs of known results on the classification of natural linear operations on arbitrary and symplectic manifolds are presented. A non-existence theorem is proved for natural deformation quantizations on Poisson manifolds and symplectic manifolds.Bibliography: 21 titles.

Four-dimensional gravity as an almost-Poisson system

NASA Astrophysics Data System (ADS)

Ita, Eyo Eyo

2015-04-01

In this paper, we examine the phase space structure of a noncanonical formulation of four-dimensional gravity referred to as the Instanton representation of Plebanski gravity (IRPG). The typical Hamiltonian (symplectic) approach leads to an obstruction to the definition of a symplectic structure on the full phase space of the IRPG. We circumvent this obstruction, using the Lagrange equations of motion, to find the appropriate generalization of the Poisson bracket. It is shown that the IRPG does not support a Poisson bracket except on the vector constraint surface. Yet there exists a fundamental bilinear operation on its phase space which produces the correct equations of motion and induces the correct transformation properties of the basic fields. This bilinear operation is known as the almost-Poisson bracket, which fails to satisfy the Jacobi identity and in this case also the condition of antisymmetry. We place these results into the overall context of nonsymplectic systems.

Multipole Vortex Blobs (MVB): Symplectic Geometry and Dynamics.

PubMed

Holm, Darryl D; Jacobs, Henry O

2017-01-01

Vortex blob methods are typically characterized by a regularization length scale, below which the dynamics are trivial for isolated blobs. In this article, we observe that the dynamics need not be trivial if one is willing to consider distributional derivatives of Dirac delta functionals as valid vorticity distributions. More specifically, a new singular vortex theory is presented for regularized Euler fluid equations of ideal incompressible flow in the plane. We determine the conditions under which such regularized Euler fluid equations may admit vorticity singularities which are stronger than delta functions, e.g., derivatives of delta functions. We also describe the symplectic geometry associated with these augmented vortex structures, and we characterize the dynamics as Hamiltonian. Applications to the design of numerical methods similar to vortex blob methods are also discussed. Such findings illuminate the rich dynamics which occur below the regularization length scale and enlighten our perspective on the potential for regularized fluid models to capture multiscale phenomena.

Symplectic molecular dynamics simulations on specially designed parallel computers.

PubMed

Borstnik, Urban; Janezic, Dusanka

2005-01-01

We have developed a computer program for molecular dynamics (MD) simulation that implements the Split Integration Symplectic Method (SISM) and is designed to run on specialized parallel computers. The MD integration is performed by the SISM, which analytically treats high-frequency vibrational motion and thus enables the use of longer simulation time steps. The low-frequency motion is treated numerically on specially designed parallel computers, which decreases the computational time of each simulation time step. The combination of these approaches means that less time is required and fewer steps are needed and so enables fast MD simulations. We study the computational performance of MD simulation of molecular systems on specialized computers and provide a comparison to standard personal computers. The combination of the SISM with two specialized parallel computers is an effective way to increase the speed of MD simulations up to 16-fold over a single PC processor.

A braided monoidal category for free super-bosons

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

Runkel, Ingo, E-mail: ingo.runkel@uni-hamburg.de

The chiral conformal field theory of free super-bosons is generated by weight one currents whose mode algebra is the affinisation of an abelian Lie super-algebra h with non-degenerate super-symmetric pairing. The mode algebras of a single free boson and of a single pair of symplectic fermions arise for even|odd dimension 1|0 and 0|2 of h, respectively. In this paper, the representations of the untwisted mode algebra of free super-bosons are equipped with a tensor product, a braiding, and an associator. In the symplectic fermion case, i.e., if h is purely odd, the braided monoidal structure is extended to representations ofmore » the Z/2Z-twisted mode algebra. The tensor product is obtained by computing spaces of vertex operators. The braiding and associator are determined by explicit calculations from three- and four-point conformal blocks.« less

Surfing on the edge: chaos versus near-integrability in the system of Jovian planets

NASA Astrophysics Data System (ADS)

Hayes, Wayne B.

2008-05-01

We demonstrate that the system of Sun and Jovian planets, integrated for 200Myr as an isolated five-body system using many sets of initial conditions all within the uncertainty bounds of their currently known positions, can display both chaos and near-integrability. The conclusion is consistent across four different integrators, including several comparisons against integrations utilizing quadruple precision. We demonstrate that the Wisdom-Holman symplectic map using simple symplectic correctors as implemented in MERCURY 6.2 gives a reliable characterization of the existence of chaos for a particular initial condition only with time-steps less than about 10d, corresponding to about 400 steps per orbit. We also integrate the canonical DE405 initial condition out to 5Gyr, and show that it has a Lyapunov time of 200-400Myr, opening the remote possibility of accurate prediction of the Jovian planetary positions for 5Gyr.

Derivation of the dipole map

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh; Boozer, Allen

2004-09-01

In our method of maps [Punjabi et al., Phy. Rev. Lett. 69, 3322 (1992), and Punjabi et al., J. Plasma Phys. 52, 91 (1994)], symplectic maps are used to calculate the trajectories of magnetic field lines in divertor tokamaks. Effects of the magnetic perturbations are calculated using the low MN map [Ali et al., Phys. Plasmas 11, 1908 (2004)] and the dipole map [Punjabi et al., Phys. Plasmas 10, 3992 (2003)]. The dipole map is used to calculate the effects of externally located current carrying coils on the trajectories of the field lines, the stochastic layer, the magnetic footprint, and the heat load distribution on the collector plates in divertor tokamaks [Punjabi et al., Phys. Plasmas 10, 3992 (2003)]. Symplectic maps are general, efficient, and preserve and respect the Hamiltonian nature of the dynamics. In this brief communication, a rigorous mathematical derivation of the dipole map is given.

Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational

DOE PAGES

Ellison, C. L.; Burby, J. W.; Qin, H.

2015-11-01

One popular technique for the numerical time advance of charged particles interacting with electric and magnetic fields according to the Lorentz force law [1], [2], [3] and [4] is the Boris algorithm. Its popularity stems from simple implementation, rapid iteration, and excellent long-term numerical fidelity [1] and [5]. Excellent long-term behavior strongly suggests the numerical dynamics exhibit conservation laws analogous to those governing the continuous Lorentz force system [6]. Moreover, without conserved quantities to constrain the numerical dynamics, algorithms typically dissipate or accumulate important observables such as energy and momentum over long periods of simulated time [6]. Identification of themore » conservative properties of an algorithm is important for establishing rigorous expectations on the long-term behavior; energy-preserving, symplectic, and volume-preserving methods each have particular implications for the qualitative numerical behavior [6], [7], [8], [9], [10] and [11].« less

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

Chen, Chuchu, E-mail: chenchuchu@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Zhang, Liying, E-mail: lyzhang@lsec.cc.ac.cn

Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the correspondingmore » discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.« less

Simple satellite orbit propagator

NASA Astrophysics Data System (ADS)

Gurfil, P.

2008-06-01

An increasing number of space missions require on-board autonomous orbit determination. The purpose of this paper is to develop a simple orbit propagator (SOP) for such missions. Since most satellites are limited by the available processing power, it is important to develop an orbit propagator that will use limited computational and memory resources. In this work, we show how to choose state variables for propagation using the simplest numerical integration scheme available-the explicit Euler integrator. The new state variables are derived by the following rationale: Apply a variation-of-parameters not on the gravity-affected orbit, but rather on the gravity-free orbit, and teart the gravity as a generalized force. This ultimately leads to a state vector comprising the inertial velocity and a modified position vector, wherein the product of velocity and time is subtracted from the inertial position. It is shown that the explicit Euler integrator, applied on the new state variables, becomes a symplectic integrator, preserving the Hamiltonian and the angular momentum (or a component thereof in the case of oblateness perturbations). The main application of the proposed propagator is estimation of mean orbital elements. It is shown that the SOP is capable of estimating the mean elements with an accuracy that is comparable to a high-order integrator that consumes an order-of-magnitude more computational time than the SOP.

Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations

NASA Astrophysics Data System (ADS)

Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio

2007-10-01

We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1×M bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a , uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes.

Suppression of Growth by Multiplicative White Noise in a Parametric Resonant System

NASA Astrophysics Data System (ADS)

Ishihara, Masamichi

2015-02-01

The growth of the amplitude in a Mathieu-like equation with multiplicative white noise is studied. To obtain an approximate analytical expression for the exponent at the extremum on parametric resonance regions, a time-interval width is introduced. To determine the exponents numerically, the stochastic differential equations are solved by a symplectic numerical method. The Mathieu-like equation contains a parameter α determined by the intensity of noise and the strength of the coupling between the variable and noise; without loss of generality, only non-negative α can be considered. The exponent is shown to decrease with α, reach a minimum and increase after that. The minimum exponent is obtained analytically and numerically. As a function of α, the minimum at α≠0, occurs on the parametric resonance regions of α=0. This minimum indicates suppression of growth by multiplicative white noise.

K-decompositions and 3d gauge theories

DOE PAGES

Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.

2016-11-24

This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K, C)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli spacemore » $$\\mathcal{L}$$ K(M) of framed flat connections on the boundary ∂M that extend to M. Our goal is to understand an open part of $$\\mathcal{L}$$ K(M) as a Lagrangian subvariety in the symplectic moduli space X un K(∂M) of framed flat connections on the boundary — and more so, as a “K 2-Lagrangian,” meaning that the K 2-avatar of the symplectic form restricts to zero. We construct an open part of $$\\mathcal{L}$$ K(M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston’s gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL(K, C)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of $$\\mathcal{L}$$ K(M) is K 2-isotropic as long as ∂M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that $$\\mathcal{L}$$ K(M) is K 2-Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K 2-Lagrangian property to a combinatorial statement. Physically, we translate the K-decomposition of an ideal triangulation of M and its symplectic properties to produce an explicit construction of 3d N = 2 superconformal field theories T K [M] resulting (conjecturally) from the compactification of K M5-branes on M. This extends known constructions for K = 2. Just as for K = 2, the theories T K [M] are described as IR fixed points of abelian Chern-Simons-matter theories. Changes of triangulation (2-3 moves) lead to abelian mirror symmetries that are all generated by the elementary duality between N f = 1 SQED and the XYZ model. In the large K limit, we find evidence that the degrees of freedom of T K [M] grow cubically in K.« less

K-decompositions and 3d gauge theories

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

Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.

This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K, C)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli spacemore » $$\\mathcal{L}$$ K(M) of framed flat connections on the boundary ∂M that extend to M. Our goal is to understand an open part of $$\\mathcal{L}$$ K(M) as a Lagrangian subvariety in the symplectic moduli space X un K(∂M) of framed flat connections on the boundary — and more so, as a “K 2-Lagrangian,” meaning that the K 2-avatar of the symplectic form restricts to zero. We construct an open part of $$\\mathcal{L}$$ K(M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston’s gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL(K, C)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of $$\\mathcal{L}$$ K(M) is K 2-isotropic as long as ∂M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that $$\\mathcal{L}$$ K(M) is K 2-Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K 2-Lagrangian property to a combinatorial statement. Physically, we translate the K-decomposition of an ideal triangulation of M and its symplectic properties to produce an explicit construction of 3d N = 2 superconformal field theories T K [M] resulting (conjecturally) from the compactification of K M5-branes on M. This extends known constructions for K = 2. Just as for K = 2, the theories T K [M] are described as IR fixed points of abelian Chern-Simons-matter theories. Changes of triangulation (2-3 moves) lead to abelian mirror symmetries that are all generated by the elementary duality between N f = 1 SQED and the XYZ model. In the large K limit, we find evidence that the degrees of freedom of T K [M] grow cubically in K.« less

Perturbative Quantum Gauge Theories on Manifolds with Boundary

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai

2018-01-01

This paper introduces a general perturbative quantization scheme for gauge theories on manifolds with boundary, compatible with cutting and gluing, in the cohomological symplectic (BV-BFV) formalism. Explicit examples, like abelian BF theory and its perturbations, including nontopological ones, are presented.

Associative Algebraic Approach to Logarithmic CFT in the Bulk: The Continuum Limit of the {gl(1|1)} Periodic Spin Chain, Howe Duality and the Interchiral Algebra

NASA Astrophysics Data System (ADS)

Gainutdinov, A. M.; Read, N.; Saleur, H.

2016-01-01

We develop in this paper the principles of an associative algebraic approach to bulk logarithmic conformal field theories (LCFTs). We concentrate on the closed {gl(1|1)} spin-chain and its continuum limit—the {c=-2} symplectic fermions theory—and rely on two technical companion papers, Gainutdinov et al. (Nucl Phys B 871:245-288, 2013) and Gainutdinov et al. (Nucl Phys B 871:289-329, 2013). Our main result is that the algebra of local Hamiltonians, the Jones-Temperley-Lieb algebra JTL N , goes over in the continuum limit to a bigger algebra than {V}, the product of the left and right Virasoro algebras. This algebra, {S}—which we call interchiral, mixes the left and right moving sectors, and is generated, in the symplectic fermions case, by the additional field {S(z,bar{z})≡ S_{αβ} ψ^α(z)bar{ψ}^β(bar{z})}, with a symmetric form {S_{αβ}} and conformal weights (1,1). We discuss in detail how the space of states of the LCFT (technically, a Krein space) decomposes onto representations of this algebra, and how this decomposition is related with properties of the finite spin-chain. We show that there is a complete correspondence between algebraic properties of finite periodic spin chains and the continuum limit. An important technical aspect of our analysis involves the fundamental new observation that the action of JTL N in the {gl(1|1)} spin chain is in fact isomorphic to an enveloping algebra of a certain Lie algebra, itself a non semi-simple version of {sp_{N-2}}. The semi-simple part of JTL N is represented by {U sp_{N-2}}, providing a beautiful example of a classical Howe duality, for which we have a non semi-simple version in the full JTL N image represented in the spin-chain. On the continuum side, simple modules over {S} are identified with "fundamental" representations of {sp_∞}.

The Frölicher-type inequalities of foliations

NASA Astrophysics Data System (ADS)

Raźny, Paweł

2017-04-01

The purpose of this article is to adapt the Frölicher-type inequality, stated and proven for complex and symplectic manifolds in Angella and Tomassini (2015), to the case of transversely holomorphic and symplectic foliations. These inequalities provide a criterion for checking whether a foliation transversely satisfies the ∂ ∂ ¯ -lemma and the ddΛ-lemma (i.e. whether the basic forms of a given foliation satisfy them). These lemmas are linked to such properties as the formality of the basic de Rham complex of a foliation and the transverse hard Lefschetz property. In particular they provide an obstruction to the existence of a transverse Kähler structure for a given foliation. In the second section we will provide some information concerning the d‧d″-lemma for a given double complex (K • , • ,d‧ ,d″) and state the main results from Angella and Tomassini (2015). We will also recall some basic facts and definitions concerning foliations. In the third section we treat the case of transversely holomorphic foliations. We also give a brief review of some properties of the basic Bott-Chern and Aeppli cohomology theories. In Section 4 we prove the symplectic version of the Frölicher-type inequality. The final 3 sections of this paper are devoted to the applications of our main theorems. In them we verify the aforementioned lemmas for some simple examples, give the orbifold versions of the Frölicher-type inequalities and show that transversely Kähler foliations satisfy both the ∂ ∂ ¯ -lemma and the ddΛ-lemma (or in other words that our main theorems provide an obstruction to the existence of a transversely Kähler structure).

Quantization of wave equations and hermitian structures in partial differential varieties

PubMed Central

Paneitz, S. M.; Segal, I. E.

1980-01-01

Sufficiently close to 0, the solution variety of a nonlinear relativistic wave equation—e.g., of the form □ϕ + m2ϕ + gϕp = 0—admits a canonical Lorentz-invariant hermitian structure, uniquely determined by the consideration that the action of the differential scattering transformation in each tangent space be unitary. Similar results apply to linear time-dependent equations or to equations in a curved asymptotically flat space-time. A close relation of the Riemannian structure to the determination of vacuum expectation values is developed and illustrated by an explicit determination of a perturbative 2-point function for the case of interaction arising from curvature. The theory underlying these developments is in part a generalization of that of M. G. Krein and collaborators concerning stability of differential equations in Hilbert space and in part a precise relation between the unitarization of given symplectic linear actions and their full probabilistic quantization. The unique causal structure in the infinite symplectic group is instrumental in these developments. PMID:16592923

Quantization of Poisson Manifolds from the Integrability of the Modular Function

NASA Astrophysics Data System (ADS)

Bonechi, F.; Ciccoli, N.; Qiu, J.; Tarlini, M.

2014-10-01

We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on , seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU( n + 1). We show that a bihamiltonian system on defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras.

Preserving Simplecticity in the Numerical Integration of Linear Beam Optics

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

Allen, Christopher K.

2017-07-01

Presented are mathematical tools and methods for the development of numerical integration techniques that preserve the symplectic condition inherent to mechanics. The intended audience is for beam physicists with backgrounds in numerical modeling and simulation with particular attention to beam optics applications. The paper focuses on Lie methods that are inherently symplectic regardless of the integration accuracy order. Section 2 provides the mathematically tools used in the sequel and necessary for the reader to extend the covered techniques. Section 3 places those tools in the context of charged-particle beam optics; in particular linear beam optics is presented in terms ofmore » a Lie algebraic matrix representation. Section 4 presents numerical stepping techniques with particular emphasis on a third-order leapfrog method. Section 5 discusses the modeling of field imperfections with particular attention to the fringe fields of quadrupole focusing magnets. The direct computation of a third order transfer matrix for a fringe field is shown.« less

Localization in quantum field theory

NASA Astrophysics Data System (ADS)

Balachandran, A. P.

In non-relativistic quantum mechanics, Born’s principle of localization is as follows: For a single particle, if a wave function ψK vanishes outside a spatial region K, it is said to be localized in K. In particular, if a spatial region K‧ is disjoint from K, a wave function ψK‧ localized in K‧ is orthogonal to ψK. Such a principle of localization does not exist compatibly with relativity and causality in quantum field theory (QFT) (Newton and Wigner) or interacting point particles (Currie, Jordan and Sudarshan). It is replaced by symplectic localization of observables as shown by Brunetti, Guido and Longo, Schroer and others. This localization gives a simple derivation of the spin-statistics theorem and the Unruh effect, and shows how to construct quantum fields for anyons and for massless particles with “continuous” spin. This review outlines the basic principles underlying symplectic localization and shows or mentions its deep implications. In particular, it has the potential to affect relativistic quantum information theory and black hole physics.

Dynamics of Three Vortices on a Sphere

NASA Astrophysics Data System (ADS)

Borisov, Alexey V.; Mamaev, Ivan S.; Kilin, Alexander A.

2018-01-01

This paper is concerned with the dynamics of vortices on a sphere. It is shown that, as a result of reduction, the problem reduces to investigating a system with a nonlinear Poisson bracket. The topology of a symplectic leaf in the case of three vortices is studied.

Semiclassical geometry of integrable systems

NASA Astrophysics Data System (ADS)

Reshetikhin, Nicolai

2018-04-01

The main result of this paper is a formula for the scalar product of semiclassical eigenvectors of two integrable systems on the same symplectic manifold. An important application of this formula is the Ponzano–Regge type of asymptotic of Racah–Wigner coefficients. Dedicated to the memory of P P Kulish.

An introduction to Lie group integrators – basics, new developments and applications

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

Celledoni, Elena, E-mail: elenac@math.ntnu.no; Marthinsen, Håkon, E-mail: hakonm@math.ntnu.no; Owren, Brynjulf, E-mail: bryn@math.ntnu.no

2014-01-15

We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion of discrete gradient methods is generalised to Lie groups.

Filtrations on Springer fiber cohomology and Kostka polynomials

NASA Astrophysics Data System (ADS)

Bellamy, Gwyn; Schedler, Travis

2018-03-01

We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This allows us to construct a canonical family of filtrations on the flag variety cohomology, and hence on irreducible representations of the Weyl group, whose Hilbert series are given by the generalized Kostka polynomials. We deduce consequences for the cohomology of all Springer fibers. In particular, this computes the grading on the zeroth Poisson homology of all classical finite W-algebras, as well as the filtration on the zeroth Hochschild homology of all quantum finite W-algebras, and we generalize to all homology degrees. As a consequence, we deduce a conjecture of Proudfoot on symplectic duality, relating in type A the Poisson homology of Slodowy slices to the intersection cohomology of nilpotent orbit closures. In the last section, we give an analogue of our main theorem in the setting of mirabolic D-modules.

Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations

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

Adesso, Gerardo; CNR-INFM Coherentia, Naples; CNISM, Unita di Salerno, Salerno

2007-10-15

We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1xM bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself andmore » the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a, uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes.« less

“SLIMPLECTIC” INTEGRATORS: VARIATIONAL INTEGRATORS FOR GENERAL NONCONSERVATIVE SYSTEMS

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

Tsang, David; Turner, Alec; Galley, Chad R.

2015-08-10

Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative interactions. In this Letter, we develop the “slimplectic” integrator, a new type of numerical integrator that shares many of the benefits of traditional symplectic integrators yet is applicable to general nonconservative systems. We utilize a fixed-time-step variational integrator formalism applied to the principle of stationary nonconservative action developed in Galley et al. As a result, the generalized momenta and energy (Noether current) evolutions are well-tracked. Wemore » discuss several example systems, including damped harmonic oscillators, Poynting–Robertson drag, and gravitational radiation reaction, by utilizing our new publicly available code to demonstrate the slimplectic integrator algorithm. Slimplectic integrators are well-suited for integrations of systems where nonconservative effects play an important role in the long-term dynamical evolution. As such they are particularly appropriate for cosmological or celestial N-body dynamics problems where nonconservative interactions, e.g., gas interactions or dissipative tides, can play an important role.« less

Local phase space and edge modes for diffeomorphism-invariant theories

NASA Astrophysics Data System (ADS)

Speranza, Antony J.

2018-02-01

We discuss an approach to characterizing local degrees of freedom of a subregion in diffeomorphism-invariant theories using the extended phase space of Donnelly and Freidel [36]. Such a characterization is important for defining local observables and entanglement entropy in gravitational theories. Traditional phase space constructions for subregions are not invariant with respect to diffeomorphisms that act at the boundary. The extended phase space remedies this problem by introducing edge mode fields at the boundary whose transformations under diffeomorphisms render the extended symplectic structure fully gauge invariant. In this work, we present a general construction for the edge mode symplectic structure. We show that the new fields satisfy a surface symmetry algebra generated by the Noether charges associated with the edge mode fields. For surface-preserving symmetries, the algebra is universal for all diffeomorphism-invariant theories, comprised of diffeomorphisms of the boundary, SL(2, ℝ) transformations of the normal plane, and, in some cases, normal shearing transformations. We also show that if boundary conditions are chosen such that surface translations are symmetries, the algebra acquires a central extension.

Sachs' free data in real connection variables

NASA Astrophysics Data System (ADS)

De Paoli, Elena; Speziale, Simone

2017-11-01

We discuss the Hamiltonian dynamics of general relativity with real connection variables on a null foliation, and use the Newman-Penrose formalism to shed light on the geometric meaning of the various constraints. We identify the equivalent of Sachs' constraint-free initial data as projections of connection components related to null rotations, i.e. the translational part of the ISO(2) group stabilising the internal null direction soldered to the hypersurface. A pair of second-class constraints reduces these connection components to the shear of a null geodesic congruence, thus establishing equivalence with the second-order formalism, which we show in details at the level of symplectic potentials. A special feature of the first-order formulation is that Sachs' propagating equations for the shear, away from the initial hypersurface, are turned into tertiary constraints; their role is to preserve the relation between connection and shear under retarded time evolution. The conversion of wave-like propagating equations into constraints is possible thanks to an algebraic Bianchi identity; the same one that allows one to describe the radiative data at future null infinity in terms of a shear of a (non-geodesic) asymptotic null vector field in the physical spacetime. Finally, we compute the modification to the spin coefficients and the null congruence in the presence of torsion.

EFT for vortices with dilaton-dependent localized flux

NASA Astrophysics Data System (ADS)

Burgess, C. P.; Diener, Ross; Williams, M.

2015-11-01

We study how codimension-two objects like vortices back-react gravitationally with their environment in theories (such as 4D or higher-dimensional supergravity) where the bulk is described by a dilaton-Maxwell-Einstein system. We do so both in the full theory, for which the vortex is an explicit classical `fat brane' solution, and in the effective theory of `point branes' appropriate when the vortices are much smaller than the scales of interest for their back-reaction (such as the transverse Kaluza-Klein scale). We extend the standard Nambu-Goto description to include the physics of flux-localization wherein the ambient flux of the external Maxwell field becomes partially localized to the vortex, generalizing the results of a companion paper [4] from N=2 supergravity as the end-point of a hierarchical limit in which the Planck mass first and then the supersymmetry breaking scale are sent to infinity. We define, in the parent supergravity model, a new symplectic frame in which, in the rigid limit, manifest symplectic invariance is preserved and the electric and magnetic Fayet-Iliopoulos terms are fully originated from the dyonic components of the embedding tensor. The supergravity origin of several features of the resulting rigid supersymmetric theory are then elucidated, such as the presence of a traceless SU(2)- Lie algebra term in the Ward identity and the existence of a central charge in the supersymmetry algebra which manifests itself as a harmless gauge transformation on the gauge vectors of the rigid theory; we show that this effect can be interpreted as a kind of "superspace non-locality" which does not affect the rigid theory on space-time. To set the stage of our analysis we take the opportunity in this paper to provide and prove the relevant identities of the most general dyonic gauging of Special-Kaehler and Quaternionic-Kaehler isometries in a generic N=2 model, which include the supersymmetry Ward identity, in a fully symplectic-covariant formalism.

How ocean lateral mixing changes Southern Ocean variability in coupled climate models

NASA Astrophysics Data System (ADS)

Pradal, M. A. S.; Gnanadesikan, A.; Thomas, J. L.

2016-02-01

The lateral mixing of tracers represents a major uncertainty in the formulation of coupled climate models. The mixing of tracers along density surfaces in the interior and horizontally within the mixed layer is often parameterized using a mixing coefficient ARedi. The models used in the Coupled Model Intercomparison Project 5 exhibit more than an order of magnitude range in the values of this coefficient used within the Southern Ocean. The impacts of such uncertainty on Southern Ocean variability have remained unclear, even as recent work has shown that this variability differs between different models. In this poster, we change the lateral mixing coefficient within GFDL ESM2Mc, a coarse-resolution Earth System model that nonetheless has a reasonable circulation within the Southern Ocean. As the coefficient varies from 400 to 2400 m2/s the amplitude of the variability varies significantly. The low-mixing case shows strong decadal variability with an annual mean RMS temperature variability exceeding 1C in the Circumpolar Current. The highest-mixing case shows a very similar spatial pattern of variability, but with amplitudes only about 60% as large. The suppression of mixing is larger in the Atlantic Sector of the Southern Ocean relatively to the Pacific sector. We examine the salinity budgets of convective regions, paying particular attention to the extent to which high mixing prevents the buildup of low-saline waters that are capable of shutting off deep convection entirely.

Clustering of Variables for Mixed Data

NASA Astrophysics Data System (ADS)

Saracco, J.; Chavent, M.

2016-05-01

This chapter presents clustering of variables which aim is to lump together strongly related variables. The proposed approach works on a mixed data set, i.e. on a data set which contains numerical variables and categorical variables. Two algorithms of clustering of variables are described: a hierarchical clustering and a k-means type clustering. A brief description of PCAmix method (that is a principal component analysis for mixed data) is provided, since the calculus of the synthetic variables summarizing the obtained clusters of variables is based on this multivariate method. Finally, the R packages ClustOfVar and PCAmixdata are illustrated on real mixed data. The PCAmix and ClustOfVar approaches are first used for dimension reduction (step 1) before applying in step 2 a standard clustering method to obtain groups of individuals.

Exact statistical results for binary mixing and reaction in variable density turbulence

NASA Astrophysics Data System (ADS)

Ristorcelli, J. R.

2017-02-01

We report a number of rigorous statistical results on binary active scalar mixing in variable density turbulence. The study is motivated by mixing between pure fluids with very different densities and whose density intensity is of order unity. Our primary focus is the derivation of exact mathematical results for mixing in variable density turbulence and we do point out the potential fields of application of the results. A binary one step reaction is invoked to derive a metric to asses the state of mixing. The mean reaction rate in variable density turbulent mixing can be expressed, in closed form, using the first order Favre mean variables and the Reynolds averaged density variance, ⟨ρ2⟩ . We show that the normalized density variance, ⟨ρ2⟩ , reflects the reduction of the reaction due to mixing and is a mix metric. The result is mathematically rigorous. The result is the variable density analog, the normalized mass fraction variance ⟨c2⟩ used in constant density turbulent mixing. As a consequence, we demonstrate that use of the analogous normalized Favre variance of the mass fraction, c″ ⁣2˜ , as a mix metric is not theoretically justified in variable density turbulence. We additionally derive expressions relating various second order moments of the mass fraction, specific volume, and density fields. The central role of the density specific volume covariance ⟨ρ v ⟩ is highlighted; it is a key quantity with considerable dynamical significance linking various second order statistics. For laboratory experiments, we have developed exact relations between the Reynolds scalar variance ⟨c2⟩ its Favre analog c″ ⁣2˜ , and various second moments including ⟨ρ v ⟩ . For moment closure models that evolve ⟨ρ v ⟩ and not ⟨ρ2⟩ , we provide a novel expression for ⟨ρ2⟩ in terms of a rational function of ⟨ρ v ⟩ that avoids recourse to Taylor series methods (which do not converge for large density differences). We have derived analytic results relating several other second and third order moments and see coupling between odd and even order moments demonstrating a natural and inherent skewness in the mixing in variable density turbulence. The analytic results have applications in the areas of isothermal material mixing, isobaric thermal mixing, and simple chemical reaction (in progress variable formulation).

Relativistic collisions as Yang-Baxter maps

NASA Astrophysics Data System (ADS)

Kouloukas, Theodoros E.

2017-10-01

We prove that one-dimensional elastic relativistic collisions satisfy the set-theoretical Yang-Baxter equation. The corresponding collision maps are symplectic and admit a Lax representation. Furthermore, they can be considered as reductions of a higher dimensional integrable Yang-Baxter map on an invariant manifold. In this framework, we study the integrability of transfer maps that represent particular periodic sequences of collisions.

Hamiltonian methods: BRST, BFV

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

Garcia, J. Antonio

2006-09-25

The range of applicability of Hamiltonian methods to gauge theories is very diverse and cover areas of research from phenomenology to mathematical physics. We review some of the areas developed in Mexico in the last decades. They cover the study of symplectic methods, BRST-BFV and BV approaches, Klauder projector program, and non perturbative technics used in the study of bound states in relativistic field theories.

Hamiltonian methods: BRST, BFV

NASA Astrophysics Data System (ADS)

García, J. Antonio

2006-09-01

The range of applicability of Hamiltonian methods to gauge theories is very diverse and cover areas of research from phenomenology to mathematical physics. We review some of the areas developed in México in the last decades. They cover the study of symplectic methods, BRST-BFV and BV approaches, Klauder projector program, and non perturbative technics used in the study of bound states in relativistic field theories.

Integral representations on supermanifolds: super Hodge duals, PCOs and Liouville forms

NASA Astrophysics Data System (ADS)

Castellani, Leonardo; Catenacci, Roberto; Grassi, Pietro Antonio

2017-01-01

We present a few types of integral transforms and integral representations that are very useful for extending to supergeometry many familiar concepts of differential geometry. Among them we discuss the construction of the super Hodge dual, the integral representation of picture changing operators of string theories and the construction of the super-Liouville form of a symplectic supermanifold.

Solar System Dynamics

NASA Technical Reports Server (NTRS)

Wisdom, Jack

2002-01-01

In these 18 years, the research has touched every major dynamical problem in the solar system, including: the effect of chaotic zones on the distribution of asteroids, the delivery of meteorites along chaotic pathways, the chaotic motion of Pluto, the chaotic motion of the outer planets and that of the whole solar system, the delivery of short period comets from the Kuiper belt, the tidal evolution of the Uranian arid Galilean satellites, the chaotic tumbling of Hyperion and other irregular satellites, the large chaotic variations of the obliquity of Mars, the evolution of the Earth-Moon system, and the resonant core- mantle dynamics of Earth and Venus. It has introduced new analytical and numerical tools that are in widespread use. Today, nearly every long-term integration of our solar system, its subsystems, and other solar systems uses algorithms that was invented. This research has all been primarily Supported by this sequence of PGG NASA grants. During this period published major investigations of tidal evolution of the Earth-Moon system and of the passage of the Earth and Venus through non-linear core-mantle resonances were completed. It has published a major innovation in symplectic algorithms: the symplectic corrector. A paper was completed on non-perturbative hydrostatic equilibrium.

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

Toroidal regularization of the guiding center Lagrangian

DOE PAGES

Burby, J. W.; Ellison, C. L.

2017-11-22

In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less

Toroidal regularization of the guiding center Lagrangian

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

Burby, J. W.; Ellison, C. L.

In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less

Experimenting with galaxies

NASA Technical Reports Server (NTRS)

Miller, Richard H.

1992-01-01

A study to demonstrate how the dynamics of galaxies may be investigated through the creation of galaxies within a computer model is presented. The numerical technique for simulating galaxies is shown to be both highly efficient and highly robust. Consideration is given to the anatomy of a galaxy, the gravitational N-body problem, numerical approaches to the N-body problem, use of the Poisson equation, and the symplectic integrator.

Application of the Yoshida-Ruth Techniques to Implicit Integration and Multi-Map Explicit Integration

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

Forest, E.; Bengtsson, J.; Reusch, M.F.

1991-04-01

The full power of Yoshida's technique is exploited to produce an arbitrary order implicit symplectic integrator and multi-map explicit integrator. This implicit integrator uses a characteristic function involving the force term alone. Also we point out the usefulness of the plain Ruth algorithm in computing Taylor series map using the techniques first introduced by Berz in his 'COSY-INFINITY' code.

Development of Multistep and Degenerate Variational Integrators for Applications in Plasma Physics

NASA Astrophysics Data System (ADS)

Ellison, Charles Leland

Geometric integrators yield high-fidelity numerical results by retaining conservation laws in the time advance. A particularly powerful class of geometric integrators is symplectic integrators, which are widely used in orbital mechanics and accelerator physics. An important application presently lacking symplectic integrators is the guiding center motion of magnetized particles represented by non-canonical coordinates. Because guiding center trajectories are foundational to many simulations of magnetically confined plasmas, geometric guiding center algorithms have high potential for impact. The motivation is compounded by the need to simulate long-pulse fusion devices, including ITER, and opportunities in high performance computing, including the use of petascale resources and beyond. This dissertation uses a systematic procedure for constructing geometric integrators --- known as variational integration --- to deliver new algorithms for guiding center trajectories and other plasma-relevant dynamical systems. These variational integrators are non-trivial because the Lagrangians of interest are degenerate - the Euler-Lagrange equations are first-order differential equations and the Legendre transform is not invertible. The first contribution of this dissertation is that variational integrators for degenerate Lagrangian systems are typically multistep methods. Multistep methods admit parasitic mode instabilities that can ruin the numerical results. These instabilities motivate the second major contribution: degenerate variational integrators. By replicating the degeneracy of the continuous system, degenerate variational integrators avoid parasitic mode instabilities. The new methods are therefore robust geometric integrators for degenerate Lagrangian systems. These developments in variational integration theory culminate in one-step degenerate variational integrators for non-canonical magnetic field line flow and guiding center dynamics. The guiding center integrator assumes coordinates such that one component of the magnetic field is zero; it is shown how to construct such coordinates for nested magnetic surface configurations. Additionally, collisional drag effects are incorporated in the variational guiding center algorithm for the first time, allowing simulation of energetic particle thermalization. Advantages relative to existing canonical-symplectic and non-geometric algorithms are numerically demonstrated. All algorithms have been implemented as part of a modern, parallel, ODE-solving library, suitable for use in high-performance simulations.

Symmetry breaking by bifundamentals

NASA Astrophysics Data System (ADS)

Schellekens, A. N.

2018-03-01

We derive all possible symmetry breaking patterns for all possible Higgs fields that can occur in intersecting brane models: bifundamentals and rank-2 tensors. This is a field-theoretic problem that was already partially solved in 1973 by Ling-Fong Li [1]. In that paper the solution was given for rank-2 tensors of orthogonal and unitary group, and U (N )×U (M ) and O (N )×O (M ) bifundamentals. We extend this first of all to symplectic groups. When formulated correctly, this turns out to be straightforward generalization of the previous results from real and complex numbers to quaternions. The extension to mixed bifundamentals is more challenging and interesting. The scalar potential has up to six real parameters. Its minima or saddle points are described by block-diagonal matrices built out of K blocks of size p ×q . Here p =q =1 for the solutions of Ling-Fong Li, and the number of possibilities for p ×q is equal to the number of real parameters in the potential, minus 1. The maximum block size is p ×q =2 ×4 . Different blocks cannot be combined, and the true minimum occurs for one choice of basic block, and for either K =1 or K maximal, depending on the parameter values.

The impact of sedimentary anisotropy on solute mixing in stacked scour-pool structures

NASA Astrophysics Data System (ADS)

Bennett, Jeremy P.; Haslauer, Claus P.; Cirpka, Olaf A.

2017-04-01

The spatial variability of hydraulic conductivity is known to have a strong impact on solute spreading and mixing. In most investigations, its local anisotropy has been neglected. Recent studies have shown that spatially varying orientation in sedimentary anisotropy can lead to twisting flow enhancing transverse mixing, but most of these studies used geologically implausible geometries. We use an object-based approach to generate stacked scour-pool structures with either isotropic or anisotropic filling which are typically reported in glacial outwash deposits. We analyze how spatially variable isotropic conductivity and variation of internal anisotropy in these features impacts transverse plume deformation and both longitudinal and transverse spreading and mixing. In five test cases, either the scalar values of conductivity or the spatial orientation of its anisotropy is varied between the scour-pool structures. Based on 100 random configurations, we compare the variability of velocity components, stretching and folding metrics, advective travel-time distributions, one and two-particle statistics in advective-dispersive transport, and the flux-related dilution indices for steady state advective-dispersive transport among the five test cases. Variation in the orientation of internal anisotropy causes strong variability in the lateral velocity components, which leads to deformation in transverse directions and enhances transverse mixing, whereas it hardly affects the variability of the longitudinal velocity component and thus longitudinal spreading and mixing. The latter is controlled by the spatial variability in the scalar values of hydraulic conductivity. Our results demonstrate that sedimentary anisotropy is important for transverse mixing, whereas it may be neglected when considering longitudinal spreading and mixing.

Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

NASA Astrophysics Data System (ADS)

Martínez-Torres, David; Miranda, Eva

2018-01-01

We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.

Antisymplectic gauge theories

NASA Astrophysics Data System (ADS)

Batalin, Igor; Marnelius, Robert

1998-02-01

A general field-antifield BV formalism for antisymplectic first class constraints is proposed. It is as general as the corresponding symplectic BFV-BRST formulation and it is demonstrated to be consistent with a previously proposed formalism for antisymplectic second class constraints through a generalized conversion to corresponding first class constraints. Thereby the basic concept of gauge symmetry is extended to apply to quite a new class of gauge theories potentially possible to exist.

Modelling rainfall amounts using mixed-gamma model for Kuantan district

NASA Astrophysics Data System (ADS)

Zakaria, Roslinazairimah; Moslim, Nor Hafizah

2017-05-01

An efficient design of flood mitigation and construction of crop growth models depend upon good understanding of the rainfall process and characteristics. Gamma distribution is usually used to model nonzero rainfall amounts. In this study, the mixed-gamma model is applied to accommodate both zero and nonzero rainfall amounts. The mixed-gamma model presented is for the independent case. The formulae of mean and variance are derived for the sum of two and three independent mixed-gamma variables, respectively. Firstly, the gamma distribution is used to model the nonzero rainfall amounts and the parameters of the distribution (shape and scale) are estimated using the maximum likelihood estimation method. Then, the mixed-gamma model is defined for both zero and nonzero rainfall amounts simultaneously. The formulae of mean and variance for the sum of two and three independent mixed-gamma variables derived are tested using the monthly rainfall amounts from rainfall stations within Kuantan district in Pahang Malaysia. Based on the Kolmogorov-Smirnov goodness of fit test, the results demonstrate that the descriptive statistics of the observed sum of rainfall amounts is not significantly different at 5% significance level from the generated sum of independent mixed-gamma variables. The methodology and formulae demonstrated can be applied to find the sum of more than three independent mixed-gamma variables.

A Bayesian Semiparametric Latent Variable Model for Mixed Responses

ERIC Educational Resources Information Center

Fahrmeir, Ludwig; Raach, Alexander

2007-01-01

In this paper we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric Gaussian regression model. We extend existing LVMs with the usual linear covariate effects by including nonparametric components for nonlinear…

New vertices and canonical quantization

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

Alexandrov, Sergei

2010-07-15

We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the Engle-Pereira-Rovelli-Livine model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this model even closer to loop quantum gravity. Second, we however argue that the quantization procedure used to derive the new models is inconsistent since it relies on the symplectic structure of the unconstrained BF theory.

AKSZ construction from reduction data

NASA Astrophysics Data System (ADS)

Bonechi, Francesco; Cabrera, Alejandro; Zabzine, Maxim

2012-07-01

We discuss a general procedure to encode the reduction of the target space geometry into AKSZ sigma models. This is done by considering the AKSZ construction with target the BFV model for constrained graded symplectic manifolds. We investigate the relation between this sigma model and the one with the reduced structure. We also discuss several examples in dimension two and three when the symmetries come from Lie group actions and systematically recover models already proposed in the literature.

Nonlinear Symplectic Attitude Estimation for Small Satellites

DTIC Science & Technology

2006-08-01

Vol. 45, No. 3, 2000, pp. 477-482. 7 Gelb, A., editor, Applied Optimal Estimation, The M.I.T. Press, Cambridge, MA, 1974. ’ Brown , R. G. and Hwang , P. Y...demonstrate orders of magnitude improvement in state and constants of motion estimation when compared to extended and iterative Kalman methods...satellites have fallen into the former category, including the ubiquitous Extended Kalman Filter (EKF).2 𔄁- 9 While this approach has been used

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.

Analysis and testing of high entrainment single nozzle jet pumps with variable mixing tubes

NASA Technical Reports Server (NTRS)

Hickman, K. E.; Hill, P. G.; Gilbert, G. B.

1972-01-01

An analytical model was developed to predict the performance characteristics of axisymmetric single-nozzle jet pumps with variable area mixing tubes. The primary flow may be subsonic or supersonic. The computer program uses integral techniques to calculate the velocity profiles and the wall static pressures that result from the mixing of the supersonic primary jet and the subsonic secondary flow. An experimental program was conducted to measure mixing tube wall static pressure variations, velocity profiles, and temperature profiles in a variable area mixing tube with a supersonic primary jet. Static pressure variations were measured at four different secondary flow rates. These test results were used to evaluate the analytical model. The analytical results compared well to the experimental data. Therefore, the analysis is believed to be ready for use to relate jet pump performance characteristics to mixing tube design.

Structural reanalysis via a mixed method. [using Taylor series for accuracy improvement

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lowder, H. E.

1975-01-01

A study is made of the approximate structural reanalysis technique based on the use of Taylor series expansion of response variables in terms of design variables in conjunction with the mixed method. In addition, comparisons are made with two reanalysis techniques based on the displacement method. These techniques are the Taylor series expansion and the modified reduced basis. It is shown that the use of the reciprocals of the sizing variables as design variables (which is the natural choice in the mixed method) can result in a substantial improvement in the accuracy of the reanalysis technique. Numerical results are presented for a space truss structure.

A variable mixing-length ratio for convection theory

NASA Technical Reports Server (NTRS)

Chan, K. L.; Wolff, C. L.; Sofia, S.

1981-01-01

It is argued that a natural choice for the local mixing length in the mixing-length theory of convection has a value proportional to the local density scale height of the convective bubbles. The resultant variable mixing-length ratio (the ratio between the mixing length and the pressure scale height) of this theory is enhanced in the superadiabatic region and approaches a constant in deeper layers. Numerical tests comparing the new mixing length successfully eliminate most of the density inversion that typically plagues conventional results. The new approach also seems to indicate the existence of granular motion at the top of the convection zone.

[Mix 10] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2011-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 4] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2011-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 5] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2011-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 13] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2007-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 3] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2010-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 14] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2007-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 7] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2004-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 16] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2004-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 6] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2007-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 12] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2004-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 1] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2010-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 2] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2010-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 8] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2007-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 11] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2007-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 15] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2004-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

[Mix 9] HMACP mixture design : combined gradation.

DOT National Transportation Integrated Search

2007-01-01

Getting Started: Begin with the Combined Gradations or Summary sheet. Here you will select dependent variables such as specification year, mix type, asphalt content, combined aggregate, and others. These variable will affect the calculation of other ...

An Analysis of Freight Forwarder Operations in an International Distribution Channel.

DTIC Science & Technology

1987-01-01

44 3. International Marketing Mix ....................... 45 4. Security Assistance Distribution Channel .......... 69 5...an item is ultimately derived from the interaction of variables in the marketing mix . Of those variables, the distribution functions seem to allow the...Component of the Marketing Mix ,"Proceedings, NCPDM Fall Meeting, National council of Physical Distribution Management, San Francisco, CA., 1982. 7

GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

Thermodynamically admissible evolution equations for non-equilibrium systems are known to possess a distinct mathematical structure. Within the GENERIC (general equation for the non-equilibrium reversible-irreversible coupling) framework of non-equilibrium thermodynamics, which is based on continuous time evolution, we investigate the possibility of preserving all the structural elements in time-discretized equations. Our approach, which follows Moser's [1] construction of symplectic integrators for Hamiltonian systems, is illustrated for the damped harmonic oscillator. Alternative approaches are sketched.

Classification of quantum groups and Belavin–Drinfeld cohomologies for orthogonal and symplectic Lie algebras

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

Kadets, Boris; Karolinsky, Eugene; Pop, Iulia

2016-05-15

In this paper we continue to study Belavin–Drinfeld cohomology introduced in Kadets et al., Commun. Math. Phys. 344(1), 1-24 (2016) and related to the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra #Mathematical Fraktur Small G#. Here we compute Belavin–Drinfeld cohomology for all non-skewsymmetric r-matrices on the Belavin–Drinfeld list for simple Lie algebras of type B, C, and D.

Sixth-Order Lie Group Integrators

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

Forest, E.

1990-03-01

In this paper we present the coefficients of several 6th order symplectic integrator of the type developed by R. Ruth. To get these results we fully exploit the connection with Lie groups. This integrator, as well as all the explicit integrators of Ruth, may be used in any equation where some sort of Lie bracket is preserved. In fact, if the Lie operator governing the equation of motion is separable into two solvable parts, the Ruth integrators can be used.

Higher-order hybrid implicit/explicit FDTD time-stepping

NASA Astrophysics Data System (ADS)

Tierens, W.

2016-12-01

Both partially implicit FDTD methods, and symplectic FDTD methods of high temporal accuracy (3rd or 4th order), are well documented in the literature. In this paper we combine them: we construct a conservative FDTD method which is fourth order accurate in time and is partially implicit. We show that the stability condition for this method depends exclusively on the explicit part, which makes it suitable for use in e.g. modelling wave propagation in plasmas.

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

On extremals of the entropy production by ‘Langevin-Kramers’ dynamics

NASA Astrophysics Data System (ADS)

Muratore-Ginanneschi, Paolo

2014-05-01

We refer as ‘Langevin-Kramers’ dynamics to a class of stochastic differential systems exhibiting a degenerate ‘metriplectic’ structure. This means that the drift field can be decomposed into a symplectic and a gradient-like component with respect to a pseudo-metric tensor associated with random fluctuations affecting increments of only a sub-set of the degrees of freedom. Systems in this class are often encountered in applications as elementary models of Hamiltonian dynamics in a heat bath eventually relaxing to a Boltzmann steady state. Entropy production control in Langevin-Kramers models differs from the now well-understood case of Langevin-Smoluchowski dynamics for two reasons. First, the definition of entropy production stemming from fluctuation theorems specifies a cost functional which does not act coercively on all degrees of freedom of control protocols. Second, the presence of a symplectic structure imposes a non-local constraint on the class of admissible controls. Using Pontryagin control theory and restricting the attention to additive noise, we show that smooth protocols attaining extremal values of the entropy production appear generically in continuous parametric families as a consequence of a trade-off between smoothness of the admissible protocols and non-coercivity of the cost functional. Uniqueness is, however, always recovered in the over-damped limit as extremal equations reduce at leading order to the Monge-Ampère-Kantorovich optimal mass-transport equations.

Validation of an ocean shelf model for the prediction of mixed-layer properties in the Mediterranean Sea west of Sardinia

NASA Astrophysics Data System (ADS)

Onken, Reiner

2017-04-01

The Regional Ocean Modeling System (ROMS) has been employed to explore the sensitivity of the forecast skill of mixed-layer properties to initial conditions, boundary conditions, and vertical mixing parameterisations. The initial and lateral boundary conditions were provided by the Mediterranean Forecasting System (MFS) or by the MERCATOR global ocean circulation model via one-way nesting; the initial conditions were additionally updated through the assimilation of observations. Nowcasts and forecasts from the weather forecast models COSMO-ME and COSMO-IT, partly melded with observations, served as surface boundary conditions. The vertical mixing was parameterised by the GLS (generic length scale) scheme Umlauf and Burchard (2003) in four different set-ups. All ROMS forecasts were validated against the observations which were taken during the REP14-MED survey to the west of Sardinia. Nesting ROMS in MERCATOR and updating the initial conditions through data assimilation provided the best agreement of the predicted mixed-layer properties with the time series from a moored thermistor chain. Further improvement was obtained by the usage of COSMO-ME atmospheric forcing, which was melded with real observations, and by the application of the k-ω vertical mixing scheme with increased vertical eddy diffusivity. The predicted temporal variability of the mixed-layer temperature was reasonably well correlated with the observed variability, while the modelled variability of the mixed-layer depth exhibited only agreement with the observations near the diurnal frequency peak. For the forecasted horizontal variability, reasonable agreement was found with observations from a ScanFish section, but only for the mesoscale wave number band; the observed sub-mesoscale variability was not reproduced by ROMS.

Seasonal Mixed Layer Heat Budget in the Southeast Tropical Atlantic

NASA Astrophysics Data System (ADS)

Scannell, H. A.; McPhaden, M. J.

2016-12-01

We analyze a mixed layer heat budget at 6ºS, 8ºE from a moored buoy of the Prediction and Research Moored Array in the Atlantic (PIRATA) to better understand the causes of seasonal mixed layer temperature variability in the southeast tropical Atlantic. This region is of interest because it is susceptible to warm biases in coupled global climate models and has historically been poorly sampled. Previous work suggests that thermodynamic changes in both latent heat loss and absorbed solar radiation dominate mixed layer properties away from the equator in the tropical Atlantic, while advection and entrainment are more important near the equator. Changes in mixed layer salinity can also influence temperature through the formation of barrier layers and density gradients. Freshwater flux from the Congo River, migration of the Intertropical Convergence Zone and advection of water masses are considered important contributors to mixed layer salinity variability in our study region. We analyze ocean temperature, salinity and meteorological data beginning in 2013 using mooring, Argo, and satellite platforms to study how seasonal temperature variability in the mixed layer is influenced by air-sea interactions and ocean dynamics.

Customer Service Analysis of Air Combat Command Vehicle Maintenance Support

DTIC Science & Technology

1993-09-01

the survey, the researchers categorized the services or variables into marketing mix components: product, price, promotion, and customer service...comparing and analyzing the variables identified in the previous three phases to determine a strategic marketing mix (46:9). After analyzing the data...service/physical distribution. Additionally, they found that customer service/physical distribution was an integral component of the marketing mix , and

Suppression of chaos at slow variables by rapidly mixing fast dynamics

NASA Astrophysics Data System (ADS)

Abramov, R.

2012-04-01

One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger mixing system would result in general increase of chaos at the slow variables.

Results of Propellant Mixing Variable Study Using Precise Pressure-Based Burn Rate Calculations

NASA Technical Reports Server (NTRS)

Stefanski, Philip L.

2014-01-01

A designed experiment was conducted in which three mix processing variables (pre-curative addition mix temperature, pre-curative addition mixing time, and mixer speed) were varied to estimate their effects on within-mix propellant burn rate variability. The chosen discriminator for the experiment was the 2-inch diameter by 4-inch long (2x4) Center-Perforated (CP) ballistic evaluation motor. Motor nozzle throat diameters were sized to produce a common targeted chamber pressure. Initial data analysis did not show a statistically significant effect. Because propellant burn rate must be directly related to chamber pressure, a method was developed that showed statistically significant effects on chamber pressure (either maximum or average) by adjustments to the process settings. Burn rates were calculated from chamber pressures and these were then normalized to a common pressure for comparative purposes. The pressure-based method of burn rate determination showed significant reduction in error when compared to results obtained from the Brooks' modification of the propellant web-bisector burn rate determination method. Analysis of effects using burn rates calculated by the pressure-based method showed a significant correlation of within-mix burn rate dispersion to mixing duration and the quadratic of mixing duration. The findings were confirmed in a series of mixes that examined the effects of mixing time on burn rate variation, which yielded the same results.

[Marketing mix in health service].

PubMed

Ameri, Cinzia; Fiorini, Fulvio

2015-01-01

The marketing mix is the combination of the marketing variables that a firm employs with the purpose to achieve the expected volume of business within its market. In the sale of goods, four variables compose the marketing mix (4 Ps): Product, Price, Point of sale and Promotion. In the case of providing services, three further elements play a role: Personnel, Physical Evidence and Processes (7 Ps). The marketing mix must be addressed to the consumers as well as to the employees of the providing firm. Furthermore, it must be interpreted as employees ability to satisfy customers (interactive marketing).

Synergies from using higher order symplectic decompositions both for ordinary differential equations and quantum Monte Carlo methods

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

Matuttis, Hans-Georg; Wang, Xiaoxing

Decomposition methods of the Suzuki-Trotter type of various orders have been derived in different fields. Applying them both to classical ordinary differential equations (ODEs) and quantum systems allows to judge their effectiveness and gives new insights for many body quantum mechanics where reference data are scarce. Further, based on data for 6 × 6 system we conclude that sampling with sign (minus-sign problem) is probably detrimental to the accuracy of fermionic simulations with determinant algorithms.

Primitive ideals of C q [ SL(3)

NASA Astrophysics Data System (ADS)

Hodges, Timothy J.; Levasseur, Thierry

1993-10-01

The primitive ideals of the Hopf algebra C q [ SL(3)] are classified. In particular it is shown that the orbits in Prim C q [ SL(3)] under the action of the representation group H ≅ C *× C * are parameterized naturally by W×W, where W is the associated Weyl group. It is shown that there is a natural one-to-one correspondence between primitive ideals of C q [ SL(3)] and symplectic leaves of the associated Poisson algebraic group SL(3, C).

Microcracks, micropores, and their petrologic interpretation for 72415 and 15418

NASA Technical Reports Server (NTRS)

Richter, D.; Simmons, G.; Siegfried, R.

1976-01-01

Lunar samples 72415 and 15418 have complex microstructures that indicate a series of fracturing and healing events. Both samples contain relatively few open microcracks but many sealed and healed microcracks. Dunite 72415 contains abundant healed cracks that formed tectonically, symplectic intergrowths spatially and probably genetically related to microcracks, and a cataclastic matrix that has been extensively sintered. Metamorphosed breccia 15418 contains many post-metamorphic healed cracks, large shock induced cracks that have been sealed with glass, and a few younger, thin, open shock induced cracks.

Instanton approach to large N Harish-Chandra-Itzykson-Zuber integrals.

PubMed

Bun, J; Bouchaud, J P; Majumdar, S N; Potters, M

2014-08-15

We reconsider the large N asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. Our method is easily generalized to the orthogonal and symplectic ensembles. We obtain an explicit solution of Matytsin's equations in the case of Wigner matrices, as well as a general expansion method in the dilute limit, when the spectrum of eigenvalues spreads over very wide regions.

On accommodating spatial interactions in a Generalized Heterogeneous Data Model (GHDM) of mixed types of dependent variables.

DOT National Transportation Integrated Search

2015-12-01

We develop an econometric framework for incorporating spatial dependence in integrated model systems of latent variables and multidimensional mixed data outcomes. The framework combines Bhats Generalized Heterogeneous Data Model (GHDM) with a spat...

Variability in case-mix adjusted in-hospital cardiac arrest rates.

PubMed

Merchant, Raina M; Yang, Lin; Becker, Lance B; Berg, Robert A; Nadkarni, Vinay; Nichol, Graham; Carr, Brendan G; Mitra, Nandita; Bradley, Steven M; Abella, Benjamin S; Groeneveld, Peter W

2012-02-01

It is unknown how in-hospital cardiac arrest (IHCA) rates vary across hospitals and predictors of variability. Measure variability in IHCA across hospitals and determine if hospital-level factors predict differences in case-mix adjusted event rates. Get with the Guidelines Resuscitation (GWTG-R) (n=433 hospitals) was used to identify IHCA events between 2003 and 2007. The American Hospital Association survey, Medicare, and US Census were used to obtain detailed information about GWTG-R hospitals. Adult patients with IHCA. Case-mix-adjusted predicted IHCA rates were calculated for each hospital and variability across hospitals was compared. A regression model was used to predict case-mix adjusted event rates using hospital measures of volume, nurse-to-bed ratio, percent intensive care unit beds, palliative care services, urban designation, volume of black patients, income, trauma designation, academic designation, cardiac surgery capability, and a patient risk score. We evaluated 103,117 adult IHCAs at 433 US hospitals. The case-mix adjusted IHCA event rate was highly variable across hospitals, median 1/1000 bed days (interquartile range: 0.7 to 1.3 events/1000 bed days). In a multivariable regression model, case-mix adjusted IHCA event rates were highest in urban hospitals [rate ratio (RR), 1.1; 95% confidence interval (CI), 1.0-1.3; P=0.03] and hospitals with higher proportions of black patients (RR, 1.2; 95% CI, 1.0-1.3; P=0.01) and lower in larger hospitals (RR, 0.54; 95% CI, 0.45-0.66; P<0.0001). Case-mix adjusted IHCA event rates varied considerably across hospitals. Several hospital factors associated with higher IHCA event rates were consistent with factors often linked with lower hospital quality of care.

Variability in Proactive and Reactive Cognitive Control Processes Across the Adult Lifespan

PubMed Central

Karayanidis, Frini; Whitson, Lisa Rebecca; Heathcote, Andrew; Michie, Patricia T.

2011-01-01

Task-switching paradigms produce a highly consistent age-related increase in mixing cost [longer response time (RT) on repeat trials in mixed-task than single-task blocks] but a less consistent age effect on switch cost (longer RT on switch than repeat trials in mixed-task blocks). We use two approaches to examine the adult lifespan trajectory of control processes contributing to mixing cost and switch cost: latent variables derived from an evidence accumulation model of choice, and event-related potentials (ERP) that temporally differentiate proactive (cue-driven) and reactive (target-driven) control processes. Under highly practiced and prepared task conditions, aging was associated with increasing RT mixing cost but reducing RT switch cost. Both effects were largely due to the same cause: an age effect for mixed-repeat trials. In terms of latent variables, increasing age was associated with slower non-decision processes, slower rate of evidence accumulation about the target, and higher response criterion. Age effects on mixing costs were evident only on response criterion, the amount of evidence required to trigger a decision, whereas age effects on switch cost were present for all three latent variables. ERPs showed age-related increases in preparation for mixed-repeat trials, anticipatory attention, and post-target interference. Cue-locked ERPs that are linked to proactive control were associated with early emergence of age differences in response criterion. These results are consistent with age effects on strategic processes controlling decision caution. Consistent with an age-related decline in cognitive flexibility, younger adults flexibly adjusted response criterion from trial-to-trial on mixed-task blocks, whereas older adults maintained a high criterion for all trials. PMID:22073037

Bipolar mixed features - Results from the comparative effectiveness for bipolar disorder (Bipolar CHOICE) study.

PubMed

Tohen, Mauricio; Gold, Alexandra K; Sylvia, Louisa G; Montana, Rebecca E; McElroy, Susan L; Thase, Michael E; Rabideau, Dustin J; Nierenberg, Andrew A; Reilly-Harrington, Noreen A; Friedman, Edward S; Shelton, Richard C; Bowden, Charles L; Singh, Vivek; Deckersbach, Thilo; Ketter, Terence A; Calabrese, Joseph R; Bobo, William V; McInnis, Melvin G

2017-08-01

DSM-5 changed the criteria from DSM-IV for mixed features in mood disorder episodes to include non-overlapping symptoms of depression and hypomania/mania. It is unknown if, by changing these criteria, the same group would qualify for mixed features. We assessed how those meeting DSM-5 criteria for mixed features compare to those meeting DSM-IV criteria. We analyzed data from 482 adult bipolar patients in Bipolar CHOICE, a randomized comparative effectiveness trial. Bipolar diagnoses were confirmed through the MINI International Neuropsychiatric Interview (MINI). Presence and severity of mood symptoms were collected with the Bipolar Inventory of Symptoms Scale (BISS) and linked to DSM-5 and DSM-IV mixed features criteria. Baseline demographics and clinical variables were compared between mood episode groups using ANOVA for continuous variables and chi-square tests for categorical variables. At baseline, the frequency of DSM-IV mixed episodes diagnoses obtained with the MINI was 17% and with the BISS was 20%. Using DSM-5 criteria, 9% of participants met criteria for hypomania/mania with mixed features and 12% met criteria for a depressive episode with mixed features. Symptom severity was also associated with increased mixed features with a high rate of mixed features in patients with mania/hypomania (63.8%) relative to those with depression (8.0%). Data on mixed features were collected at baseline only and thus do not reflect potential patterns in mixed features within this sample across the study duration. The DSM-5 narrower, non-overlapping definition of mixed episodes resulted in fewer patients who met mixed criteria compared to DSM-IV. Copyright © 2017. Published by Elsevier B.V.

Tropical warm pool rainfall variability and impact on upper ocean variability throughout the Madden-Julian oscillation

NASA Astrophysics Data System (ADS)

Thompson, Elizabeth J.

Heating and rain freshening often stabilize the upper tropical ocean, bringing the ocean mixed layer depth to the sea surface. Thin mixed layer depths concentrate subsequent fluxes of heat, momentum, and freshwater in a thin layer. Rapid heating and cooling of the tropical sea surface is important for controlling or triggering atmospheric convection. Ocean mixed layer depth and SST variability due to rainfall events have not been as comprehensively explored as the ocean's response to heating or momentum fluxes, but are very important to understand in the tropical warm pool where precipitation exceeds evaporation and many climate phenomena such as ENSO and the MJO (Madden Julian Oscillation) originate. The first part of the dissertation investigates tropical, oceanic convective and stratiform rainfall variability and determines how to most accurately estimate rainfall accumulation with radar from each rain type. The second, main part of the dissertation uses central Indian Ocean salinity and temperature microstructure measurements and surrounding radar-derived rainfall maps throughout two DYNAMO MJO events to determine the impact of precipitating systems on upper-ocean mixed layer depth and resulting SST variability. The ocean mixed layer was as shallow as 0-5 m during 528/1071 observation hours throughout 2 MJOs (54% of the data record). Out of 43 observation days, thirty-eight near-surface mixed layer depth events were attributed to freshwater stabilization, called rain-formed mixed layers (RFLs). Thirty other mixed layer stratification events were classified as diurnal warm layers (DWLs) due to stable temperature stratification by daytime heating. RFLs and DWLs were observed to interact in two ways: 1) RFLs fill preexisting DWLs and add to total near-surface mixed layer stratification, which occurred ten times; 2) RFLs last long enough to heat, creating a new DWL on top of the RFL, which happened nine times. These combination stratification events were responsible for the highest SST warming rates and some of the highest SSTs leading up to the most active precipitation and wind stage of the each MJO. DWLs without RFL interaction helped produce the highest SSTs in suppressed MJO conditions. As storm intensity, frequency, duration, and the ability of storms to maintain stratiform rain areas increased, RFLS became more common in the disturbed and active MJO phases. Along with the barrier layer, DWL and RFL stratification events helped suppress wind-mixing, cooling, and mixed layer deepening throughout the MJO. We hypothesize that both salinity and temperature stratification events, and their interactions, are important for controlling SST variability and therefore MJO initiation in the Indian Ocean. Most RFLs were caused by submesoscale and mesoscale convective systems with stratiform rain components and local rain accumulations above 10 mm but with winds mostly below 8 m s-1. We hypothesize that the stratiform rain components of storms helped stratify the ocean by providing weak but widespread, steady, long-lived freshwater fluxes. Although generally limited to rain rates ≤ 10 mm hr-1, it is demonstrated that stratiform rain can exert a strong buoyancy flux into the ocean, i.e. as high as maximum daytime solar heating. Storm morphology and the preexisting vertical structure of ocean stability were critical in determining ocean mixed layer depth variability in the presence of rain. Therefore, we suggest that high spatial and temporal resolution coupled ocean-atmosphere models that can parameterize or resolve storm morphology as well as ocean mixed layer and barrier layer evolution are needed to reproduce the diurnal and intraseasonal SST variability documented throughout the MJO.

Dynamic Latent Trait Models with Mixed Hidden Markov Structure for Mixed Longitudinal Outcomes.

PubMed

Zhang, Yue; Berhane, Kiros

2016-01-01

We propose a general Bayesian joint modeling approach to model mixed longitudinal outcomes from the exponential family for taking into account any differential misclassification that may exist among categorical outcomes. Under this framework, outcomes observed without measurement error are related to latent trait variables through generalized linear mixed effect models. The misclassified outcomes are related to the latent class variables, which represent unobserved real states, using mixed hidden Markov models (MHMM). In addition to enabling the estimation of parameters in prevalence, transition and misclassification probabilities, MHMMs capture cluster level heterogeneity. A transition modeling structure allows the latent trait and latent class variables to depend on observed predictors at the same time period and also on latent trait and latent class variables at previous time periods for each individual. Simulation studies are conducted to make comparisons with traditional models in order to illustrate the gains from the proposed approach. The new approach is applied to data from the Southern California Children Health Study (CHS) to jointly model questionnaire based asthma state and multiple lung function measurements in order to gain better insight about the underlying biological mechanism that governs the inter-relationship between asthma state and lung function development.

Time variable eddy mixing in the global Sea Surface Salinity maxima

NASA Astrophysics Data System (ADS)

Busecke, J. J. M.; Abernathey, R.; Gordon, A. L.

2016-12-01

Lateral mixing by mesoscale eddies is widely recognized as a crucial mechanism for the global ocean circulation and the associated heat/salt/tracer transports. The Salinity in the Upper Ocean Processes Study (SPURS) confirmed the importance of eddy mixing for the surface salinity fields even in the center of the subtropical gyre of the North Atlantic. We focus on the global salinity maxima due to their role as indicators for global changes in the hydrological cycle as well as providing the source water masses for the shallow overturning circulation. We introduce a novel approach to estimate the contribution of eddy mixing to the global sea surface salinity maxima. Using a global 2D tracer experiments in a 1/10 degree MITgcm setup driven by observed surface velocities, we analyze the effect of eddy mixing using a water mass framework, thus focussing on the diffusive flux across surface isohalines. This enables us to diagnose temporal variability on seasonal to inter annual time scales, revealing regional differences in the mechanism causing temporal variability.Sensitivity experiments with various salinity backgrounds reveal robust inter annual variability caused by changes in the surface velocity fields potentially forced by large scale climate.

Interannual variability in phytoplankton pigment distribution during the spring transition along the west coast of North America

NASA Technical Reports Server (NTRS)

Thomas, A. C.; Strub, P. T.

1989-01-01

A 5-year time series of coastal zone color scanner imagery (1980-1983, 1986) is used to examine changes in the large-scale pattern of chlorophyll pigment concentration coincident with the spring transition in winds and currents along the west coast of North America. The data show strong interannual variability in the timing and spatial patterns of pigment concentration at the time of the transition event. Interannual variability in the response of pigment concentration to the spring transition appears to be a function of spatial and temporal variability in vertical nutrient flux induced by wind mixing and/or the upwelling initiated at the time of the transition. Interannual differences in the mixing regime are illustrated with a one-dimensional mixing model.

Higher and lowest order mixed finite element approximation of subsurface flow problems with solutions of low regularity

NASA Astrophysics Data System (ADS)

Bause, Markus

2008-02-01

In this work we study mixed finite element approximations of Richards' equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61-78]), the Raviart- Thomas mixed finite element method ( RT0) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565-581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373-394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869-1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148-167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701-724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi- Douglas- Marini element ( BDM1) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM1 approach to the RT0 one is observed, which however is less significant for the accompanying solute transport.

Geographic variation in mixed-conifer forest fire regimes in California

Treesearch

Beaty R. Matthew; Taylor Alan H.

2008-01-01

This paper reviews recent research from California on geographic variability in mixed conifer(MC) forest fire regimes. MC forests are typically described as having experienced primarilyfrequent, low to moderate severity burns prior to fire suppression that created a mosaic ofvegetation patches with variable structure. Research...

Robust high-precision attitude control for flexible spacecraft with improved mixed H2/H∞ control strategy under poles assignment constraint

NASA Astrophysics Data System (ADS)

Liu, Chuang; Ye, Dong; Shi, Keke; Sun, Zhaowei

2017-07-01

A novel improved mixed H2/H∞ control technique combined with poles assignment theory is presented to achieve attitude stabilization and vibration suppression simultaneously for flexible spacecraft in this paper. The flexible spacecraft dynamics system is described and transformed into corresponding state space form. Based on linear matrix inequalities (LMIs) scheme and poles assignment theory, the improved mixed H2/H∞ controller does not restrict the equivalence of the two Lyapunov variables involved in H2 and H∞ performance, which can reduce conservatives compared with traditional mixed H2/H∞ controller. Moreover, it can eliminate the coupling of Lyapunov matrix variables and system matrices by introducing slack variable that provides additional degree of freedom. Several simulations are performed to demonstrate the effectiveness and feasibility of the proposed method in this paper.

The classical dynamic symmetry for the U(1) -Kepler problems

NASA Astrophysics Data System (ADS)

Bouarroudj, Sofiane; Meng, Guowu

2018-01-01

For the Jordan algebra of hermitian matrices of order n ≥ 2, we let X be its submanifold consisting of rank-one semi-positive definite elements. The composition of the cotangent bundle map πX: T∗ X → X with the canonical map X → CP n - 1 (i.e., the map that sends a given hermitian matrix to its column space), pulls back the Kähler form of the Fubini-Study metric on CP n - 1 to a real closed differential two-form ωK on T∗ X. Let ωX be the canonical symplectic form on T∗ X and μ a real number. A standard fact says that ωμ ≔ωX + 2 μωK turns T∗ X into a symplectic manifold, hence a Poisson manifold with Poisson bracket {,}μ. In this article we exhibit a Poisson realization of the simple real Lie algebra su(n , n) on the Poisson manifold (T∗ X ,{,}μ) , i.e., a Lie algebra homomorphism from su(n , n) to (C∞(T∗ X , R) ,{,}μ). Consequently one obtains the Laplace-Runge-Lenz vector for the classical U(1) -Kepler problem of level n and magnetic charge μ. Since the McIntosh-Cisneros-Zwanziger-Kepler problems (MICZ-Kepler Problems) are the U(1) -Kepler problems of level 2, the work presented here is a direct generalization of the work by A. Barut and G. Bornzin (1971) on the classical dynamic symmetry for the MICZ-Kepler problems.

Crossover ensembles of random matrices and skew-orthogonal polynomials

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

Kumar, Santosh, E-mail: skumar.physics@gmail.com; Pandey, Akhilesh, E-mail: ap0700@mail.jnu.ac.in

2011-08-15

Highlights: > We study crossover ensembles of Jacobi family of random matrices. > We consider correlations for orthogonal-unitary and symplectic-unitary crossovers. > We use the method of skew-orthogonal polynomials and quaternion determinants. > We prove universality of spectral correlations in crossover ensembles. > We discuss applications to quantum conductance and communication theory problems. - Abstract: In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving time-reversal symmetry breaking. In the present paper we givemore » details of the work. We start with Dyson's Brownian motion description of random matrix ensembles and obtain universal hierarchic relations among the unfolded correlation functions. For arbitrary dimensions we derive the joint probability density (jpd) of eigenvalues for all transitions leading to unitary ensembles as equilibrium ensembles. We focus on the orthogonal-unitary and symplectic-unitary crossovers and give generic expressions for jpd of eigenvalues, two-point kernels and n-level correlation functions. This involves generalization of the theory of skew-orthogonal polynomials to crossover ensembles. We also consider crossovers in the circular ensembles to show the generality of our method. In the large dimensionality limit, correlations in spectra with arbitrary initial density are shown to be universal when expressed in terms of a rescaled symmetry breaking parameter. Applications of our crossover results to communication theory and quantum conductance problems are also briefly discussed.« less

Section sigma models coupled to symplectic duality bundles on Lorentzian four-manifolds

NASA Astrophysics Data System (ADS)

Lazaroiu, C. I.; Shahbazi, C. S.

2018-06-01

We give the global mathematical formulation of a class of generalized four-dimensional theories of gravity coupled to scalar matter and to Abelian gauge fields. In such theories, the scalar fields are described by a section of a surjective pseudo-Riemannian submersion π over space-time, whose total space carries a Lorentzian metric making the fibers into totally-geodesic connected Riemannian submanifolds. In particular, π is a fiber bundle endowed with a complete Ehresmann connection whose transport acts through isometries between the fibers. In turn, the Abelian gauge fields are "twisted" by a flat symplectic vector bundle defined over the total space of π. This vector bundle is endowed with a vertical taming which locally encodes the gauge couplings and theta angles of the theory and gives rise to the notion of twisted self-duality, of crucial importance to construct the theory. When the Ehresmann connection of π is integrable, we show that our theories are locally equivalent to ordinary Einstein-Scalar-Maxwell theories and hence provide a global non-trivial extension of the universal bosonic sector of four-dimensional supergravity. In this case, we show using a special trivializing atlas of π that global solutions of such models can be interpreted as classical "locally-geometric" U-folds. In the non-integrable case, our theories differ locally from ordinary Einstein-Scalar-Maxwell theories and may provide a geometric description of classical U-folds which are "locally non-geometric".

Deriving Surface NO2 Mixing Ratios from DISCOVER-AQ ACAM Observations: A Method to Assess Surface NO2 Spatial Variability

NASA Astrophysics Data System (ADS)

Silverman, M. L.; Szykman, J.; Chen, G.; Crawford, J. H.; Janz, S. J.; Kowalewski, M. G.; Lamsal, L. N.; Long, R.

2015-12-01

Studies have shown that satellite NO2 columns are closely related to ground level NO2 concentrations, particularly over polluted areas. This provides a means to assess surface level NO2 spatial variability over a broader area than what can be monitored from ground stations. The characterization of surface level NO2 variability is important to understand air quality in urban areas, emissions, health impacts, photochemistry, and to evaluate the performance of chemical transport models. Using data from the NASA DISCOVER-AQ campaign in Baltimore/Washington we calculate NO2 mixing ratios from the Airborne Compact Atmospheric Mapper (ACAM), through four different methods to derive surface concentration from column measurements. High spectral resolution lidar (HSRL) mixed layer heights, vertical P3B profiles, and CMAQ vertical profiles are used to scale ACAM vertical column densities. The derived NO2 mixing ratios are compared to EPA ground measurements taken at Padonia and Edgewood. We find similar results from scaling with HSRL mixed layer heights and normalized P3B vertical profiles. The HSRL mixed layer heights are then used to scale ACAM vertical column densities across the DISCOVER-AQ flight pattern to assess spatial variability of NO2 over the area. This work will help define the measurement requirements for future satellite instruments.

A Mixed-Methodological Examination of Investment Model Variables among Abused and Nonabused College Women

ERIC Educational Resources Information Center

Dardis, Christina M.; Kelley, Erika L.; Edwards, Katie M.; Gidycz, Christine A.

2013-01-01

Objective: This study assessed abused and nonabused women's perceptions of Investment Model (IM) variables (ie, relationship investment, satisfaction, commitment, quality of alternatives) utilizing a mixed-methods design. Participants: Participants included 102 college women, approximately half of whom were in abusive dating relationships.…

Mixed features in patients with a major depressive episode: the BRIDGE-II-MIX study.

PubMed

Perugi, Giulio; Angst, Jules; Azorin, Jean-Michel; Bowden, Charles L; Mosolov, Sergey; Reis, Joao; Vieta, Eduard; Young, Allan H

2015-03-01

To estimate the frequency of mixed states in patients diagnosed with major depressive episode (MDE) according to conceptually different definitions and to compare their clinical validity. This multicenter, multinational cross-sectional Bipolar Disorders: Improving Diagnosis, Guidance and Education (BRIDGE)-II-MIX study enrolled 2,811 adult patients experiencing an MDE. Data were collected per protocol on sociodemographic variables, current and past psychiatric symptoms, and clinical variables that are risk factors for bipolar disorder. The frequency of mixed features was determined by applying both DSM-5 criteria and a priori described Research-Based Diagnostic Criteria (RBDC). Clinical variables associated with mixed features were assessed using logistic regression. Overall, 212 patients (7.5%) fulfilled DSM-5 criteria for MDE with mixed features (DSM-5-MXS), and 818 patients (29.1%) fulfilled diagnostic criteria for a predefined RBDC depressive mixed state (RBDC-MXS). The most frequent manic/hypomanic symptoms were irritable mood (32.6%), emotional/mood lability (29.8%), distractibility (24.4%), psychomotor agitation (16.1%), impulsivity (14.5%), aggression (14.2%), racing thoughts (11.8%), and pressure to keep talking (11.4%). Euphoria (4.6%), grandiosity (3.7%), and hypersexuality (2.6%) were less represented. In multivariate logistic regression analysis, RBDC-MXS was associated with the largest number of variables including diagnosis of bipolar disorder, family history of mania, lifetime suicide attempts, duration of the current episode > 1 month, atypical features, early onset, history of antidepressant-induced mania/hypomania, and lifetime comorbidity with anxiety, alcohol and substance use disorders, attention-deficit/hyperactivity disorder, and borderline personality disorder. Depressive mixed state, defined as the presence of 3 or more manic/hypomanic features, was present in around one-third of patients experiencing an MDE. The valid symptom, illness course and family history RBDC criteria we assessed identified 4 times more MDE patients as having mixed features and yielded statistically more robust associations with several illness characteristics of bipolar disorder than did DSM-5 criteria. © Copyright 2015 Physicians Postgraduate Press, Inc.

Non-commutative methods in quantum mechanics

NASA Astrophysics Data System (ADS)

Millard, Andrew Clive

1997-09-01

Non-commutativity appears in physics almost hand in hand with quantum mechanics. Non-commuting operators corresponding to observables lead to Heisenberg's Uncertainty Principle, which is often used as a prime example of how quantum mechanics transcends 'common sense', while the operators that generate a symmetry group are usually given in terms of their commutation relations. This thesis discusses a number of new developments which go beyond the usual stopping point of non-commuting quantities as matrices with complex elements. Chapter 2 shows how certain generalisations of quantum mechanics, from using complex numbers to using other (often non-commutative) algebras, can still be written as linear systems with symplectic phase flows. Chapter 3 deals with Adler's trace dynamics, a non-linear graded generalisation of Hamiltonian dynamics with supersymmetry applications, where the phase space coordinates are (generally non-commuting) operators, and reports on aspects of a demonstration that the statistical averages of the dynamical variables obey the rules of complex quantum field theory. The last two chapters discuss specific aspects of quaternionic quantum mechanics. Chapter 4 reports a generalised projective representation theory and presents a structure theorem that categorises quaternionic projective representations. Chapter 5 deals with a generalisation of the coherent states formalism and examines how it may be applied to two commonly used groups.

Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction

NASA Astrophysics Data System (ADS)

Fehér, L.; Klimčík, C.

2012-07-01

The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars-Schneider IIIb system from a quasi-Hamiltonian reduction of the internally fused double SU(n)×SU(n). In particular, the reduced spectral functions depending respectively on the first and second SU(n) factor of the double engender two toric moment maps on the IIIb phase space CP(n-1) that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z) mapping class group of the torus with one boundary component is shown to act on the quasi-Hamiltonian double by automorphisms and, upon reduction, the standard generator S of the mapping class group is proved to descend to the Ruijsenaars self-duality symplectomorphism that exchanges the toric moment maps. We give also two new presentations of this duality map: one as the composition of two Delzant symplectomorphisms and the other as the composition of three Dehn twist symplectomorphisms realized by Goldman twist flows. Through the well-known relation between quasi-Hamiltonian manifolds and moduli spaces, our results rigorously establish the validity of the interpretation [going back to Gorsky and Nekrasov] of the IIIb system in terms of flat SU(n) connections on the one-holed torus.

Advanced supersonic propulsion system technology study, phase 2

NASA Technical Reports Server (NTRS)

Allan, R. D.

1975-01-01

Variable cycle engines were identified, based on the mixed-flow low-bypass-ratio augmented turbofan cycle, which has shown excellent range capability in the AST airplane. The best mixed-flow augmented turbofan engine was selected based on range in the AST Baseline Airplane. Selected variable cycle engine features were added to this best conventional baseline engine, and the Dual-Cycle VCE and Double-Bypass VCE were defined. The conventional mixed-flow turbofan and the Double-Bypass VCE were on the subjects of engine preliminary design studies to determine mechanical feasibility, confirm weight and dimensional estimates, and identify the necessary technology considered not yet available. Critical engine components were studied and incorporated into the variable cycle engine design.

Variable mixer propulsion cycle

NASA Technical Reports Server (NTRS)

Rundell, D. J.; Mchugh, D. P.; Foster, T.; Brown, R. H. (Inventor)

1978-01-01

A design technique, method and apparatus are delineated for controlling the bypass gas stream pressure and varying the bypass ratio of a mixed flow gas turbine engine in order to achieve improved performance. The disclosed embodiments each include a mixing device for combining the core and bypass gas streams. The variable area mixing device permits the static pressures of the core and bypass streams to be balanced prior to mixing at widely varying bypass stream pressure levels. The mixed flow gas turbine engine therefore operates efficiently over a wide range of bypass ratios and the dynamic pressure of the bypass stream is maintained at a level which will keep the engine inlet airflow matched to an optimum design level throughout a wide range of engine thrust settings.

Lump and rogue waves for the variable-coefficient Kadomtsev-Petviashvili equation in a fluid

NASA Astrophysics Data System (ADS)

Jia, Xiao-Yue; Tian, Bo; Du, Zhong; Sun, Yan; Liu, Lei

2018-04-01

Under investigation in this paper is the variable-coefficient Kadomtsev-Petviashvili equation, which describes the long waves with small amplitude and slow dependence on the transverse coordinate in a single-layer shallow fluid. Employing the bilinear form and symbolic computation, we obtain the lump, mixed lump-stripe soliton and mixed rogue wave-stripe soliton solutions. Discussions indicate that the variable coefficients are related to both the lump soliton’s velocity and amplitude. Mixed lump-stripe soliton solutions display two different properties, fusion and fission. Mixed rogue wave-stripe soliton solutions show that a rogue wave arises from one of the stripe solitons and disappears into the other. When the time approaches 0, rogue wave’s energy reaches the maximum. Interactions between a lump soliton and one-stripe soliton, and between a rogue wave and a pair of stripe solitons, are shown graphically.

Mixed Methods Analysis of Multicultural Identity and Psychological Help Seeking Beliefs in College Students

ERIC Educational Resources Information Center

Walter, Jeffrey P.

2012-01-01

Research on the psychological help-seeking beliefs and behaviors of college students has provided evidence for differences among students based on demographic factors, with different variables being salient for different cultural groups. This mixed methods study focuses on understanding how common psychological help-seeking variables, including…

Central Tropical Pacific Variability And ENSO Response To Changing Climate Boundary Conditions: Evidence From Individual Line Island Foraminifera

NASA Astrophysics Data System (ADS)

Rustic, G. T.; Polissar, P. J.; Ravelo, A. C.; White, S. M.

2017-12-01

The El Niño Southern Oscillation (ENSO) plays a dominant role in Earth's climate variability. Paleoceanographic evidence suggests that ENSO has changed in the past, and these changes have been linked to large-scale climatic shifts. While a close relationship between ENSO evolution and climate boundary conditions has been predicted, testing these predictions remains challenging. These climate boundary conditions, including insolation, the mean surface temperature gradient of the tropical Pacific, global ice volume, and tropical thermocline depth, often co-vary and may work together to suppress or enhance the ocean-atmosphere feedbacks that drive ENSO variability. Furthermore, suitable paleo-archives spanning multiple climate states are sparse. We have aimed to test ENSO response to changing climate boundary conditions by generating new reconstructions of mixed-layer variability from sedimentary archives spanning the last three glacial-interglacial cycles from the Central Tropical Pacific Line Islands, where El Niño is strongly expressed. We analyzed Mg/Ca ratios from individual foraminifera to reconstruct mixed-layer variability at discrete time intervals representing combinations of climatic boundary conditions from the middle Holocene to Marine Isotope Stage (MIS) 8. We observe changes in the mixed-layer temperature variability during MIS 5 and during the previous interglacial (MIS 7) showing significant reductions in ENSO amplitude. Differences in variability during glacial and interglacial intervals are also observed. Additionally, we reconstructed mixed-layer and thermocline conditions using multi-species Mg/Ca and stable isotope measurements to more fully characterize the state of the Central Tropical Pacific during these intervals. These reconstructions provide us with a unique view of Central Tropical Pacific variability and water-column structure at discrete intervals under varying boundary climate conditions with which to assess factors that shape ENSO variability.

Bilinear, trilinear forms, and exact solution of certain fourth order integrable difference equations

NASA Astrophysics Data System (ADS)

Sahadevan, R.; Rajakumar, S.

2008-03-01

A systematic investigation of finding bilinear or trilinear representations of fourth order autonomous ordinary difference equation, x(n +4)=F(x(n),x(n+1),x(n+2),x(n+3)) or xn +4=F(xn,xn +1,xn +2,xn +3), is made. As an illustration, we consider fourth order symplectic integrable difference equations reported by [Capel and Sahadevan, Physica A 289, 86 (2001)] and derived their bilinear or trilinear forms. Also, it is shown that the obtained bilinear representations admit exact solution of rational form.

Optimal control of underactuated mechanical systems: A geometric approach

NASA Astrophysics Data System (ADS)

Colombo, Leonardo; Martín De Diego, David; Zuccalli, Marcela

2010-08-01

In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics of the optimal control problem. These developments will allow us to develop a new class of geometric integrators based on discrete variational calculus.

Disordered two-dimensional electron systems with chiral symmetry

NASA Astrophysics Data System (ADS)

Markoš, P.; Schweitzer, L.

2012-10-01

We review the results of our recent numerical investigations on the electronic properties of disordered two dimensional systems with chiral unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular interest is the behavior of the density of states and the logarithmic scaling of the smallest Lyapunov exponents in the vicinity of the chiral quantum critical point in the band center at E=0. The observed peaks or depressions in the density of states, the distribution of the critical conductances, and the possible non-universality of the critical exponents for certain chiral unitary models are discussed.

Boundary qKZ equation and generalized Razumov Stroganov sum rules for open IRF models

NASA Astrophysics Data System (ADS)

Di Francesco, P.

2005-11-01

We find higher-rank generalizations of the Razumov-Stroganov sum rules at q = -ei π/(k+1) for Ak-1 models with open boundaries, by constructing polynomial solutions of level-1 boundary quantum Knizhnik-Zamolodchikov equations for U_q(\\frak {sl}(k)) . The result takes the form of a character of the symplectic group, that leads to a generalization of the number of vertically symmetric alternating sign matrices. We also investigate the other combinatorial point q = -1, presumably related to the geometry of nilpotent matrix varieties.

Area-Preserving Diffeomorphisms, W∞ and { U}q [sl(2)] in Chern-Simons Theory and the Quantum Hall System

NASA Astrophysics Data System (ADS)

Kogan, Ian I.

We discuss a quantum { U}q [sl(2)] symmetry in the Landau problem, which naturally arises due to the relation between { U}q [sl(2)] and the group of magnetic translations. The latter is connected with W∞ and area-preserving (symplectic) diffeomorphisms which are the canonical transformations in the two-dimensional phase space. We shall discuss the hidden quantum symmetry in a 2 + 1 gauge theory with the Chern-Simons term and in a quantum Hall system, which are both connected with the Landau problem.

Quantifying inter- and intra-population niche variability using hierarchical bayesian stable isotope mixing models.

PubMed

Semmens, Brice X; Ward, Eric J; Moore, Jonathan W; Darimont, Chris T

2009-07-09

Variability in resource use defines the width of a trophic niche occupied by a population. Intra-population variability in resource use may occur across hierarchical levels of population structure from individuals to subpopulations. Understanding how levels of population organization contribute to population niche width is critical to ecology and evolution. Here we describe a hierarchical stable isotope mixing model that can simultaneously estimate both the prey composition of a consumer diet and the diet variability among individuals and across levels of population organization. By explicitly estimating variance components for multiple scales, the model can deconstruct the niche width of a consumer population into relevant levels of population structure. We apply this new approach to stable isotope data from a population of gray wolves from coastal British Columbia, and show support for extensive intra-population niche variability among individuals, social groups, and geographically isolated subpopulations. The analytic method we describe improves mixing models by accounting for diet variability, and improves isotope niche width analysis by quantitatively assessing the contribution of levels of organization to the niche width of a population.

Clustering of samples and variables with mixed-type data

PubMed Central

Edelmann, Dominic; Kopp-Schneider, Annette

2017-01-01

Analysis of data measured on different scales is a relevant challenge. Biomedical studies often focus on high-throughput datasets of, e.g., quantitative measurements. However, the need for integration of other features possibly measured on different scales, e.g. clinical or cytogenetic factors, becomes increasingly important. The analysis results (e.g. a selection of relevant genes) are then visualized, while adding further information, like clinical factors, on top. However, a more integrative approach is desirable, where all available data are analyzed jointly, and where also in the visualization different data sources are combined in a more natural way. Here we specifically target integrative visualization and present a heatmap-style graphic display. To this end, we develop and explore methods for clustering mixed-type data, with special focus on clustering variables. Clustering of variables does not receive as much attention in the literature as does clustering of samples. We extend the variables clustering methodology by two new approaches, one based on the combination of different association measures and the other on distance correlation. With simulation studies we evaluate and compare different clustering strategies. Applying specific methods for mixed-type data proves to be comparable and in many cases beneficial as compared to standard approaches applied to corresponding quantitative or binarized data. Our two novel approaches for mixed-type variables show similar or better performance than the existing methods ClustOfVar and bias-corrected mutual information. Further, in contrast to ClustOfVar, our methods provide dissimilarity matrices, which is an advantage, especially for the purpose of visualization. Real data examples aim to give an impression of various kinds of potential applications for the integrative heatmap and other graphical displays based on dissimilarity matrices. We demonstrate that the presented integrative heatmap provides more information than common data displays about the relationship among variables and samples. The described clustering and visualization methods are implemented in our R package CluMix available from https://cran.r-project.org/web/packages/CluMix. PMID:29182671

Hamiltonian structure of real Monge - Ampère equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-06-01

The variational principle for the real homogeneous Monge - Ampère equation in two dimensions is shown to contain three arbitrary functions of four variables. There exist two different specializations of this variational principle where the Lagrangian is degenerate and furthermore contains an arbitrary function of two variables. The Hamiltonian formulation of these degenerate Lagrangian systems requires the use of Dirac's theory of constraints. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. Thus the real homogeneous Monge - Ampère equation in two dimensions admits two classes of infinitely many Hamiltonian operators, namely a family of local, as well as another family non-local Hamiltonian operators and symplectic 2-forms which depend on arbitrary functions of two variables. The simplest non-local Hamiltonian operator corresponds to the Kac - Moody algebra of vector fields and functions on the unit circle. Hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair. In the case of real Monge - Ampère equations with constant right-hand side this compatible pair is the only pair of Hamiltonian operators that survives. Then the complete integrability of all these real Monge - Ampère equations follows by Magri's theorem. Some of the remarkable properties we have obtained for the Hamiltonian structure of the real homogeneous Monge - Ampère equation in two dimensions turn out to be generic to the real homogeneous Monge - Ampère equation and the geodesic flow for the complex homogeneous Monge - Ampère equation in arbitrary number of dimensions. Hence among all integrable nonlinear evolution equations in one space and one time dimension, the real homogeneous Monge - Ampère equation is distinguished as one that retains its character as an integrable system in multiple dimensions.

A method for fitting regression splines with varying polynomial order in the linear mixed model.

PubMed

Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

2006-02-15

The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

ENSO modulation of tropical Indian Ocean subseasonal variability

NASA Astrophysics Data System (ADS)

Jung, Eunsil; Kirtman, Ben P.

2016-12-01

In this study, we use 30 years of retrospective climate model forecasts and observational estimates to show that El Niño/Southern Oscillation (ENSO) affects the amplitude of subseasonal variability of sea surface temperature (SST) in the southwest Indian Ocean, an important Tropical Intraseasonal Oscillation (TISO) onset region. The analysis shows that deeper background mixed-layer depths and warmer upper ocean conditions during El Niño reduce the amplitude of the subseasonal SST variability over Seychelles-Chagos Thermocline Ridge (SCTR), which may reduce SST-wind coupling and the amplitude of TISO variability. The opposite holds for La Niña where the shallower mixed-layer depth enhances SST variability over SCTR, which may increase SST-wind coupling and the amplitude of TISO variability.

Extending existing structural identifiability analysis methods to mixed-effects models.

PubMed

Janzén, David L I; Jirstrand, Mats; Chappell, Michael J; Evans, Neil D

2018-01-01

The concept of structural identifiability for state-space models is expanded to cover mixed-effects state-space models. Two methods applicable for the analytical study of the structural identifiability of mixed-effects models are presented. The two methods are based on previously established techniques for non-mixed-effects models; namely the Taylor series expansion and the input-output form approach. By generating an exhaustive summary, and by assuming an infinite number of subjects, functions of random variables can be derived which in turn determine the distribution of the system's observation function(s). By considering the uniqueness of the analytical statistical moments of the derived functions of the random variables, the structural identifiability of the corresponding mixed-effects model can be determined. The two methods are applied to a set of examples of mixed-effects models to illustrate how they work in practice. Copyright © 2017 Elsevier Inc. All rights reserved.

A Second-Order Conditionally Linear Mixed Effects Model with Observed and Latent Variable Covariates

ERIC Educational Resources Information Center

Harring, Jeffrey R.; Kohli, Nidhi; Silverman, Rebecca D.; Speece, Deborah L.

2012-01-01

A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a…

Qualitative Contrast between Knowledge-Limited Mixed-State and Variable-Resources Models of Visual Change Detection

ERIC Educational Resources Information Center

Nosofsky, Robert M.; Donkin, Chris

2016-01-01

We report an experiment designed to provide a qualitative contrast between knowledge-limited versions of mixed-state and variable-resources (VR) models of visual change detection. The key data pattern is that observers often respond "same" on big-change trials, while simultaneously being able to discriminate between same and small-change…

Mixed boundary-value problem for an orthotropic rectangular strip with variable coefficients of elasticity

NASA Astrophysics Data System (ADS)

Sargsyan, M. Z.; Poghosyan, H. M.

2018-04-01

A dynamical problem for a rectangular strip with variable coefficients of elasticity is solved by an asymptotic method. It is assumed that the strip is orthotropic, the elasticity coefficients are exponential functions of y, and mixed boundary conditions are posed. The solution of the inner problem is obtained using Bessel functions.

Empirical Models for the Shielding and Reflection of Jet Mixing Noise by a Surface

NASA Technical Reports Server (NTRS)

Brown, Cliff

2015-01-01

Empirical models for the shielding and refection of jet mixing noise by a nearby surface are described and the resulting models evaluated. The flow variables are used to non-dimensionalize the surface position variables, reducing the variable space and producing models that are linear function of non-dimensional surface position and logarithmic in Strouhal frequency. A separate set of coefficients are determined at each observer angle in the dataset and linear interpolation is used to for the intermediate observer angles. The shielding and rejection models are then combined with existing empirical models for the jet mixing and jet-surface interaction noise sources to produce predicted spectra for a jet operating near a surface. These predictions are then evaluated against experimental data.

Empirical Models for the Shielding and Reflection of Jet Mixing Noise by a Surface

NASA Technical Reports Server (NTRS)

Brown, Clifford A.

2016-01-01

Empirical models for the shielding and reflection of jet mixing noise by a nearby surface are described and the resulting models evaluated. The flow variables are used to non-dimensionalize the surface position variables, reducing the variable space and producing models that are linear function of non-dimensional surface position and logarithmic in Strouhal frequency. A separate set of coefficients are determined at each observer angle in the dataset and linear interpolation is used to for the intermediate observer angles. The shielding and reflection models are then combined with existing empirical models for the jet mixing and jet-surface interaction noise sources to produce predicted spectra for a jet operating near a surface. These predictions are then evaluated against experimental data.

Directional nonlinear guided wave mixing: Case study of counter-propagating shear horizontal waves

NASA Astrophysics Data System (ADS)

Hasanian, Mostafa; Lissenden, Cliff J.

2018-04-01

While much nonlinear ultrasonics research has been conducted on higher harmonic generation, wave mixing provides the potential for sensitive measurements of incipient damage unencumbered by instrumentation nonlinearity. Studies of nonlinear ultrasonic wave mixing, both collinear and noncollinear, for bulk waves have shown the robust capability of wave mixing for early damage detection. One merit of bulk wave mixing lies in their non-dispersive nature, but guided waves enable inspection of otherwise inaccessible material and a variety of mixing options. Co-directional guided wave mixing was studied previously, but arbitrary direction guided wave mixing has not been addressed until recently. Wave vector analysis is applied to study variable mixing angles to find wave mode triplets (two primary waves and a secondary wave) resulting in the phase matching condition. As a case study, counter-propagating Shear Horizontal (SH) guided wave mixing is analyzed. SH wave interactions generate a secondary Lamb wave mode that is readily receivable. Reception of the secondary Lamb wave mode is compared for an angle beam transducer, an air coupled transducer, and a laser Doppler vibrometer (LDV). Results from the angle beam and air coupled transducers are quite consistent, while the LDV measurement is plagued by variability issues.

A Water Model Study on Mixing Behavior of the Two-Layered Bath in Bottom Blown Copper Smelting Furnace

NASA Astrophysics Data System (ADS)

Shui, Lang; Cui, Zhixiang; Ma, Xiaodong; Jiang, Xu; Chen, Mao; Xiang, Yong; Zhao, Baojun

2018-05-01

The bottom-blown copper smelting furnace is a novel copper smelter developed in recent years. Many advantages of this furnace have been found, related to bath mixing behavior under its specific gas injection scheme. This study aims to use an oil-water double-phased laboratory-scale model to investigate the impact of industry-adjustable variables on bath mixing time, including lower layer thickness, gas flow rate, upper layer thickness and upper layer viscosity. Based on experimental results, an overall empirical relationship of mixing time in terms of these variables has been correlated, which provides the methodology for industry to optimize mass transfer in the furnace.

Closing the Seasonal Ocean Surface Temperature Balance in the Eastern Tropical Oceans from Remote Sensing and Model Reanalyses

NASA Technical Reports Server (NTRS)

Roberts, J. Brent; Clayson, Carol A.

2012-01-01

The Eastern tropical ocean basins are regions of significant atmosphere-ocean interaction and are important to variability across subseasonal to decadal time scales. The numerous physical processes at play in these areas strain the abilities of coupled general circulation models to accurately reproduce observed upper ocean variability. Furthermore, limitations in the observing system of important terms in the surface temperature balance (e.g., turbulent and radiative heat fluxes, advection) introduce uncertainty into the analyses of processes controlling sea surface temperature variability. This study presents recent efforts to close the surface temperature balance through estimation of the terms in the mixed layer temperature budget using state-of-the-art remotely sensed and model-reanalysis derived products. A set of twelve net heat flux estimates constructed using combinations of radiative and turbulent heat flux products - including GEWEX-SRB, ISCCP-SRF, OAFlux, SeaFlux, among several others - are used with estimates of oceanic advection, entrainment, and mixed layer depth variability to investigate the seasonal variability of ocean surface temperatures. Particular emphasis is placed on how well the upper ocean temperature balance is, or is not, closed on these scales using the current generation of observational and model reanalysis products. That is, the magnitudes and spatial variability of residual imbalances are addressed. These residuals are placed into context within the current uncertainties of the surface net heat fluxes and the role of the mixed layer depth variability in scaling the impact of those uncertainties, particularly in the shallow mixed layers of the Eastern tropical ocean basins.

PyCOOL — A Cosmological Object-Oriented Lattice code written in Python

NASA Astrophysics Data System (ADS)

Sainio, J.

2012-04-01

There are a number of different phenomena in the early universe that have to be studied numerically with lattice simulations. This paper presents a graphics processing unit (GPU) accelerated Python program called PyCOOL that solves the evolution of scalar fields in a lattice with very precise symplectic integrators. The program has been written with the intention to hit a sweet spot of speed, accuracy and user friendliness. This has been achieved by using the Python language with the PyCUDA interface to make a program that is easy to adapt to different scalar field models. In this paper we derive the symplectic dynamics that govern the evolution of the system and then present the implementation of the program in Python and PyCUDA. The functionality of the program is tested in a chaotic inflation preheating model, a single field oscillon case and in a supersymmetric curvaton model which leads to Q-ball production. We have also compared the performance of a consumer graphics card to a professional Tesla compute card in these simulations. We find that the program is not only accurate but also very fast. To further increase the usefulness of the program we have equipped it with numerous post-processing functions that provide useful information about the cosmological model. These include various spectra and statistics of the fields. The program can be additionally used to calculate the generated curvature perturbation. The program is publicly available under GNU General Public License at https://github.com/jtksai/PyCOOL. Some additional information can be found from http://www.physics.utu.fi/tiedostot/theory/particlecosmology/pycool/.

Aspects géométriques et intégrables des modèles de matrices aléatoires

NASA Astrophysics Data System (ADS)

Marchal, Olivier

2010-12-01

This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of integrable systems. The variety of these applications shows why matrix models are important from a mathematical point of view. First, the thesis will focus on the study of the merging of two intervals of the eigenvalues density near a singular point. Specifically, we will show why this special limit gives universal equations from the Painlevé II hierarchy of integrable systems theory. Then, following the approach of (bi) orthogonal polynomials introduced by Mehta to compute partition functions, we will find Riemann-Hilbert and isomonodromic problems connected to matrix models, making the link with the theory of Jimbo, Miwa and Ueno. In particular, we will describe how the hermitian two-matrix models provide a degenerate case of Jimbo-Miwa-Ueno's theory that we will generalize in this context. Furthermore, the loop equations method, with its central notions of spectral curve and topological expansion, will lead to the symplectic invariants of algebraic geometry recently proposed by Eynard and Orantin. This last point will be generalized to the case of non-hermitian matrix models (arbitrary beta) paving the way to "quantum algebraic geometry" and to the generalization of symplectic invariants to "quantum curves". Finally, this set up will be applied to combinatorics in the context of topological string theory, with the explicit computation of an hermitian random matrix model enumerating the Gromov-Witten invariants of a toric Calabi-Yau threefold.

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

Sainio, J., E-mail: jani.sainio@utu.fi; Department of Physics and Astronomy, University of Turku, FI-20014 Turku

There are a number of different phenomena in the early universe that have to be studied numerically with lattice simulations. This paper presents a graphics processing unit (GPU) accelerated Python program called PyCOOL that solves the evolution of scalar fields in a lattice with very precise symplectic integrators. The program has been written with the intention to hit a sweet spot of speed, accuracy and user friendliness. This has been achieved by using the Python language with the PyCUDA interface to make a program that is easy to adapt to different scalar field models. In this paper we derive themore » symplectic dynamics that govern the evolution of the system and then present the implementation of the program in Python and PyCUDA. The functionality of the program is tested in a chaotic inflation preheating model, a single field oscillon case and in a supersymmetric curvaton model which leads to Q-ball production. We have also compared the performance of a consumer graphics card to a professional Tesla compute card in these simulations. We find that the program is not only accurate but also very fast. To further increase the usefulness of the program we have equipped it with numerous post-processing functions that provide useful information about the cosmological model. These include various spectra and statistics of the fields. The program can be additionally used to calculate the generated curvature perturbation. The program is publicly available under GNU General Public License at https://github.com/jtksai/PyCOOL. Some additional information can be found from http://www.physics.utu.fi/tiedostot/theory/particlecosmology/pycool/.« less

Effect of mixed mutans streptococci colonization on caries development.

PubMed

Seki, M; Yamashita, Y; Shibata, Y; Torigoe, H; Tsuda, H; Maeno, M

2006-02-01

To evaluate the clinical importance of mixed mutans streptococci colonization in predicting caries in preschool children. Caries prevalence was examined twice, with a 6-month interval, in 410 preschool children aged 3-4 years at baseline. A commercial strip method was used to evaluate the mutans streptococci score in plaque collected from eight selected interdental spaces and in saliva. Mutans streptococci typing polymerase chain reaction (PCR) assays (Streptococcus sobrinus and Streptococcus mutans, including serotypes c, e, and f) were performed using colonies on the strips as template. Twenty variables were examined in a univariate analysis to predict caries development: questionnaire variables, results of clinical examination, mutans streptococci scores, and PCR detection of S. sobrinus and S. mutans (including serotypes c, e, and f). Sixteen variables showed statistically significant associations (P < 0.04) in the univariate analysis. However, when entered into a logistic regression, only five variables remained significant (P < 0.05): caries experience at baseline; mixed colonization of S. sobrinus and S. mutans including S. mutans serotypes; high plaque mutans streptococci score; habitual use of sweet drinks; and nonuse of fluoride toothpaste. 'Mixed mutans streptococci colonization' is a novel measure correlated with caries development in their primary dentition.

The Effect of the Interannual Variability of the OH Sink on the Interannual Variability of the Atmospheric Methane Mixing Ratio and Carbon Stable Isotope Composition

NASA Astrophysics Data System (ADS)

Guillermo Nuñez Ramirez, Tonatiuh; Houweling, Sander; Marshall, Julia; Williams, Jason; Brailsford, Gordon; Schneising, Oliver; Heimann, Martin

2013-04-01

The atmospheric hydroxyl radical concentration (OH) varies due to changes in the incoming UV radiation, in the abundance of atmospheric species involved in the production, recycling and destruction of OH molecules and due to climate variability. Variability in carbon monoxide emissions from biomass burning induced by El Niño Southern Oscillation are particularly important. Although the OH sink accounts for the oxidation of approximately 90% of atmospheric CH4, the effect of the variability in the distribution and strength of the OH sink on the interannual variability of atmospheric methane (CH4) mixing ratio and stable carbon isotope composition (δ13C-CH4) has often been ignored. To show this effect we simulated the atmospheric signals of CH4 in a three-dimensional atmospheric transport model (TM3). ERA Interim reanalysis data provided the atmospheric transport and temperature variability from 1990 to 2010. We performed simulations using time dependent OH concentration estimations from an atmospheric chemistry transport model and an atmospheric chemistry climate model. The models assumed a different set of reactions and algorithms which caused a very different strength and distribution of the OH concentration. Methane emissions were based on published bottom-up estimates including inventories, upscaled estimations and modeled fluxes. The simulations also included modeled concentrations of atomic chlorine (Cl) and excited oxygen atoms (O(1D)). The isotopic signal of the sources and the fractionation factors of the sinks were based on literature values, however the isotopic signal from wetlands and enteric fermentation processes followed a linear relationship with a map of C4 plant fraction. The same set of CH4emissions and stratospheric reactants was used in all simulations. Two simulations were done per OH field: one in which the CH4 sources were allowed to vary interannually, and a second where the sources were climatological. The simulated mixing ratios and isotopic compositions at global reference stations were used to construct more robust indicators such as global and zonal means and interhemispheric differences. We also compared the model CH4 mixing ratio to satellite observations, for the period 2003 to 2004 with SCIAMACHY and from 2009 to 2010 with GOSAT. The interannual variability of the different OH fields imprinted an interannual variation of the atmospheric CH4 mixing ratio with a magnitude of ±10 ppb, which is comparable to the effect of all sources combined. Meanwhile its effect on the interannual variability of δ13C-CH4 was minor (< 10%). The interannual variability of the mixing ratio interhemispheric difference is dominated by the sources because the OH sink is concentrated in the tropics, thus its interannual variability affects both hemispheres. Meanwhile, although the OH plays an important role in the establishment of an interhemispheric gradient of δ13C-CH4, the interannual variation of this gradient is negligibly affected by the choice of OH field. Overall the study showed that the variability of the OH sink plays a significant role in the interannual variability of the atmospheric methane mixing ratio, and must be considered to improve our understanding of the recent trends in the global methane budget.

Scale model performance test investigation of exhaust system mixers for an Energy Efficient Engine /E3/ propulsion system

NASA Technical Reports Server (NTRS)

Kuchar, A. P.; Chamberlin, R.

1980-01-01

A scale model performance test was conducted as part of the NASA Energy Efficient Engine (E3) Program, to investigate the geometric variables that influence the aerodynamic design of exhaust system mixers for high-bypass, mixed-flow engines. Mixer configuration variables included lobe number, penetration and perimeter, as well as several cutback mixer geometries. Mixing effectiveness and mixer pressure loss were determined using measured thrust and nozzle exit total pressure and temperature surveys. Results provide a data base to aid the analysis and design development of the E3 mixed-flow exhaust system.

Olivine-hosted melt inclusions record efficient mixing of mantle melts in continental flood basalt provinces

NASA Astrophysics Data System (ADS)

Jennings, E. S.; Gibson, S. A.; Maclennan, J.; Heinonen, J. S.

2017-12-01

Primitive melt inclusions trapped in various minerals found in global ridge settings have been shown to record highly variable magmatic compositions. Mantle melting is expected to be near-fractional, producing a wide range of melt compositions that must accumulate and mix in crustal magma chambers. In primitive rocks, the melt inclusion variability observed in major, trace and isotope geochemistry is consistent to the first order with partial melting of variably depleted mantle, and indicate that the host phases began to crystallise prior to the completion of melt aggregation and mixing. We present new major and trace element data from a large number of rehomogenised olivine-hosted melt inclusions from the Cretaceous Paraná-Etendeka and Jurassic Karoo continental flood basalt (CFB) provinces [1]. We show that the major element chemistry of the melt inclusions can be severely disrupted by the rehomogenisation process and, as a consequence, their initial compositions cannot easily be back-calculated. However, despite the age of the samples, the trace element geochemistry of the melt inclusions is well-preserved. Despite coming from near-liquidus olivines from primitive picrites and ferropicrites, the inclusions are remarkably homogeneous; none of the anticipated variability in incompatible trace element compositions is observed. When considered alongside literature data, it appears that variability in primitive melts - as recorded by melt inclusions - is low in CFBs and OIBs relative to ridge settings, e.g. Iceland. We suggest that the tectonic setting imposes a control on the mixing of mantle melts: hot, plume-derived melts generated beneath relatively thick lithosphere may be prone to efficient mixing, perhaps due to their low viscosity, long transport pathways, and/or a superliquidus emplacement temperature [1]. This interpretation is supported by the almost non-existent variability of olivine-hosted inclusions from ferropicrite samples: these magmas represents the deepest, hottest and lowest viscosity magma of all the samples considered. [1] Jennings E. S., Gibson S. A., Maclennan J. and Heinonen J. S. (2017) Deep mixing of mantle melts beneath continental flood basalt provinces: Constraints from olivine-hosted melt inclusions in primitive magmas. Geochimica et Cosmochimica Acta 196, 36-57.

Regularization of Mickelsson generators for nonexceptional quantum groups

NASA Astrophysics Data System (ADS)

Mudrov, A. I.

2017-08-01

Let g' ⊂ g be a pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces C N-2 ⊂ C N and U q (g') ⊂ U q (g) be a pair of quantum groups with a triangular decomposition U q (g) = U q (g-) U q (g+) U q (h). Let Z q (g, g') be the corresponding step algebra. We assume that its generators are rational trigonometric functions h ∗ → U q (g±). We describe their regularization such that the resulting generators do not vanish for any choice of the weight.

On a new class of completely integrable nonlinear wave equations. I. Infinitely many conservation laws

NASA Astrophysics Data System (ADS)

Nutku, Y.

1985-06-01

We point out a class of nonlinear wave equations which admit infinitely many conserved quantities. These equations are characterized by a pair of exact one-forms. The implication that they are closed gives rise to equations, the characteristics and Riemann invariants of which are readily obtained. The construction of the conservation laws requires the solution of a linear second-order equation which can be reduced to canonical form using the Riemann invariants. The hodograph transformation results in a similar linear equation. We discuss also the symplectic structure and Bäcklund transformations associated with these equations.

How many invariant polynomials are needed to decide local unitary equivalence of qubit states?

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

Maciążek, Tomasz; Faculty of Physics, University of Warsaw, ul. Hoża 69, 00-681 Warszawa; Oszmaniec, Michał

2013-09-15

Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e., by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure.

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.

Equivariant branes and equivariant homological mirror symmetry

NASA Astrophysics Data System (ADS)

Ashwinkumar, Meer; Tan, Meng-Chwan

2018-03-01

We describe supersymmetric A-branes and B-branes in open N =(2 ,2 ) dynamically gauged nonlinear sigma models (GNLSM), placing emphasis on toric manifold target spaces. For a subset of toric manifolds, these equivariant branes have a mirror description as branes in gauged Landau-Ginzburg models with neutral matter. We then study correlation functions in the topological A-twisted version of the GNLSM and identify their values with open Hamiltonian Gromov-Witten invariants. Supersymmetry breaking can occur in the A-twisted GNLSM due to nonperturbative open symplectic vortices, and we canonically Becchi-Rouet-Stora-Tyutin quantize the mirror theory to analyze this phenomenon.

Qualitative and quantitative behaviour of planetary systems; Proceedings of the 3rd Alexander von Humboldt Colloquium on Celestial Mechanics, Ramsau, Austria, Mar. 29-Apr. 4, 1992

NASA Astrophysics Data System (ADS)

Dvorak, R.; Henrard, J.

1993-06-01

Topics addressed include planetary theories, the Sitnikov problem, asteroids, resonance, general dynamical systems, and chaos and stability. Particular attention is given to recent progress in the theory and application of symplectic integrators, a computer-aided analysis of the Sitnikov problem, the chaotic behavior of trajectories for the asteroidal resonances, and the resonant motion in the restricted three-body problem. Also discussed are the second order long-period motion of Hyperion, meteorites from the asteroid 6 Hebe, and least squares parameter estimation in chaotic differential equations.

Symplectic modeling of beam loading in electromagnetic cavities

DOE PAGES

Abell, Dan T.; Cook, Nathan M.; Webb, Stephen D.

2017-05-22

Simulating beam loading in radio frequency accelerating structures is critical for understanding higher-order mode effects on beam dynamics, such as beam break-up instability in energy recovery linacs. Full wave simulations of beam loading in radio frequency structures are computationally expensive, and while reduced models can ignore essential physics, it can be difficult to generalize. Here, we present a self-consistent algorithm derived from the least-action principle which can model an arbitrary number of cavity eigenmodes and with a generic beam distribution. It has been implemented in our new Open Library for Investigating Vacuum Electronics (OLIVE).

Polynomial approximation of Poincare maps for Hamiltonian system

NASA Technical Reports Server (NTRS)

Froeschle, Claude; Petit, Jean-Marc

1992-01-01

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Exponential Methods for the Time Integration of Schroedinger Equation

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

Cano, B.; Gonzalez-Pachon, A.

2010-09-30

We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

Qudit quantum computation on matrix product states with global symmetry

NASA Astrophysics Data System (ADS)

Wang, Dongsheng; Stephen, David; Raussendorf, Robert

Resource states that contain nontrivial symmetry-protected topological order are identified for universal measurement-based quantum computation. Our resource states fall into two classes: one as the qudit generalizations of the qubit cluster state, and the other as the higher-symmetry generalizations of the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) state, namely, with unitary, orthogonal, or symplectic symmetry. The symmetry in cluster states protects information propagation (identity gate), while the higher symmetry in AKLT-type states enables nontrivial gate computation. This work demonstrates a close connection between measurement-based quantum computation and symmetry-protected topological order.

Qudit quantum computation on matrix product states with global symmetry

NASA Astrophysics Data System (ADS)

Wang, Dong-Sheng; Stephen, David T.; Raussendorf, Robert

2017-03-01

Resource states that contain nontrivial symmetry-protected topological order are identified for universal single-qudit measurement-based quantum computation. Our resource states fall into two classes: one as the qudit generalizations of the one-dimensional qubit cluster state, and the other as the higher-symmetry generalizations of the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) state, namely, with unitary, orthogonal, or symplectic symmetry. The symmetry in cluster states protects information propagation (identity gate), while the higher symmetry in AKLT-type states enables nontrivial gate computation. This work demonstrates a close connection between measurement-based quantum computation and symmetry-protected topological order.

Stochastic transport models for mixing in variable-density turbulence

NASA Astrophysics Data System (ADS)

Bakosi, J.; Ristorcelli, J. R.

2011-11-01

In variable-density (VD) turbulent mixing, where very-different- density materials coexist, the density fluctuations can be an order of magnitude larger than their mean. Density fluctuations are non-negligible in the inertia terms of the Navier-Stokes equation which has both quadratic and cubic nonlinearities. Very different mixing rates of different materials give rise to large differential accelerations and some fundamentally new physics that is not seen in constant-density turbulence. In VD flows material mixing is active in a sense far stronger than that applied in the Boussinesq approximation of buoyantly-driven flows: the mass fraction fluctuations are coupled to each other and to the fluid momentum. Statistical modeling of VD mixing requires accounting for basic constraints that are not important in the small-density-fluctuation passive-scalar-mixing approximation: the unit-sum of mass fractions, bounded sample space, and the highly skewed nature of the probability densities become essential. We derive a transport equation for the joint probability of mass fractions, equivalent to a system of stochastic differential equations, that is consistent with VD mixing in multi-component turbulence and consistently reduces to passive scalar mixing in constant-density flows.

The value of seasonal forecasting and crop mix adaptation to climate variability for agriculture under climate change

NASA Astrophysics Data System (ADS)

Choi, H. S.; Schneider, U.; Schmid, E.; Held, H.

2012-04-01

Changes to climate variability and frequency of extreme weather events are expected to impose damages to the agricultural sector. Seasonal forecasting and long range prediction skills have received attention as an option to adapt to climate change because seasonal climate and yield predictions could improve farmers' management decisions. The value of seasonal forecasting skill is assessed with a crop mix adaptation option in Spain where drought conditions are prevalent. Yield impacts of climate are simulated for six crops (wheat, barely, cotton, potato, corn and rice) with the EPIC (Environmental Policy Integrated Climate) model. Daily weather data over the period 1961 to 1990 are used and are generated by the regional climate model REMO as reference period for climate projection. Climate information and its consequent yield variability information are given to the stochastic agricultural sector model to calculate the value of climate information in the agricultural market. Expected consumers' market surplus and producers' revenue is compared with and without employing climate forecast information. We find that seasonal forecasting benefits not only consumers but also producers if the latter adopt a strategic crop mix. This mix differs from historical crop mixes by having higher shares of crops which fare relatively well under climate change. The corresponding value of information is highly sensitive to farmers' crop mix choices.

Coupled effects of vertical mixing and benthic grazing on phytoplankton populations in shallow, turbid estuaries

USGS Publications Warehouse

Koseff, Jeffrey R.; Holen, Jacqueline K.; Monismith, Stephen G.; Cloern, James E.

1993-01-01

Coastal ocean waters tend to have very different patterns of phytoplankton biomass variability from the open ocean, and the connections between physical variability and phytoplankton bloom dynamics are less well established for these shallow systems. Predictions of biological responses to physical variability in these environments is inherently difficult because the recurrent seasonal patterns of mixing are complicated by aperiodic fluctuations in river discharge and the high-frequency components of tidal variability. We might expect, then, less predictable and more complex bloom dynamics in these shallow coastal systems compared with the open ocean. Given this complex and dynamic physical environment, can we develop a quantitative framework to define the physical regimes necessary for bloom inception, and can we identify the important mechanisms of physical-biological coupling that lead to the initiation and termination of blooms in estuaries and shallow coastal waters? Numerical modeling provides one approach to address these questions. Here we present results of simulation experiments with a refined version of Cloern's (1991) model in which mixing processes are treated more realistically to reflect the dynamic nature of turbulence generation in estuaries. We investigated several simple models for the turbulent mixing coefficient. We found that the addition of diurnal tidal variation to Cloern's model greatly reduces biomass growth indicating that variations of mixing on the time scale of hours are crucial. Furthermore, we found that for conditions representative of South San Francisco Bay, numerical simulations only allowed for bloom development when the water column was stratified and when minimal mixing was prescribed in the upper layer. Stratification, however, itself is not sufficient to ensure that a bloom will develop: minimal wind stirring is a further prerequisite to bloom development in shallow turbid estuaries with abundant populations of benthic suspension feeders.

Determining the Effect of the Lunar Nodal Cycle on Tidal Mixing and North Pacific Climate Variability

NASA Astrophysics Data System (ADS)

Ullman, D. J.; Schmittner, A.; Danabasoglu, G.; Norton, N. J.; Müller, M.

2016-02-01

Oscillations in the moon's orbit around the earth modulate regional tidal dissipation with a periodicity of 18.6 years. In regions where the diurnal tidal constituents dominate diapycnal mixing, this Lunar Nodal Cycle (LNC) may be significant enough to influence ocean circulation, sea surface temperature, and climate variability. Such periodicity in the LNC as an external forcing may provide a mechanistic source for Pacific decadal variability (i.e. Pacific Decadal Oscillation, PDO) where diurnal tidal constituents are strong. We have introduced three enhancements to the latest version of the Community Earth System Model (CESM) to better simulate tidal-forced mixing. First, we have produced a sub-grid scale bathymetry scheme that better resolves the vertical distribution of the barotropic energy flux in regions where the native CESM grid does not resolve high spatial-scale bathymetric features. Second, we test a number of alternative barotropic tidal constituent energy flux fields that are derived from various satellite altimeter observations and tidal models. Third, we introduce modulations of the individual diurnal and semi-diurnal tidal constituents, ranging from monthly to decadal periods, as derived from the full lunisolar tidal potential. Using both ocean-only and fully-coupled configurations, we test the influence of these enhancements, particularly the LNC modulations, on ocean mixing and bidecadal climate variability in CESM.

Model reduction method using variable-separation for stochastic saddle point problems

NASA Astrophysics Data System (ADS)

Jiang, Lijian; Li, Qiuqi

2018-02-01

In this paper, we consider a variable-separation (VS) method to solve the stochastic saddle point (SSP) problems. The VS method is applied to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs) in a mixed formulation. The aim of such a technique is to construct a reduced basis approximation of the solution of the SSP problems. The VS method attempts to get a low rank separated representation of the solution for SSP in a systematic enrichment manner. No iteration is performed at each enrichment step. In order to satisfy the inf-sup condition in the mixed formulation, we enrich the separated terms for the primal system variable at each enrichment step. For the SSP problems by regularization or penalty, we propose a more efficient variable-separation (VS) method, i.e., the variable-separation by penalty method. This can avoid further enrichment of the separated terms in the original mixed formulation. The computation of the variable-separation method decomposes into offline phase and online phase. Sparse low rank tensor approximation method is used to significantly improve the online computation efficiency when the number of separated terms is large. For the applications of SSP problems, we present three numerical examples to illustrate the performance of the proposed methods.

Evaluating the impacts of reducing the number of hot mix asphalt plant testing acceptance criteria on mix variability.

DOT National Transportation Integrated Search

2012-11-01

The acceptance testing of Hot Mix Asphalt (HMA) conducted at the HMA production facility is an : important portion of the overall acceptance process used by the Connecticut Department of : Transportation (ConnDOT) for paving projects. In 2004, ConnDO...

Dual Formulations of Mixed Finite Element Methods with Applications

PubMed Central

Gillette, Andrew; Bajaj, Chandrajit

2011-01-01

Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail. PMID:21984841

The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications

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

Mei, Lijie, E-mail: bxhanm@126.com; Wu, Xinyuan, E-mail: xywu@nju.edu.cn

In general, extended Runge–Kutta–Nyström (ERKN) methods are more effective than traditional Runge–Kutta–Nyström (RKN) methods in dealing with oscillatory Hamiltonian systems. However, the theoretical analysis for ERKN methods, such as the order conditions, the symplectic conditions and the symmetric conditions, becomes much more complicated than that for RKN methods. Therefore, it is a bottleneck to construct high-order ERKN methods efficiently. In this paper, we first establish the ERKN group Ω for ERKN methods and the RKN group G for RKN methods, respectively. We then rigorously show that ERKN methods are a natural extension of RKN methods, that is, there exists anmore » epimorphism η of the ERKN group Ω onto the RKN group G. This epimorphism gives a global insight into the structure of the ERKN group by the analysis of its kernel and the corresponding RKN group G. Meanwhile, we establish a particular mapping φ of G into Ω so that each image element is an ideal representative element of the congruence class in Ω. Furthermore, an elementary theoretical analysis shows that this map φ can preserve many structure-preserving properties, such as the order, the symmetry and the symplecticity. From the epimorphism η together with its section φ, we may gain knowledge about the structure of the ERKN group Ω via the RKN group G. In light of the theoretical analysis of this paper, we obtain high-order structure-preserving ERKN methods in an effective way for solving oscillatory Hamiltonian systems. Numerical experiments are carried out and the results are very promising, which strongly support our theoretical analysis presented in this paper.« less

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

NASA Technical Reports Server (NTRS)

Rauch, Kevin P.; Holman, Matthew

1999-01-01

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

Continuum limit and symmetries of the periodic gℓ(1|1) spin chain

NASA Astrophysics Data System (ADS)

Gainutdinov, A. M.; Read, N.; Saleur, H.

2013-06-01

This paper is the first in a series devoted to the study of logarithmic conformal field theories (LCFT) in the bulk. Building on earlier work in the boundary case, our general strategy consists in analyzing the algebraic properties of lattice regularizations (quantum spin chains) of these theories. In the boundary case, a crucial step was the identification of the space of states as a bimodule over the Temperley-Lieb (TL) algebra and the quantum group Uqsℓ(2). The extension of this analysis in the bulk case involves considerable difficulties, since the Uqsℓ(2) symmetry is partly lost, while the TL algebra is replaced by a much richer version (the Jones-Temperley-Lieb — JTL — algebra). Even the simplest case of the gℓ(1|1) spin chain — corresponding to the c=-2 symplectic fermions theory in the continuum limit — presents very rich aspects, which we will discuss in several papers. In this first work, we focus on the symmetries of the spin chain, that is, the centralizer of the JTL algebra in the alternating tensor product of the gℓ(1|1) fundamental representation and its dual. We prove that this centralizer is only a subalgebra of Uqsℓ(2) at q=i that we dub Uqoddsℓ(2). We then begin the analysis of the continuum limit of the JTL algebra: using general arguments about the regularization of the stress-energy tensor, we identify families of JTL elements going over to the Virasoro generators Ln,L in the continuum limit. We then discuss the sℓ(2) symmetry of the (continuum limit) symplectic fermions theory from the lattice and JTL point of view. The analysis of the spin chain as a bimodule over Uqoddsℓ(2) and JTLN is discussed in the second paper of this series.

DYNAMIC STABILITY OF THE SOLAR SYSTEM: STATISTICALLY INCONCLUSIVE RESULTS FROM ENSEMBLE INTEGRATIONS

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

Zeebe, Richard E., E-mail: zeebe@soest.hawaii.edu

Due to the chaotic nature of the solar system, the question of its long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of nearby orbits. Destabilization of the inner planets, leading to close encounters and/or collisions can be initiated through a large increase in Mercury's eccentricity, with a currently assumed likelihood of ∼1%. However, little is known at present about the robustness of this number. Here I report ensemble integrations of the full equations of motion of the eight planets and Pluto over 5 Gyr, including contributions from general relativity. The resultsmore » show that different numerical algorithms lead to statistically different results for the evolution of Mercury's eccentricity (e{sub M}). For instance, starting at present initial conditions (e{sub M}≃0.21), Mercury's maximum eccentricity achieved over 5 Gyr is, on average, significantly higher in symplectic ensemble integrations using heliocentric rather than Jacobi coordinates and stricter error control. In contrast, starting at a possible future configuration (e{sub M}≃0.53), Mercury's maximum eccentricity achieved over the subsequent 500 Myr is, on average, significantly lower using heliocentric rather than Jacobi coordinates. For example, the probability for e{sub M} to increase beyond 0.53 over 500 Myr is >90% (Jacobi) versus only 40%-55% (heliocentric). This poses a dilemma because the physical evolution of the real system—and its probabilistic behavior—cannot depend on the coordinate system or the numerical algorithm chosen to describe it. Some tests of the numerical algorithms suggest that symplectic integrators using heliocentric coordinates underestimate the odds for destabilization of Mercury's orbit at high initial e{sub M}.« less

Quantitative analysis of eyes and other optical systems in linear optics.

PubMed

Harris, William F; Evans, Tanya; van Gool, Radboud D

2017-05-01

To show that 14-dimensional spaces of augmented point P and angle Q characteristics, matrices obtained from the ray transference, are suitable for quantitative analysis although only the latter define an inner-product space and only on it can one define distances and angles. The paper examines the nature of the spaces and their relationships to other spaces including symmetric dioptric power space. The paper makes use of linear optics, a three-dimensional generalization of Gaussian optics. Symmetric 2 × 2 dioptric power matrices F define a three-dimensional inner-product space which provides a sound basis for quantitative analysis (calculation of changes, arithmetic means, etc.) of refractive errors and thin systems. For general systems the optical character is defined by the dimensionally-heterogeneous 4 × 4 symplectic matrix S, the transference, or if explicit allowance is made for heterocentricity, the 5 × 5 augmented symplectic matrix T. Ordinary quantitative analysis cannot be performed on them because matrices of neither of these types constitute vector spaces. Suitable transformations have been proposed but because the transforms are dimensionally heterogeneous the spaces are not naturally inner-product spaces. The paper obtains 14-dimensional spaces of augmented point P and angle Q characteristics. The 14-dimensional space defined by the augmented angle characteristics Q is dimensionally homogenous and an inner-product space. A 10-dimensional subspace of the space of augmented point characteristics P is also an inner-product space. The spaces are suitable for quantitative analysis of the optical character of eyes and many other systems. Distances and angles can be defined in the inner-product spaces. The optical systems may have multiple separated astigmatic and decentred refracting elements. © 2017 The Authors Ophthalmic & Physiological Optics © 2017 The College of Optometrists.

Extracting a mix parameter from 2D radiography of variable density flow

NASA Astrophysics Data System (ADS)

Kurien, Susan; Doss, Forrest; Livescu, Daniel

2017-11-01

A methodology is presented for extracting quantities related to the statistical description of the mixing state from the 2D radiographic image of a flow. X-ray attenuation through a target flow is given by the Beer-Lambert law which exponentially damps the incident beam intensity by a factor proportional to the density, opacity and thickness of the target. By making reasonable assumptions for the mean density, opacity and effective thickness of the target flow, we estimate the contribution of density fluctuations to the attenuation. The fluctuations thus inferred may be used to form the correlation of density and specific-volume, averaged across the thickness of the flow in the direction of the beam. This correlation function, denoted by b in RANS modeling, quantifies turbulent mixing in variable density flows. The scheme is tested using DNS data computed for variable-density buoyancy-driven mixing. We quantify the deficits in the extracted value of b due to target thickness, Atwood number, and modeled noise in the incident beam. This analysis corroborates the proposed scheme to infer the mix parameter from thin targets at moderate to low Atwood numbers. The scheme is then applied to an image of counter-shear flow obtained from experiments at the National Ignition Facility. US Department of Energy.

The sensitivity of primary productivity to intra-seasonal mixed layer variability in the sub-Antarctic Zone of the Atlantic Ocean

NASA Astrophysics Data System (ADS)

Joubert, W. R.; Swart, S.; Tagliabue, A.; Thomalla, S. J.; Monteiro, P. M. S.

2014-03-01

The seasonal cycle of primary productivity is impacted by seasonal and intra-seasonal dynamics of the mixed layer through the changing balance between mixing and buoyancy forcing, which regulates nutrient supply and light availability. Of particular recent interest is the role of synoptic scale events in supplying nutrients, particularly iron, to the euphotic zone in the Sub Antarctic Zone (SAZ), where phytoplankton blooms occur throughout summer. In this study, we present high resolution measurements of net community production (NCP) constrained by ΔO2/Ar ratios, and mixed layer depth (MLD) in the Atlantic SAZ. We found a non-linear relationship between NCP and MLD, with the highest and most variable NCP observed in shallow MLDs (< 45 m). We propose that NCP variability in the SAZ may be driven by alternating states of synoptic-scale deepening of the mixed layer, leading to the entrainment of iron (dFe), followed by restratification, allowing rapid growth in an iron replete, high light environment. Synoptic iron fluxes into the euphotic zone based on water column dFe profiles and high resolution glider MLD data, reveal a potentially significant contribution of "new iron" which could sustain NCP throughout summer. Future process studies will help elaborate these findings further.

Tropical Cyclone Footprint in the Ocean Mixed Layer Observed by Argo in the Northwest Pacific

DTIC Science & Technology

2014-10-25

668. Hu, A., and G. A. Meehl (2009), Effect of the Atlantic hurricanes on the oceanic meridional overturning circulation and heat transport, Geo...atmospheric circulation [Hart et al., 2007]. Several studies, based on observations and modeling, suggest that TC-induced energy input and mixing may play...an important role in climate variability through regulating the oceanic general circulation and its variability [e.g., Emanuel, 2001; Sriver and Huber

Applications of MIDAS regression in analysing trends in water quality

NASA Astrophysics Data System (ADS)

Penev, Spiridon; Leonte, Daniela; Lazarov, Zdravetz; Mann, Rob A.

2014-04-01

We discuss novel statistical methods in analysing trends in water quality. Such analysis uses complex data sets of different classes of variables, including water quality, hydrological and meteorological. We analyse the effect of rainfall and flow on trends in water quality utilising a flexible model called Mixed Data Sampling (MIDAS). This model arises because of the mixed frequency in the data collection. Typically, water quality variables are sampled fortnightly, whereas the rain data is sampled daily. The advantage of using MIDAS regression is in the flexible and parsimonious modelling of the influence of the rain and flow on trends in water quality variables. We discuss the model and its implementation on a data set from the Shoalhaven Supply System and Catchments in the state of New South Wales, Australia. Information criteria indicate that MIDAS modelling improves upon simplistic approaches that do not utilise the mixed data sampling nature of the data.

Clustering "N" Objects into "K" Groups under Optimal Scaling of Variables.

ERIC Educational Resources Information Center

van Buuren, Stef; Heiser, Willem J.

1989-01-01

A method based on homogeneity analysis (multiple correspondence analysis or multiple scaling) is proposed to reduce many categorical variables to one variable with "k" categories. The method is a generalization of the sum of squared distances cluster analysis problem to the case of mixed measurement level variables. (SLD)

77 FR 29644 - Agency Information Collection Activities: Proposed Collection; Comment Request

Federal Register 2010, 2011, 2012, 2013, 2014

2012-05-18

... reliability and construct validity of survey items and composites. (c) Case mix adjustment analysis--Assess the variables that may be considered as case mix adjusters. These preliminary research activities are...

Solvency supervision based on a total balance sheet approach

NASA Astrophysics Data System (ADS)

Pitselis, Georgios

2009-11-01

In this paper we investigate the adequacy of the own funds a company requires in order to remain healthy and avoid insolvency. Two methods are applied here; the quantile regression method and the method of mixed effects models. Quantile regression is capable of providing a more complete statistical analysis of the stochastic relationship among random variables than least squares estimation. The estimated mixed effects line can be considered as an internal industry equation (norm), which explains a systematic relation between a dependent variable (such as own funds) with independent variables (e.g. financial characteristics, such as assets, provisions, etc.). The above two methods are implemented with two data sets.

Conventional Energy and Macronutrient Variables Distort the Accuracy of Children’s Dietary Reports: Illustrative Data from a Validation Study of Effect of Order Prompts

PubMed Central

Baxter, Suzanne Domel; Smith, Albert F.; Hardin, James W.; Nichols, Michele D.

2008-01-01

Objective Validation-study data are used to illustrate that conventional energy and macronutrient (protein, carbohydrate, fat) variables, which disregard accuracy of reported items and amounts, misrepresent reporting accuracy. Reporting-error-sensitive variables are proposed which classify reported items as matches or intrusions, and reported amounts as corresponding or overreported. Methods 58 girls and 63 boys were each observed eating school meals on 2 days separated by ≥4 weeks, and interviewed the morning after each observation day. One interview per child had forward-order (morning-to-evening) prompts; one had reverse-order prompts. Original food-item-level analyses found a sex-x-order prompt interaction for omission rates. Current analyses compared reference (observed) and reported information transformed to energy and macronutrients. Results Using conventional variables, reported amounts were less than reference amounts (ps<0.001; paired t-tests); report rates were higher for the first than second interview for energy, protein, and carbohydrate (ps≤0.049; mixed models). Using reporting-error-sensitive variables, correspondence rates were higher for girls with forward- but boys with reverse-order prompts (ps≤0.041; mixed models); inflation ratios were lower with reverse- than forward-order prompts for energy, carbohydrate, and fat (ps≤0.045; mixed models). Conclusions Conventional variables overestimated reporting accuracy and masked order prompt and sex effects. Reporting-error-sensitive variables are recommended when assessing accuracy for energy and macronutrients in validation studies. PMID:16959308

Quality control analysis : part I : asphaltic concrete.

DOT National Transportation Integrated Search

1964-11-01

This report deals with the statistical evaluation of results from several hot mix plants to determine the pattern of variability with respect to bituminous hot mix characteristics. : Individual tests results when subjected to frequency distribution i...

SMD-based numerical stochastic perturbation theory

NASA Astrophysics Data System (ADS)

Dalla Brida, Mattia; Lüscher, Martin

2017-05-01

The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schrödinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.

Cellular Precipitates Of Iron Oxide in Olivine in a Stratospheric Interplanetary Dust Particle

NASA Technical Reports Server (NTRS)

Rietmeijer, Frans J. M.

1996-01-01

The petrology of a massive olivine-sulphide interplanetary dust particle shows melting of Fe,Ni-sulphide plus complete loss of sulphur and subsequent quenching to a mixture of iron-oxides and Fe,Ni-metal. Oxidation of the fayalite component in olivine produced maghemite discs and cellular intergrowths with olivine and rare andradite-rich garnet. Cellular reactions require no long-range solid-state diffusion and are kinetically favourable during pyrometamorphic oxidation. Local melting of the cellular intergrowths resulted in three dimensional symplectic textures. Dynamic pyrometamorphism of this asteroidal particle occurred at approx. 1100 C during atmospheric entry flash (5-15 s) heating.

Symplectic analysis of three-dimensional Abelian topological gravity

NASA Astrophysics Data System (ADS)

Cartas-Fuentevilla, R.; Escalante, Alberto; Herrera-Aguilar, Alfredo

2017-02-01

A detailed Faddeev-Jackiw quantization of an Abelian topological gravity is performed; we show that this formalism is equivalent and more economical than Dirac's method. In particular, we identify the complete set of constraints of the theory, from which the number of physical degrees of freedom is explicitly computed. We prove that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide with each other. Moreover, we perform the Faddeev-Jackiw analysis of the theory at the chiral point, and the full set of constraints and the generalized Faddeev-Jackiw brackets are constructed. Finally we compare our results with those found in the literature and we discuss some remarks and prospects.

Projective limits of state spaces I. Classical formalism

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2017-01-01

In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski (1977) and Andrzej Okołów (2009, 2013, 2014), which describes the states of a quantum (field) theory as projective families of density matrices. A short reading guide to the series can be found in [27]. The present first paper aims at clarifying the classical structures that underlies this formalism, namely projective limits of symplectic manifolds [27, subsection 2.1]. In particular, this allows us to discuss accurately the issues hindering an easy implementation of the dynamics in this context, and to formulate a strategy for overcoming them [27, subsection 4.1].

Computational tools and lattice design for the PEP-II B-Factory

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

Cai, Y.; Irwin, J.; Nosochkov, Y.

1997-02-01

Several accelerator codes were used to design the PEP-II lattices, ranging from matrix-based codes, such as MAD and DIMAD, to symplectic-integrator codes, such as TRACY and DESPOT. In addition to element-by-element tracking, we constructed maps to determine aberration strengths. Furthermore, we have developed a fast and reliable method (nPB tracking) to track particles with a one-turn map. This new technique allows us to evaluate performance of the lattices on the entire tune-plane. Recently, we designed and implemented an object-oriented code in C++ called LEGO which integrates and expands upon TRACY and DESPOT. {copyright} {ital 1997 American Institute of Physics.}

Computational tools and lattice design for the PEP-II B-Factory

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

Cai Yunhai; Irwin, John; Nosochkov, Yuri

1997-02-01

Several accelerator codes were used to design the PEP-II lattices, ranging from matrix-based codes, such as MAD and DIMAD, to symplectic-integrator codes, such as TRACY and DESPOT. In addition to element-by-element tracking, we constructed maps to determine aberration strengths. Furthermore, we have developed a fast and reliable method (nPB tracking) to track particles with a one-turn map. This new technique allows us to evaluate performance of the lattices on the entire tune-plane. Recently, we designed and implemented an object-oriented code in C++ called LEGO which integrates and expands upon TRACY and DESPOT.

Interpretation of Higher Order Magnetic effects in the Spectra of Transition Metal Ions in Terms of SO(5) and Sp(10)

NASA Astrophysics Data System (ADS)

Hansen, J. E.; Judd, B. R.; Raassen, A. J. J.; Uylings, P. H. M.

1997-04-01

Small discrepancies in the fitted energy levels of the configurations 3dN of transition metal ions are ascribed to effective three-electron magnetic operators yi. Surprisingly it has been found that, of the 16 possible operators with ranks 1 in both spin and orbital spaces, four operators labeled by the irreducible representation (irrep) (11) of SO(5) are sufficient to obtain results which appear to be limited by the errors in the experimental energy levels. An interpretation is given involving products of operators labeled by the irreps of SO(5) and the symplectic group Sp(10).

Point form relativistic quantum mechanics and relativistic SU(6)

NASA Technical Reports Server (NTRS)

Klink, W. H.

1993-01-01

The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.

The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

NASA Astrophysics Data System (ADS)

Giordano, C. M.; Cincotta, P. M.

2018-05-01

In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S', estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S' coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.

Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme

NASA Astrophysics Data System (ADS)

Mandziuk, Margaret; Schlick, Tamar

1995-05-01

The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- ( Δt) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance ( Δt ≈ 7 fs here) leads to instability, and higher-order resonances ( n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.

Hamiltonian structure and Darboux theorem for families of generalized Lotka-Volterra systems

NASA Astrophysics Data System (ADS)

Hernández-Bermejo, Benito; Fairén, Víctor

1998-11-01

This work is devoted to the establishment of a Poisson structure for a format of equations known as generalized Lotka-Volterra systems. These equations, which include the classical Lotka-Volterra systems as a particular case, have been deeply studied in the literature. They have been shown to constitute a whole hierarchy of systems, the characterization of which is made in the context of simple algebra. Our main result is to show that this algebraic structure is completely translatable into the Poisson domain. Important Poisson structures features, such as the symplectic foliation and the Darboux canonical representation, rise as a result of rather simple matrix manipulations.

Lyapunov Exponents of Minimizing Measures for Globally Positive Diffeomorphisms in All Dimensions

NASA Astrophysics Data System (ADS)

Arnaud, M.-C.

2016-05-01

The globally positive diffeomorphisms of the 2 n-dimensional annulus are important because they represent what happens close to a completely elliptic periodic point of a symplectic diffeomorphism where the torsion is positive definite. For these globally positive diffeomorphisms, an Aubry-Mather theory was developed by Garibaldi and Thieullen that provides the existence of some minimizing measures. Using the two Green bundles {G_-} and {G_+} that can be defined along the support of these minimizing measures, we will prove that there is a deep link between: the angle between {G_-} and {G_+} along the support of the considered measure {μ};

Towards a bulk description of higher spin SYK

NASA Astrophysics Data System (ADS)

González, Hernán A.; Grumiller, Daniel; Salzer, Jakob

2018-05-01

We consider on the bulk side extensions of the Sachdev-Ye-Kitaev (SYK) model to Yang-Mills and higher spins. To this end we study generalizations of the Jackiw-Teitelboim (JT) model in the BF formulation. Our main goal is to obtain generalizations of the Schwarzian action, which we achieve in two ways: by considering the on-shell action supplemented by suitable boundary terms compatible with all symmetries, and by applying the Lee-Wald-Zoupas formalism to analyze the symplectic structure of dilaton gravity. We conclude with a discussion of the entropy (including log-corrections from higher spins) and a holographic dictionary for the generalized SYK/JT correspondence.

Variability of the subtropical mode water in the Southwest Pacific

NASA Astrophysics Data System (ADS)

Fernandez, Denise; Sutton, Philip; Bowen, Melissa

2017-09-01

The variability of Subtropical Mode Water (STMW) in the Southwest Pacific is investigated using a 28 year-long time series (1986-2014) of high-resolution expendable bathythermograph data north of New Zealand (PX06) and a shorter time series, the Roemmich-Gilson monthly Argo optimal interpolation for the 2004-2014 period. The variability in STMW inventories is compared to the variability in air-sea heat fluxes, mixed layer depths and transport of the East Auckland Current (EAUC) to assess both the atmospheric and oceanic roles influencing the formation and decay of STMW. The STMW north of New Zealand has a short lifespan with little persistence of the water mass from 1 year to the next one. Deeper mixed layers and negative anomalies in surface heat fluxes are correlated with increased formation of STMW. The heat content of the STMW layer is anticorrelated with inventories, particularly during the El Niño years. This suggests that large volumes of STMW are coincident with cooler conditions in the prior winter and less oceanic heat storage. There is significant seasonal and interannual variability in STMW inventories, however there are no trends in STMW properties, including its core layer temperature over the last decade. The variability of the winter EAUC transport is highly correlated with the STMW inventories and thermocline depth in the following spring, suggesting ocean dynamics deepen the thermocline and precondition for deeper mixed layers.

Selection of latent variables for multiple mixed-outcome models

PubMed Central

ZHOU, LING; LIN, HUAZHEN; SONG, XINYUAN; LI, YI

2014-01-01

Latent variable models have been widely used for modeling the dependence structure of multiple outcomes data. However, the formulation of a latent variable model is often unknown a priori, the misspecification will distort the dependence structure and lead to unreliable model inference. Moreover, multiple outcomes with varying types present enormous analytical challenges. In this paper, we present a class of general latent variable models that can accommodate mixed types of outcomes. We propose a novel selection approach that simultaneously selects latent variables and estimates parameters. We show that the proposed estimator is consistent, asymptotically normal and has the oracle property. The practical utility of the methods is confirmed via simulations as well as an application to the analysis of the World Values Survey, a global research project that explores peoples’ values and beliefs and the social and personal characteristics that might influence them. PMID:27642219

Concurrent generation of multivariate mixed data with variables of dissimilar types.

PubMed

Amatya, Anup; Demirtas, Hakan

2016-01-01

Data sets originating from wide range of research studies are composed of multiple variables that are correlated and of dissimilar types, primarily of count, binary/ordinal and continuous attributes. The present paper builds on the previous works on multivariate data generation and develops a framework for generating multivariate mixed data with a pre-specified correlation matrix. The generated data consist of components that are marginally count, binary, ordinal and continuous, where the count and continuous variables follow the generalized Poisson and normal distributions, respectively. The use of the generalized Poisson distribution provides a flexible mechanism which allows under- and over-dispersed count variables generally encountered in practice. A step-by-step algorithm is provided and its performance is evaluated using simulated and real-data scenarios.

Probe-specific mixed-model approach to detect copy number differences using multiplex ligation-dependent probe amplification (MLPA)

PubMed Central

González, Juan R; Carrasco, Josep L; Armengol, Lluís; Villatoro, Sergi; Jover, Lluís; Yasui, Yutaka; Estivill, Xavier

2008-01-01

Background MLPA method is a potentially useful semi-quantitative method to detect copy number alterations in targeted regions. In this paper, we propose a method for the normalization procedure based on a non-linear mixed-model, as well as a new approach for determining the statistical significance of altered probes based on linear mixed-model. This method establishes a threshold by using different tolerance intervals that accommodates the specific random error variability observed in each test sample. Results Through simulation studies we have shown that our proposed method outperforms two existing methods that are based on simple threshold rules or iterative regression. We have illustrated the method using a controlled MLPA assay in which targeted regions are variable in copy number in individuals suffering from different disorders such as Prader-Willi, DiGeorge or Autism showing the best performace. Conclusion Using the proposed mixed-model, we are able to determine thresholds to decide whether a region is altered. These threholds are specific for each individual, incorporating experimental variability, resulting in improved sensitivity and specificity as the examples with real data have revealed. PMID:18522760

The design of control system of livestock feeding processing

NASA Astrophysics Data System (ADS)

Sihombing, Juna; Napitupulu, Humala L.; Hidayati, Juliza

2018-03-01

PT. XYZ is a company that produces animal feed. One type of animal feed produced is 105 ISA P. In carrying out its production process, PT. XYZ faces the problem of rejected feed amounts during 2014 to June 2015 due to the amount of animal feed that exceeds the standard feed quality of 13% of moisture content and 3% for ash content. Therefore, the researchers analyzed the relationship between factors affecting the quality and extent of damage by using regression and correlation and determine the optimum value of each processing process. Analysis results found that variables affecting product quality are mixing time, steam conditioning temperature and cooling time. The most dominant variable affecting the product moisture content is mixing time with the correlation coefficient of (0.7959) and the most dominant variable affecting the ash content of the product during the processing is mixing time with the correlation coefficient of (0.8541). The design of the proposed product processing control is to run the product processing process with mixing time 235 seconds, steam conditioning temperature 87 0C and cooling time 192 seconds. Product quality 105 ISA P obtained by using this design is with 12.16% moisture content and ash content of 2.59%.

A Priori Subgrid Scale Modeling for a Droplet Laden Temporal Mixing Layer

NASA Technical Reports Server (NTRS)

Okongo, Nora; Bellan, Josette

2000-01-01

Subgrid analysis of a transitional temporal mixing layer with evaporating droplets has been performed using a direct numerical simulation (DNS) database. The DNS is for a Reynolds number (based on initial vorticity thickness) of 600, with droplet mass loading of 0.2. The gas phase is computed using a Eulerian formulation, with Lagrangian droplet tracking. Since Large Eddy Simulation (LES) of this flow requires the computation of unfiltered gas-phase variables at droplet locations from filtered gas-phase variables at the grid points, it is proposed to model these by assuming the gas-phase variables to be given by the filtered variables plus a correction based on the filtered standard deviation, which can be computed from the sub-grid scale (SGS) standard deviation. This model predicts unfiltered variables at droplet locations better than simply interpolating the filtered variables. Three methods are investigated for modeling the SGS standard deviation: Smagorinsky, gradient and scale-similarity. When properly calibrated, the gradient and scale-similarity methods give results in excellent agreement with the DNS.

Quantification of the inherent uncertainty in the relaxation modulus and creep compliance of asphalt mixes

NASA Astrophysics Data System (ADS)

Kassem, Hussein A.; Chehab, Ghassan R.; Najjar, Shadi S.

2017-08-01

Advanced material characterization of asphalt concrete is essential for realistic and accurate performance prediction of flexible pavements. However, such characterization requires rigorous testing regimes that involve mechanical testing of a large number of laboratory samples at various conditions and set-ups. Advanced measurement instrumentation in addition to meticulous and accurate data analysis and analytical representation are also of high importance. Such steps as well as the heterogeneous nature of asphalt concrete (AC) constitute major factors of inherent variability. Thus, it is imperative to model and quantify the variability of the needed asphalt material's properties, mainly the linear viscoelastic response functions such as: relaxation modulus, E(t), and creep compliance, D(t). The objective of this paper is to characterize the inherent uncertainty of both E(t) and D(t) over the time domain of their master curves. This is achieved through a probabilistic framework using Monte Carlo simulations and First Order approximations, utilizing E^{*} data for six AC mixes with at least eight replicates per mix. The study shows that the inherent variability, presented by the coefficient of variation (COV), in E(t) and D(t) is low at small reduced times, and increases with the increase in reduced time. At small reduced times, the COV in E(t) and D(t) are similar in magnitude; however, differences become significant at large reduced times. Additionally, the probability distributions and COVs of E(t) and D(t) are mix dependent. Finally, a case study is considered in which the inherent uncertainty in D(t) is forward propagated to assess the effect of variability on the predicted number of cycles to fatigue failure of an asphalt mix.

Variation in nutrients formulated and nutrients supplied on 5 California dairies.

PubMed

Rossow, H A; Aly, S S

2013-01-01

Computer models used in ration formulation assume that nutrients supplied by a ration formulation are the same as the nutrients presented in front of the cow in the final ration. Deviations in nutrients due to feed management effects such as dry matter changes (i.e., rain), loading, mixing, and delivery errors are assumed to not affect delivery of nutrients to the cow and her resulting milk production. To estimate how feed management affects nutrients supplied to the cow and milk production, and determine if nutrients can serve as indexes of feed management practices, weekly total mixed ration samples were collected and analyzed for 4 pens (close-up cows, fresh cows, high-milk-producing, and low-milk-producing cows, if available) for 7 to 12 wk on 5 commercial California dairies. Differences among nutrient analyses from these samples and nutrients from the formulated rations were analyzed by PROC MIXED of SAS (SAS Institute Inc., Cary, NC). Milk fat and milk protein percentages did not vary as much [coefficient of variation (CV) = 18 to 33%] as milk yield (kg; CV = 16 to 47 %) across all dairies and pens. Variability in nutrients delivered were highest for macronutrient fat (CV = 22%), lignin (CV = 15%), and ash (CV = 11%) percentages and micronutrients Fe (mg/kg; CV = 48%), Na (%; CV = 42%), and Zn (mg/kg; CV = 38%) for the milking pens across all dairies. Partitioning of the variability in random effects of nutrients delivered and intraclass correlation coefficients showed that variability in lignin percentage of TMR had the highest correlation with variability in milk yield and milk fat percentage, followed by fat and crude protein percentages. But, variability in ash, fat, and lignin percentages of total mixed ration had the highest correlation with variability in milk protein percentage. Therefore, lignin, fat, and ash may be the best indices of feed management to include effects of variability in nutrients on variability in milk yield, milk fat, and milk protein percentages in ration formulation models. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Spatial Variability of Sources and Mixing State of Atmospheric Particles in a Metropolitan Area.

PubMed

Ye, Qing; Gu, Peishi; Li, Hugh Z; Robinson, Ellis S; Lipsky, Eric; Kaltsonoudis, Christos; Lee, Alex K Y; Apte, Joshua S; Robinson, Allen L; Sullivan, Ryan C; Presto, Albert A; Donahue, Neil M

2018-05-30

Characterizing intracity variations of atmospheric particulate matter has mostly relied on fixed-site monitoring and quantifying variability in terms of different bulk aerosol species. In this study, we performed ground-based mobile measurements using a single-particle mass spectrometer to study spatial patterns of source-specific particles and the evolution of particle mixing state in 21 areas in the metropolitan area of Pittsburgh, PA. We selected sampling areas based on traffic density and restaurant density with each area ranging from 0.2 to 2 km 2 . Organics dominate particle composition in all of the areas we sampled while the sources of organics differ. The contribution of particles from traffic and restaurant cooking varies greatly on the neighborhood scale. We also investigate how primary and aged components in particles mix across the urban scale. Lastly we quantify and map the particle mixing state for all areas we sampled and discuss the overall pattern of mixing state evolution and its implications. We find that in the upwind and downwind of the urban areas, particles are more internally mixed while in the city center, particle mixing state shows large spatial heterogeneity that is mostly driven by emissions. This study is to our knowledge, the first study to perform fine spatial scale mapping of particle mixing state using ground-based mobile measurement and single-particle mass spectrometry.

Interannual control of plankton communities by deep winter mixing and prey/predator interactions in the NW Mediterranean: Results from a 30-year 3D modeling study

NASA Astrophysics Data System (ADS)

Auger, P. A.; Ulses, C.; Estournel, C.; Stemmann, L.; Somot, S.; Diaz, F.

2014-05-01

A realistic modeling approach is designed to address the role of winter mixing on the interannual variability of plankton dynamics in the north-western (NW) Mediterranean basin. For the first time, a high-resolution coupled hydrodynamic-biogeochemical model (Eco3m-S) covering a 30-year period (1976-2005) is validated on available in situ and satellite data for the NW Mediterranean. In this region, cold, dry winds in winter often lead to deep convection and strong upwelling of nutrients into the euphotic layer. High nutrient contents at the end of winter then support the development of a strong spring bloom of phytoplankton. Model results indicate that annual primary production is not affected by winter mixing due to seasonal balance (minimum in winter and maximum in spring). However, the total annual water column-integrated phytoplankton biomass appears to be favored by winter mixing because zooplankton grazing activity is low in winter and early spring. This reduced grazing is explained here by the rarefaction of prey due to both light limitation and the effect of mixing-induced dilution on prey/predator interactions. A negative impact of winter mixing on winter zooplankton biomass is generally simulated except for mesozooplankton. This difference is assumed to stem from the lower parameterized mortality, top trophic position and detritivorous diet of mesozooplankton in the model. Moreover, model suggests that the variability of annual mesozooplankton biomass is principally modulated by the effects of winter mixing on winter biomass. Thus, interannual variability of winter nutrient contents in the euphotic layer, resulting from winter mixing, would control spring primary production and thus annual mesozooplankton biomass. Our results show a bottom-up control of mesozooplankton communities, as observed at a coastal location of the Ligurian Sea.

Mixed-severity fire regimes in the northern Rocky Mountains: consequences of fire exclusion and options for the future

Treesearch

Stephen F. Arno; David J. Parsons; Robert E. Keane

2000-01-01

Findings from fire history studies have increasingly indicated that many forest ecosystems in the northern Rocky Mountains were shaped by mixed-severity fire regimes, characterized by fires of variable severities at intervals averaging between about 30 and 100 years. Perhaps because mixed-severity fire regimes and their resulting vegetational patterns are difficult to...

Mixed effects versus fixed effects modelling of binary data with inter-subject variability.

PubMed

Murphy, Valda; Dunne, Adrian

2005-04-01

The question of whether or not a mixed effects model is required when modelling binary data with inter-subject variability and within subject correlation was reported in this journal by Yano et al. (J. Pharmacokin. Pharmacodyn. 28:389-412 [2001]). That report used simulation experiments to demonstrate that, under certain circumstances, the use of a fixed effects model produced more accurate estimates of the fixed effect parameters than those produced by a mixed effects model. The Laplace approximation to the likelihood was used when fitting the mixed effects model. This paper repeats one of those simulation experiments, with two binary observations recorded for every subject, and uses both the Laplace and the adaptive Gaussian quadrature approximations to the likelihood when fitting the mixed effects model. The results show that the estimates produced using the Laplace approximation include a small number of extreme outliers. This was not the case when using the adaptive Gaussian quadrature approximation. Further examination of these outliers shows that they arise in situations in which the Laplace approximation seriously overestimates the likelihood in an extreme region of the parameter space. It is also demonstrated that when the number of observations per subject is increased from two to three, the estimates based on the Laplace approximation no longer include any extreme outliers. The root mean squared error is a combination of the bias and the variability of the estimates. Increasing the sample size is known to reduce the variability of an estimator with a consequent reduction in its root mean squared error. The estimates based on the fixed effects model are inherently biased and this bias acts as a lower bound for the root mean squared error of these estimates. Consequently, it might be expected that for data sets with a greater number of subjects the estimates based on the mixed effects model would be more accurate than those based on the fixed effects model. This is borne out by the results of a further simulation experiment with an increased number of subjects in each set of data. The difference in the interpretation of the parameters of the fixed and mixed effects models is discussed. It is demonstrated that the mixed effects model and parameter estimates can be used to estimate the parameters of the fixed effects model but not vice versa.

Density-ratio effects on buoyancy-driven variable-density turbulent mixing

NASA Astrophysics Data System (ADS)

Aslangil, Denis; Livescu, Daniel; Banerjee, Arindam

2017-11-01

Density-ratio effects on the turbulent mixing of two incompressible, miscible fluids with different densities subject to constant acceleration are studied by means of high-resolution Direct Numerical Simulations. In a triply periodic domain, turbulence is generated by stirring in response to the differential buoyancy forces within the flow. Later, as the fluids become molecularly mixed, dissipation starts to overcome turbulence generation by bouyancy. Thus, the flow evolution includes both turbulence growth and decay, and it displays features present in the core region of the mixing layer of the Rayleigh-Taylor as well as Richtmyer-Meshkov instabilities. We extend the previous studies by investigating a broad range of density-ratio, from 1-14.4:1, corresponding to Atwood numbers of 0.05-0.87. Here, we focus on the Atwood number dependence of mixing-efficiency, that is defined based on the energy-conversion ratios from potential energy to total and turbulent kinetic energies, the decay characteristics of buoyancy-assisted variable-density homogeneous turbulence, and the effects of high density-ratios on the turbulence structure and mixing process. Authors acknowledge financial support from DOE-SSAA (DE-NA0003195) and NSF CAREER (#1453056) awards.

Variable optical delay using population oscillation and four-wave-mixing in semiconductor optical amplifiers.

PubMed

Su, Hui; Kondratko, Piotr; Chuang, Shun L

2006-05-29

We investigate variable optical delay of a microwave modulated optical beam in semiconductor optical amplifier/absorber waveguides with population oscillation (PO) and nearly degenerate four-wave-mixing (NDFWM) effects. An optical delay variable between 0 and 160 ps with a 1.0 GHz bandwidth is achieved in an InGaAsP/InP semiconductor optical amplifier (SOA) and shown to be electrically and optically controllable. An analytical model of optical delay is developed and found to agree well with the experimental data. Based on this model, we obtain design criteria to optimize the delay-bandwidth product of the optical delay in semiconductor optical amplifiers and absorbers.

Variable prospective financing in the Danish hospital sector and the development of a Danish case-mix system.

PubMed

Ankjaer-Jensen, Anni; Rosling, Pernille; Bilde, Lone

2006-08-01

This article aims to describe and assess the Danish case-mix system, the cost accounting applied in setting national tariffs and the introduction of variable, prospective payment in the Danish hospital sector. The tariffs are calculated as a national average from hospital data gathered in a national cost database. However, uncertainty, mainly resulting from the definition of cost centres at the individual hospital, implies that the cost weights may not fully reflect the hospital treatment cost. As variable prospective payment of hospitals currently only applies to 20% of a hospital's budget, the incentives and the effects on productivity, quality and equality are still limited.

A joint modeling and estimation method for multivariate longitudinal data with mixed types of responses to analyze physical activity data generated by accelerometers.

PubMed

Li, Haocheng; Zhang, Yukun; Carroll, Raymond J; Keadle, Sarah Kozey; Sampson, Joshua N; Matthews, Charles E

2017-11-10

A mixed effect model is proposed to jointly analyze multivariate longitudinal data with continuous, proportion, count, and binary responses. The association of the variables is modeled through the correlation of random effects. We use a quasi-likelihood type approximation for nonlinear variables and transform the proposed model into a multivariate linear mixed model framework for estimation and inference. Via an extension to the EM approach, an efficient algorithm is developed to fit the model. The method is applied to physical activity data, which uses a wearable accelerometer device to measure daily movement and energy expenditure information. Our approach is also evaluated by a simulation study. Copyright © 2017 John Wiley & Sons, Ltd.

Features of Red Sea Water Masses

NASA Astrophysics Data System (ADS)

Kartadikaria, Aditya; Hoteit, Ibrahim

2015-04-01

Features of Red Sea water mass can be divided into three types but best to be grouped into two different classes that are split at the potential density line σθ=27.4. The surface water (0-50 m) and the intermediate water (50-200 m) have nearly identical types of water mass. They appear as a maxima salinity layer for the water mass that has σθ > 26.0, and as a minimum salinity layer for water mass that has σθ < 26.0. These types of water masses are strongly affected by mixing that is controlled by seasonal variability, fresh water intrusion of the Gulf of Aden Intermediate Water (GAIW), and eddies variability. Two types of mixing; isopycnal and diapycnal mixing are part of important physical phenomena that explain the change of water mass in the Red Sea. The isopycnal mixing occurs at the neutral potential density line, connecting the Red Sea with its adjacent channel, the Gulf of Aden. Diapycnal mixing is found as a dominant mixing mode in the surface of the Red Sea Water and mainly due to energetic eddy activity. Density gradients, across which diapycnal mixing occurs, in the Red Sea are mainly due to large variations in salinity. The isolation of an extreme haline water mass below the thermocline contributes to the generation of the latitudinal shift and low diapycnal mixing. This finding further explains the difference of spatial kinetic mixing between the RSW and the Indian Ocean basin.

Water sources and mixing in riparian wetlands revealed by tracers and geospatial analysis.

PubMed

Lessels, Jason S; Tetzlaff, Doerthe; Birkel, Christian; Dick, Jonathan; Soulsby, Chris

2016-01-01

Mixing of waters within riparian zones has been identified as an important influence on runoff generation and water quality. Improved understanding of the controls on the spatial and temporal variability of water sources and how they mix in riparian zones is therefore of both fundamental and applied interest. In this study, we have combined topographic indices derived from a high-resolution Digital Elevation Model (DEM) with repeated spatially high-resolution synoptic sampling of multiple tracers to investigate such dynamics of source water mixing. We use geostatistics to estimate concentrations of three different tracers (deuterium, alkalinity, and dissolved organic carbon) across an extended riparian zone in a headwater catchment in NE Scotland, to identify spatial and temporal influences on mixing of source waters. The various biogeochemical tracers and stable isotopes helped constrain the sources of runoff and their temporal dynamics. Results show that spatial variability in all three tracers was evident in all sampling campaigns, but more pronounced in warmer dryer periods. The extent of mixing areas within the riparian area reflected strong hydroclimatic controls and showed large degrees of expansion and contraction that was not strongly related to topographic indices. The integrated approach of using multiple tracers, geospatial statistics, and topographic analysis allowed us to classify three main riparian source areas and mixing zones. This study underlines the importance of the riparian zones for mixing soil water and groundwater and introduces a novel approach how this mixing can be quantified and the effect on the downstream chemistry be assessed.

Discrete-continuous variable structural synthesis using dual methods

NASA Technical Reports Server (NTRS)

Schmit, L. A.; Fleury, C.

1980-01-01

Approximation concepts and dual methods are extended to solve structural synthesis problems involving a mix of discrete and continuous sizing type of design variables. Pure discrete and pure continuous variable problems can be handled as special cases. The basic mathematical programming statement of the structural synthesis problem is converted into a sequence of explicit approximate primal problems of separable form. These problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple nonnegativity constraints on the dual variables. A newly devised gradient projection type of algorithm called DUAL 1, which includes special features for handling dual function gradient discontinuities that arise from the discrete primal variables, is used to find the solution of each dual problem. Computational implementation is accomplished by incorporating the DUAL 1 algorithm into the ACCESS 3 program as a new optimizer option. The power of the method set forth is demonstrated by presenting numerical results for several example problems, including a pure discrete variable treatment of a metallic swept wing and a mixed discrete-continuous variable solution for a thin delta wing with fiber composite skins.

Small area estimation for semicontinuous data.

PubMed

Chandra, Hukum; Chambers, Ray

2016-03-01

Survey data often contain measurements for variables that are semicontinuous in nature, i.e. they either take a single fixed value (we assume this is zero) or they have a continuous, often skewed, distribution on the positive real line. Standard methods for small area estimation (SAE) based on the use of linear mixed models can be inefficient for such variables. We discuss SAE techniques for semicontinuous variables under a two part random effects model that allows for the presence of excess zeros as well as the skewed nature of the nonzero values of the response variable. In particular, we first model the excess zeros via a generalized linear mixed model fitted to the probability of a nonzero, i.e. strictly positive, value being observed, and then model the response, given that it is strictly positive, using a linear mixed model fitted on the logarithmic scale. Empirical results suggest that the proposed method leads to efficient small area estimates for semicontinuous data of this type. We also propose a parametric bootstrap method to estimate the MSE of the proposed small area estimator. These bootstrap estimates of the MSE are compared to the true MSE in a simulation study. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Influence of bulk microphysics schemes upon Weather Research and Forecasting (WRF) version 3.6.1 nor'easter simulations

NASA Astrophysics Data System (ADS)

Nicholls, Stephen D.; Decker, Steven G.; Tao, Wei-Kuo; Lang, Stephen E.; Shi, Jainn J.; Mohr, Karen I.

2017-03-01

This study evaluated the impact of five single- or double-moment bulk microphysics schemes (BMPSs) on Weather Research and Forecasting model (WRF) simulations of seven intense wintertime cyclones impacting the mid-Atlantic United States; 5-day long WRF simulations were initialized roughly 24 h prior to the onset of coastal cyclogenesis off the North Carolina coastline. In all, 35 model simulations (five BMPSs and seven cases) were run and their associated microphysics-related storm properties (hydrometer mixing ratios, precipitation, and radar reflectivity) were evaluated against model analysis and available gridded radar and ground-based precipitation products. Inter-BMPS comparisons of column-integrated mixing ratios and mixing ratio profiles reveal little variability in non-frozen hydrometeor species due to their shared programming heritage, yet their assumptions concerning snow and graupel intercepts, ice supersaturation, snow and graupel density maps, and terminal velocities led to considerable variability in both simulated frozen hydrometeor species and radar reflectivity. WRF-simulated precipitation fields exhibit minor spatiotemporal variability amongst BMPSs, yet their spatial extent is largely conserved. Compared to ground-based precipitation data, WRF simulations demonstrate low-to-moderate (0.217-0.414) threat scores and a rainfall distribution shifted toward higher values. Finally, an analysis of WRF and gridded radar reflectivity data via contoured frequency with altitude diagrams (CFADs) reveals notable variability amongst BMPSs, where better performing schemes favored lower graupel mixing ratios and better underlying aggregation assumptions.

Influence of Bulk Microphysics Schemes upon Weather Research and Forecasting (WRF) Version 3.6.1 Nor'easter Simulations.

PubMed

Nicholls, Stephen D; Decker, Steven G; Tao, Wei-Kuo; Lang, Stephen E; Shi, Jainn J; Mohr, Karen I

2017-01-01

This study evaluated the impact of five, single- or double- moment bulk microphysics schemes (BMPSs) on Weather Research and Forecasting model (WRF) simulations of seven, intense winter time cyclones impacting the Mid-Atlantic United States. Five-day long WRF simulations were initialized roughly 24 hours prior to the onset of coastal cyclogenesis off the North Carolina coastline. In all, 35 model simulations (5 BMPSs and seven cases) were run and their associated microphysics-related storm properties (hydrometer mixing ratios, precipitation, and radar reflectivity) were evaluated against model analysis and available gridded radar and ground-based precipitation products. Inter-BMPS comparisons of column-integrated mixing ratios and mixing ratio profiles reveal little variability in non-frozen hydrometeor species due to their shared programming heritage, yet their assumptions concerning snow and graupel intercepts, ice supersaturation, snow and graupel density maps, and terminal velocities lead to considerable variability in both simulated frozen hydrometeor species and radar reflectivity. WRF-simulated precipitation fields exhibit minor spatio-temporal variability amongst BMPSs, yet their spatial extent is largely conserved. Compared to ground-based precipitation data, WRF-simulations demonstrate low-to-moderate (0.217-0.414) threat scores and a rainfall distribution shifted toward higher values. Finally, an analysis of WRF and gridded radar reflectivity data via contoured frequency with altitude (CFAD) diagrams reveals notable variability amongst BMPSs, where better performing schemes favored lower graupel mixing ratios and better underlying aggregation assumptions.

Influence of Bulk Microphysics Schemes upon Weather Research and Forecasting (WRF) Version 3.6.1 Nor'easter Simulations

PubMed Central

Nicholls, Stephen D.; Decker, Steven G.; Tao, Wei-Kuo; Lang, Stephen E.; Shi, Jainn J.; Mohr, Karen I.

2018-01-01

This study evaluated the impact of five, single- or double- moment bulk microphysics schemes (BMPSs) on Weather Research and Forecasting model (WRF) simulations of seven, intense winter time cyclones impacting the Mid-Atlantic United States. Five-day long WRF simulations were initialized roughly 24 hours prior to the onset of coastal cyclogenesis off the North Carolina coastline. In all, 35 model simulations (5 BMPSs and seven cases) were run and their associated microphysics-related storm properties (hydrometer mixing ratios, precipitation, and radar reflectivity) were evaluated against model analysis and available gridded radar and ground-based precipitation products. Inter-BMPS comparisons of column-integrated mixing ratios and mixing ratio profiles reveal little variability in non-frozen hydrometeor species due to their shared programming heritage, yet their assumptions concerning snow and graupel intercepts, ice supersaturation, snow and graupel density maps, and terminal velocities lead to considerable variability in both simulated frozen hydrometeor species and radar reflectivity. WRF-simulated precipitation fields exhibit minor spatio-temporal variability amongst BMPSs, yet their spatial extent is largely conserved. Compared to ground-based precipitation data, WRF-simulations demonstrate low-to-moderate (0.217–0.414) threat scores and a rainfall distribution shifted toward higher values. Finally, an analysis of WRF and gridded radar reflectivity data via contoured frequency with altitude (CFAD) diagrams reveals notable variability amongst BMPSs, where better performing schemes favored lower graupel mixing ratios and better underlying aggregation assumptions. PMID:29697705

Influence of Bulk Microphysics Schemes upon Weather Research and Forecasting (WRF) Version 3.6.1 Nor'easter Simulations

NASA Technical Reports Server (NTRS)

Nicholls, Stephen D.; Decker, Steven G.; Tao, Wei-Kuo; Lang, Stephen E.; Shi, Jainn J.; Mohr, Karen Irene

2017-01-01

This study evaluated the impact of five single- or double-moment bulk microphysics schemes (BMPSs) on Weather Research and Forecasting model (WRF) simulations of seven intense wintertime cyclones impacting the mid-Atlantic United States; 5-day long WRF simulations were initialized roughly 24 hours prior to the onset of coastal cyclogenesis off the North Carolina coastline. In all, 35 model simulations (five BMPSs and seven cases) were run and their associated microphysics-related storm properties (hydrometer mixing ratios, precipitation, and radar reflectivity) were evaluated against model analysis and available gridded radar and ground-based precipitation products. Inter-BMPS comparisons of column-integrated mixing ratios and mixing ratio profiles reveal little variability in non-frozen hydrometeor species due to their shared programming heritage, yet their assumptions concerning snow and graupel intercepts, ice supersaturation, snow and graupel density maps, and terminal velocities led to considerable variability in both simulated frozen hydrometeor species and radar reflectivity. WRF-simulated precipitation fields exhibit minor spatiotemporal variability amongst BMPSs, yet their spatial extent is largely conserved. Compared to ground-based precipitation data, WRF simulations demonstrate low-to-moderate (0.217 to 0.414) threat scores and a rainfall distribution shifted toward higher values. Finally, an analysis of WRF and gridded radar reflectivity data via contoured frequency with altitude (CFAD) diagrams reveals notable variability amongst BMPSs, where better performing schemes favored lower graupel mixing ratios and better underlying aggregation assumptions.

Surface Salinity Variability in the North Atlantic During Recent Decades

NASA Technical Reports Server (NTRS)

Haekkinen, Sirpa

2001-01-01

The sea surface salinity (SSS) variability in the North Atlantic is investigated using numerical model simulations for the last 50 years based on atmospheric forcing variability from Comprehensive Atmosphere Ocean Data Set (COADS) and National Center for Environmental Prediction / National Center for Atmospheric Research (NCEP/NCAR) Reanalysis. The largest interannual and longer term variability occurs in two regions: the Labrador Sea and the North Equatorial Countercurrent (NECC) region. In both regions the seasonality of the surface salinity variability is prominent with the maximum standard deviation occurring in the summer/fall period. In the Labrador Sea the summer SSS anomalies far exceed those of wintertime in amplitude. The interannual SSS variability in the subpolar gyre can be attributed to two factors: excess ice melt and heat flux (i.e. deep mixing) variations. On the other hand, heat flux variability can also lead to meridional overturning changes on decadal time scales such that weak overturning is manifested in fresh surface conditions in the subpolar gyre. The overturning changes also influence the NECC region SSS variability. Moreover, the subpolar freshening events are expected to occur during the negative phase of North Atlantic Oscillation which is associated with a weak wintertime surface heat loss in the subpolar gyre. No excess sea ice melt or precipitation is necessary for the formation of the fresh anomalies, because with the lack of wide-spread deep mixing, the fresh water that would be expected based on climatology, would accumulate at the surface. Thus, the fresh water 'conveyor' in the Atlantic operates via the overturning circulation such that deep mixing inserts fresh water while removing heat from the water column.

Fluid mixing in droplet-based microfluidics with T junction and convergent-divergent sinusoidal microchannels.

PubMed

Yang, Li; Li, Shanshan; Liu, Jixiao; Cheng, Jingmeng

2018-02-01

To explore and utilize the advantages of droplet-based microfluidics, hydrodynamics, and mixing process within droplets traveling though the T junction channel and convergent-divergent sinusoidal microchannels are studied by numerical simulations and experiments, respectively. In the T junction channel, the mixing efficiency is significantly influenced by the twirling effect, which controls the initial distributions of the mixture during the droplet formation stage. Therefore, the internal recirculating flow can create a convection mechanism, thus improving mixing. The twirling effect is noticeably influenced by the velocity of the continuous phase; in the sinusoidal channel, the Dean vortices and droplet deformation are induced by centrifugal force and alternative velocity gradient, thus enhancing the mixing efficiency. The best mixing occurred when the droplet size is comparable with the channel width. Finally, we propose a unique optimized structure, which includes a T junction inlet joined to a sinusoidal channel. In this structure, the mixing of fluids in the droplets follows two routes: One is the twirling effect and symmetric recirculation flow in the straight channel. The other is the asymmetric recirculation and droplet deformation in the winding and variable cross-section. Among the three structures, the optimized structure has the best mixing efficiency at the shortest mixing time (0.25 ms). The combination of the twirling effect, variable cross-section effect, and Dean vortices greatly intensifies the chaotic flow. This study provides the insight of the mixing process and may benefit the design and operations of droplet-based microfluidics. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Small-scale spatial variability of soil microbial community composition and functional diversity in a mixed forest

NASA Astrophysics Data System (ADS)

Wang, Qiufeng; Tian, Jing; Yu, Guirui

2014-05-01

Patterns in the spatial distribution of organisms provide important information about mechanisms that regulate the diversity and complexity of soil ecosystems. Therefore, information on spatial distribution of microbial community composition and functional diversity is urgently necessary. The spatial variability on a 26×36 m plot and vertical distribution (0-10 cm and 10-20 cm) of soil microbial community composition and functional diversity were studied in a natural broad-leaved Korean pine (Pinus koraiensis) mixed forest soil in Changbai Mountain. The phospholipid fatty acid (PLFA) pattern was used to characterize the soil microbial community composition and was compared with the community substrate utilization pattern using Biolog. Bacterial biomass dominated and showed higher variability than fungal biomass at all scales examined. The microbial biomass decreased with soil depths increased and showed less variability in lower 10-20 cm soil layer. The Shannon-Weaver index value for microbial functional diversity showed higher variability in upper 0-10 cm than lower 10-20 cm soil layer. Carbohydrates, carboxylic acids, polymers and amino acids are the main carbon sources possessing higher utilization efficiency or utilization intensity. At the same time, the four carbon source types contributed to the differentiation of soil microbial communities. This study suggests the higher diversity and complexity for this mix forest ecosystem. To determine the driving factors that affect this spatial variability of microorganism is the next step for our study.

Development of criteria for the use of asphalt-rubber as a Stress-Absorbing Membrane Interlayer (SAMI)

NASA Astrophysics Data System (ADS)

Newcomb, D. E.; McKeen, R. G.

1983-12-01

This report documents over 2 years of research efforts to characterize asphalt-rubber mixtures to be used in Stress-Absorbing Membrane Interlayers (SAMI). The purpose of these SAMIs is to retard or prevent reflection cracking in asphalt-concrete overlays. Several laboratory experiments and one field trial were conducted to define significant test methods and parameters for incorporation into construction design and specification documents. Test methods used in this study included a modified softening point test, force-ductility, and Schweyer viscosity. Variables investigated included (1) Laboratory-mixing temperature; (2) Rubber type; (3) Laboratory storage time; (4) Laboratory storage condition; (5) Laboratory batch replication; (6) Laboratory mixing time; (7) Field mixing time; (8) Laboratory test temperature; (9) Force-Ductility elongation rates; and (10) Asphalt grade. It was found that mixing temperature, mixing time, rubber type, and asphalt grade all have significant effects upon the behavior of asphalt-rubber mixtures. Significant variability was also noticed in different laboratory batch replications. Varying laboratory test temperature and force-ductility elongation rate revealed further differences in asphalt-rubber mixtures.

Accounting for sub-pixel variability of clouds and/or unresolved spectral variability, as needed, with generalized radiative transfer theory

DOE PAGES

Davis, Anthony B.; Xu, Feng; Collins, William D.

2015-03-01

Atmospheric hyperspectral VNIR sensing struggles with sub-pixel variability of clouds and limited spectral resolution mixing molecular lines. Our generalized radiative transfer model addresses both issues with new propagation kernels characterized by power-law decay in space.

The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables.

ERIC Educational Resources Information Center

Ethington, Corinna A.

1987-01-01

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical variables. The analysis of mixed matrices produced estimates that closely approximated the model parameters except where dichotomous variables were…

Stand-replacing patches within a ‘mixed severity’ fire regime: quantitative characterization using recent fires in a long-established natural fire area

Treesearch

B.M. Collins; S.L. Stephens

2010-01-01

The complexity inherent in variable, or mixed-severity fire regimes makes quantitative characterization of important fire regime attributes (e.g., proportion of landscape burned at different severities, size and distribution of stand-replacing patches) difficult. As a result, there is ambiguity associated with the term ‘mixed-severity’. We address...

SST Control by Subsurface Mixing During Indian Ocean Monsoons

DTIC Science & Technology

2015-09-30

1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. SST Control by Subsurface Mixing during Indian Ocean ...quantify the variability in upper ocean mixing associated with changes in barrier layer thickness and strength across the BoB and under different...These objectives directly target the fundamental role that upper ocean dynamics play in the complex air-sea interactions of the northern Indian Ocean

Seasonal cycle of oceanic mixed layer and upper-ocean heat fluxes in the Mediterranean Sea from in-situ observations.

NASA Astrophysics Data System (ADS)

Houpert, Loïc; Testor, Pierre; Durrieu de Madron, Xavier; Estournel, Claude; D'Ortenzio, Fabrizio

2013-04-01

Heat fluxes across the ocean-atmosphere interface play a crucial role in the upper turbulent mixing. The depth reached by this turbulent mixing is indicated by an homogenization of seawater properties in the surface layer, and is defined as the Mixed Layer Depth (MLD). The thickness of the mixed layer determines also the heat content of the layer that directly interacts with the atmosphere. The seasonal variability of these air-sea fluxes is crucial in the calculation of heat budget. An improvement in the estimate of these fluxes is needed for a better understanding of the Mediterranean ocean circulation and climate, in particular in Regional Climate Models. There are few estimations of surface heat fluxes based on oceanic observations in the Mediterranean, and none of them are based on mixed layer observations. So, we proposed here new estimations of these upper-ocean heat fluxes based on mixed layer. We present high resolution Mediterranean climatology (0.5°) of the mean MLD based on a comprehensive collection of temperature profiles of last 43 years (1969-2012). The database includes more than 150,000 profiles, merging CTD, XBT, ARGO Profiling floats, and gliders observations. This dataset is first used to describe the seasonal cycle of the mixed layer depth on the whole Mediterranean on a monthly climatological basis. Our analysis discriminates several regions with coherent behaviors, in particular the deep water formation sites, characterized by significant differences in the winter mixing intensity. Heat storage rates (HSR) were calculated as the time rate of change of the heat content integrated from the surface down to a specific depth that is defined as the MLD plus an integration constant. Monthly climatology of net heat flux (NHF) from ERA-Interim reanalysis was balanced by the 1°x1° resolution heat storage rate climatology. Local heat budget balance and seasonal variability in the horizontal heat flux are then discussed by taking into account uncertainties, due to errors in monthly value estimation and to intra-annual and inter-annual variability.

Water-vapour variability within a convective boundary-layer assessed by large-eddy simulations and IHOP_2002 observations

NASA Astrophysics Data System (ADS)

Couvreux, F.; Guichard, F.; Redelsperger, J. L.; Kiemle, C.; Masson, V.; Lafore, J. P.; Flamant, C.

2005-10-01

This study presents a comprehensive analysis of the variability of water vapour in a growing convective boundary-layer (CBL) over land, highlighting the complex links between advection, convective activity and moisture heterogeneity in the boundary layer. A Large-eddy Simulation (LES) is designed, based on observations, and validated, using an independent data-set collected during the International H2O Project (IHOP 2002) fieldexperiment. Ample information about the moisture distribution in space and time, as well as other important CBL parameters are acquired by mesonet stations, balloon soundings, instruments on-board two aircraft and the DLR airborne water-vapour differential-absorption lidar. Because it can deliver two-dimensional cross-sections at high spatial resolution (140 m horizontal, 200 m vertical), the airborne lidar offers valuable insights of small-scale moisture-variability throughout the CBL. The LES is able to reproduce the development of the CBL in the morning and early afternoon, as assessed by comparisons of simulated mean profiles of key meteorological variables with sounding data. Simulated profiles of the variance of water-vapour mixing-ratio were found to be in good agreement with the lidar-derived counterparts. Finally, probability-density functions of potential temperature, vertical velocity and water-vapour mixing-ratio calculated from the LES show great consistency with those derived from aircraft in situ measurements in the middle of the CBL. Downdraughts entrained from above the CBL are governing the scale of moisture variability. Characteristic length-scales are found to be larger for water-vapour mixing-ratio than for temperature.The observed water-vapour variability exhibits contributions from different scales. The influence of the mesoscale (larger than LES domain size, i.e. 10 km) on the smaller-scale variability is assessed using LES and observations. The small-scale variability of water vapour is found to be important and to be driven by the dynamics of the CBL. Both lidar observations and LES evidence that dry downdraughts entrained from above the CBL are governing the scale of moisture variability. Characteristic length-scales are found to be larger for water-vapour mixing-ratio than for temperature and vertical velocity. In particular, intrusions of drier free-troposphere air from above the growing CBL impose a marked negative skewness on the water-vapour distribution within it, both as observed and in the simulation.

Future of endemic flora of biodiversity hotspots in India.

PubMed

Chitale, Vishwas Sudhir; Behera, Mukund Dev; Roy, Partha Sarthi

2014-01-01

India is one of the 12 mega biodiversity countries of the world, which represents 11% of world's flora in about 2.4% of global land mass. Approximately 28% of the total Indian flora and 33% of angiosperms occurring in India are endemic. Higher human population density in biodiversity hotspots in India puts undue pressure on these sensitive eco-regions. In the present study, we predict the future distribution of 637 endemic plant species from three biodiversity hotspots in India; Himalaya, Western Ghats, Indo-Burma, based on A1B scenario for year 2050 and 2080. We develop individual variable based models as well as mixed models in MaxEnt by combining ten least co-related bioclimatic variables, two disturbance variables and one physiography variable as predictor variables. The projected changes suggest that the endemic flora will be adversely impacted, even under such a moderate climate scenario. The future distribution is predicted to shift in northern and north-eastern direction in Himalaya and Indo-Burma, while in southern and south-western direction in Western Ghats, due to cooler climatic conditions in these regions. In the future distribution of endemic plants, we observe a significant shift and reduction in the distribution range compared to the present distribution. The model predicts a 23.99% range reduction and a 7.70% range expansion in future distribution by 2050, while a 41.34% range reduction and a 24.10% range expansion by 2080. Integration of disturbance and physiography variables along with bioclimatic variables in the models improved the prediction accuracy. Mixed models provide most accurate results for most of the combinations of climatic and non-climatic variables as compared to individual variable based models. We conclude that a) regions with cooler climates and higher moisture availability could serve as refugia for endemic plants in future climatic conditions; b) mixed models provide more accurate results, compared to single variable based models.

Future of Endemic Flora of Biodiversity Hotspots in India

PubMed Central

Chitale, Vishwas Sudhir; Behera, Mukund Dev; Roy, Partha Sarthi

2014-01-01

India is one of the 12 mega biodiversity countries of the world, which represents 11% of world's flora in about 2.4% of global land mass. Approximately 28% of the total Indian flora and 33% of angiosperms occurring in India are endemic. Higher human population density in biodiversity hotspots in India puts undue pressure on these sensitive eco-regions. In the present study, we predict the future distribution of 637 endemic plant species from three biodiversity hotspots in India; Himalaya, Western Ghats, Indo-Burma, based on A1B scenario for year 2050 and 2080. We develop individual variable based models as well as mixed models in MaxEnt by combining ten least co-related bioclimatic variables, two disturbance variables and one physiography variable as predictor variables. The projected changes suggest that the endemic flora will be adversely impacted, even under such a moderate climate scenario. The future distribution is predicted to shift in northern and north-eastern direction in Himalaya and Indo-Burma, while in southern and south-western direction in Western Ghats, due to cooler climatic conditions in these regions. In the future distribution of endemic plants, we observe a significant shift and reduction in the distribution range compared to the present distribution. The model predicts a 23.99% range reduction and a 7.70% range expansion in future distribution by 2050, while a 41.34% range reduction and a 24.10% range expansion by 2080. Integration of disturbance and physiography variables along with bioclimatic variables in the models improved the prediction accuracy. Mixed models provide most accurate results for most of the combinations of climatic and non-climatic variables as compared to individual variable based models. We conclude that a) regions with cooler climates and higher moisture availability could serve as refugia for endemic plants in future climatic conditions; b) mixed models provide more accurate results, compared to single variable based models. PMID:25501852

Local short-term variability in solar irradiance

NASA Astrophysics Data System (ADS)

Lohmann, Gerald M.; Monahan, Adam H.; Heinemann, Detlev

2016-05-01

Characterizing spatiotemporal irradiance variability is important for the successful grid integration of increasing numbers of photovoltaic (PV) power systems. Using 1 Hz data recorded by as many as 99 pyranometers during the HD(CP)2 Observational Prototype Experiment (HOPE), we analyze field variability of clear-sky index k* (i.e., irradiance normalized to clear-sky conditions) and sub-minute k* increments (i.e., changes over specified intervals of time) for distances between tens of meters and about 10 km. By means of a simple classification scheme based on k* statistics, we identify overcast, clear, and mixed sky conditions, and demonstrate that the last of these is the most potentially problematic in terms of short-term PV power fluctuations. Under mixed conditions, the probability of relatively strong k* increments of ±0.5 is approximately twice as high compared to increment statistics computed without conditioning by sky type. Additionally, spatial autocorrelation structures of k* increment fields differ considerably between sky types. While the profiles for overcast and clear skies mostly resemble the predictions of a simple model published by , this is not the case for mixed conditions. As a proxy for the smoothing effects of distributed PV, we finally show that spatial averaging mitigates variability in k* less effectively than variability in k* increments, for a spatial sensor density of 2 km-2.

Formulation characteristics and in vitro release testing of cyclosporine ophthalmic ointments.

PubMed

Dong, Yixuan; Qu, Haiou; Pavurala, Naresh; Wang, Jiang; Sekar, Vasanthakumar; Martinez, Marilyn N; Fahmy, Raafat; Ashraf, Muhammad; Cruz, Celia N; Xu, Xiaoming

2018-06-10

The aim of the present study was to investigate the relationship between formulation/process variables versus the critical quality attributes (CQAs) of cyclosporine ophthalmic ointments and to explore the feasibility of using an in vitro approach to assess product sameness. A definitive screening design (DSD) was used to evaluate the impact of formulation and process variables. The formulation variables included drug percentage, percentage of corn oil and lanolin alcohol. The process variables studied were mixing temperature, mixing time and the method of mixing. The quality and performance attributes examined included drug assay, content uniformity, image analysis, rheology (storage modulus, shear viscosity) and in vitro drug release. Of the formulation variables evaluated, the percentage of the drug substance and the percentage of corn oil in the matrix were the most influential factors with respect to in vitro drug release. Conversely, the process parameters tested were observed to have minimal impact. An evaluation of the release mechanism of cyclosporine from the ointment revealed an interplay between formulation (e.g. physicochemical properties of the drug and ointment matrix type) and the release medium. These data provide a scientific basis to guide method development for in vitro drug release testing of ointment dosage forms. These results demonstrate that the in vitro methods used in this investigation were fit-for-purpose for detecting formulation and process changes and therefore amenable to assessment of product sameness. Published by Elsevier B.V.

U.S. Army Custom Segmentation System

DTIC Science & Technology

2007-06-01

segmentation is individual or intergroup differences in response to marketing - mix variables. Presumptions about segments: •different demands in a...product or service category, •respond differently to changes in the marketing mix Criteria for segments: •The segments must exist in the environment

Infrared thermography-driven flaw detection and evaluation of hot mix asphalt pavements.

DOT National Transportation Integrated Search

2010-01-01

This research was conducted to study more realistic explanations of how variables are created and : dealt with during hot mix asphalt (HMA) paving construction. Several paving projects across the : state of Nebraska have been visited where sensory de...

Incorporation of Fixed Installation Costs into Optimization of Groundwater Remediation with a New Efficient Surrogate Nonlinear Mixed Integer Optimization Algorithm

NASA Astrophysics Data System (ADS)

Shoemaker, Christine; Wan, Ying

2016-04-01

Optimization of nonlinear water resources management issues which have a mixture of fixed (e.g. construction cost for a well) and variable (e.g. cost per gallon of water pumped) costs has been not well addressed because prior algorithms for the resulting nonlinear mixed integer problems have required many groundwater simulations (with different configurations of decision variable), especially when the solution space is multimodal. In particular heuristic methods like genetic algorithms have often been used in the water resources area, but they require so many groundwater simulations that only small systems have been solved. Hence there is a need to have a method that reduces the number of expensive groundwater simulations. A recently published algorithm for nonlinear mixed integer programming using surrogates was shown in this study to greatly reduce the computational effort for obtaining accurate answers to problems involving fixed costs for well construction as well as variable costs for pumping because of a substantial reduction in the number of groundwater simulations required to obtain an accurate answer. Results are presented for a US EPA hazardous waste site. The nonlinear mixed integer surrogate algorithm is general and can be used on other problems arising in hydrology with open source codes in Matlab and python ("pySOT" in Bitbucket).

A Clifford analysis approach to superspace

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

Bie, H. de; Sommen, F.

A new framework for studying superspace is given, based on methods from Clifford analysis. This leads to the introduction of both orthogonal and symplectic Clifford algebra generators, allowing for an easy and canonical introduction of a super-Dirac operator, a super-Laplace operator and the like. This framework is then used to define a super-Hodge coderivative, which, together with the exterior derivative, factorizes the Laplace operator. Finally both the cohomology of the exterior derivative and the homology of the Hodge operator on the level of polynomial-valued super-differential forms are studied. This leads to some interesting graphical representations and provides a better insightmore » in the definition of the Berezin-integral.« less

Quantum dressing orbits on compact groups

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Šťovíček, Pavel

1993-02-01

The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decompositon in the general case. Quantum dressing orbits are described explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient “coherent states” are introduced and a correspondence between classical and quantum observables is given.

Integration over families of Lagrangian submanifolds in BV formalism

NASA Astrophysics Data System (ADS)

Mikhailov, Andrei

2018-03-01

Gauge fixing is interpreted in BV formalism as a choice of Lagrangian submanifold in an odd symplectic manifold (the BV phase space). A natural construction defines an integration procedure on families of Lagrangian submanifolds. In string perturbation theory, the moduli space integrals of higher genus amplitudes can be interpreted in this way. We discuss the role of gauge symmetries in this construction. We derive the conditions which should be imposed on gauge symmetries for the consistency of our integration procedure. We explain how these conditions behave under the deformations of the worldsheet theory. In particular, we show that integrated vertex operator is actually an inhomogeneous differential form on the space of Lagrangian submanifolds.

The Motion of a Charged Particle on a Riemannian Surface under a Non-Zero Magnetic Field

NASA Astrophysics Data System (ADS)

Castilho, César

2001-03-01

In this paper we study the motion of a charged particle on a Riemmanian surface under the influence of a positive magnetic field B. Using Moser's Twist Theorem and ideas from classical pertubation theory we find sufficient conditions to perpetually trap the motion of a particle with a sufficient large charge in a neighborhood of a level set of the magnetic field. The conditions on the level set of the magnetic field that guarantee the trapping are local and hold near all non-degenerate critical local minima or maxima of B. Using symplectic reduction we apply the results of our work to certain S1-invariant magnetic fields on R3.

On propagation of energy flux in de Sitter spacetime

NASA Astrophysics Data System (ADS)

Hoque, Sk Jahanur; Virmani, Amitabh

2018-04-01

In this paper, we explore propagation of energy flux in the future Poincaré patch of de Sitter spacetime. We present two results. First, we compute the flux integral of energy using the symplectic current density of the covariant phase space approach on hypersurfaces of constant radial physical distance. Using this computation we show that in the tt-projection, the integrand in the energy flux expression on the cosmological horizon is same as that on the future null infinity. This suggests that propagation of energy flux in de Sitter spacetime is sharp. Second, we relate our energy flux expression in tt-projection to a previously obtained expression using the Isaacson stress-tensor approach.

The Kirillov picture for the Wigner particle

NASA Astrophysics Data System (ADS)

Gracia-Bondía, J. M.; Lizzi, F.; Várilly, J. C.; Vitale, P.

2018-06-01

We discuss the Kirillov method for massless Wigner particles, usually (mis)named ‘continuous spin’ or ‘infinite spin’ particles. These appear in Wigner’s classification of the unitary representations of the Poincaré group, labelled by elements of the enveloping algebra of the Poincaré Lie algebra. Now, the coadjoint orbit procedure introduced by Kirillov is a prelude to quantization. Here we exhibit for those particles the classical Casimir functions on phase space, in parallel to quantum representation theory. A good set of position coordinates are identified on the coadjoint orbits of the Wigner particles; the stabilizer subgroups and the symplectic structures of these orbits are also described. In memory of E C G Sudarshan.

Block structured adaptive mesh and time refinement for hybrid, hyperbolic + N-body systems

NASA Astrophysics Data System (ADS)

Miniati, Francesco; Colella, Phillip

2007-11-01

We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov’s method for hydrodynamics; a symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented.

On the adiabatic limit of Hadamard states

NASA Astrophysics Data System (ADS)

Drago, Nicolò; Gérard, Christian

2017-08-01

We consider the adiabatic limit of Hadamard states for free quantum Klein-Gordon fields, when the background metric and the field mass are slowly varied from their initial to final values. If the Klein-Gordon field stays massive, we prove that the adiabatic limit of the initial vacuum state is the (final) vacuum state, by extending to the symplectic framework the adiabatic theorem of Avron-Seiler-Yaffe. In cases when only the field mass is varied, using an abstract version of the mode decomposition method we can also consider the case when the initial or final mass vanishes, and the initial state is either a thermal state or a more general Hadamard state.

Localization in abelian Chern-Simons theory

NASA Astrophysics Data System (ADS)

McLellan, B. D. K.

2013-02-01

Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected, and abelian. The abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. The partition function is then formally computed using the technique of non-abelian localization. This study leads to a natural identification of the abelian Reidemeister-Ray-Singer torsion as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections for the class of Sasakian three-manifolds. The torsion part of the abelian Chern-Simons partition function is computed explicitly in terms of Seifert data for a given Sasakian three-manifold.

Non-commutative geometry of the h-deformed quantum plane

NASA Astrophysics Data System (ADS)

Cho, S.; Madore, J.; Park, K. S.

1998-03-01

The h-deformed quantum plane is a counterpart of the q-deformed one in the set of quantum planes which are covariant under those quantum deformations of GL(2) which admit a central determinant. We have investigated the non-commutative geometry of the h-deformed quantum plane. There is a two-parameter family of torsion-free linear connections, a one-parameter sub-family of which are compatible with a skew-symmetric non-degenerate bilinear map. The skew-symmetric map resembles a symplectic 2-form and induces a metric. It is also shown that the extended h-deformed quantum plane is a non-commutative version of the Poincaré half-plane, a surface of constant negative Gaussian

Unimodularity criteria for Poisson structures on foliated manifolds

NASA Astrophysics Data System (ADS)

Pedroza, Andrés; Velasco-Barreras, Eduardo; Vorobiev, Yury

2018-03-01

We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria for regular Poisson manifolds related to the notion of the Reeb class. In particular, we show that the unimodularity of the transverse Poisson structure of the leaf is a necessary condition for the semilocal unimodular property. Our main tool is an explicit formula for a bigraded decomposition of modular vector fields of a coupling Poisson structure on a foliated manifold. Moreover, we also exploit the notion of the modular class of a Poisson foliation and its relationship with the Reeb class.

Population mixing for leukaemia, lymphoma and CNS tumours in teenagers and young adults in England, 1996-2005.

PubMed

van Laar, Marlous; Stark, Daniel P; McKinney, Patricia; Parslow, Roger C; Kinsey, Sally E; Picton, Susan V; Feltbower, Richard G

2014-09-23

Little aetiological epidemiological research has been undertaken for major cancers occurring in teenagers and young adults (TYA). Population mixing, as a possible proxy for infectious exposure, has been well researched for childhood malignancies. We aimed to investigate effects of population mixing in this older age group using an English national cancer dataset. Cases of leukaemia, lymphoma and central nervous system (CNS) tumours amongst 15-24 year olds in England (diagnosed 1996-2005) were included in the study. Data were obtained by ward of diagnosis and linked to 1991 census variables including population mixing (Shannon index); data on person-weighted population density and deprivation (Townsend score) were also used and considered as explanatory variables. Associations between TYA cancer incidence and census variables were investigated using negative binomial regression, and results presented as incidence rate ratios (IRR) with 95% confidence intervals (CI). A total of 6251 cases of leukaemia (21%), lymphoma (49%) and CNS tumours (30%) were analysed. Higher levels of population mixing were associated with a significant decrease in the incidence of CNS tumours (IRR=0.83, 95% CI=0.75-0.91), accounted for by astrocytomas and 'other CNS tumours'; however, there was no association with leukaemia or lymphoma. Incidence of CNS tumours and lymphoma was 3% lower in more deprived areas (IRR=0.97, 95% CI=0.96-0.99 and IRR=0.97, 95% CI=.96-0.98 respectively). Population density was not associated with the incidence of leukaemia, lymphoma or CNS tumours. Our results suggest a possible role for environmental risk factors with population correlates in the aetiology of CNS tumours amongst TYAs. Unlike studies of childhood cancer, associations between population mixing and the incidence of leukaemia and lymphoma were not observed.

Wave mixing in coupled phononic crystals via a variable stiffness mechanism

NASA Astrophysics Data System (ADS)

Lee, Gil-Yong; Chong, Christopher; Kevrekidis, Panayotis G.; Yang, Jinkyu

2016-10-01

We investigate wave mixing effects in a phononic crystal that couples the wave dynamics of two channels - primary and control ones - via a variable stiffness mechanism. We demonstrate analytically and numerically that the wave transmission in the primary channel can be manipulated by the control channel's signal. We show that the application of control waves allows the selection of a specific mode through the primary channel. We also demonstrate that the mixing of two wave modes is possible whereby a modulation effect is observed. A detailed study of the design parameters is also carried out to optimize the switching capabilities of the proposed system. Finally, we verify that the system can fulfill both switching and amplification functionalities, potentially enabling the realization of an acoustic transistor.

GAMBIT: A Parameterless Model-Based Evolutionary Algorithm for Mixed-Integer Problems.

PubMed

Sadowski, Krzysztof L; Thierens, Dirk; Bosman, Peter A N

2018-01-01

Learning and exploiting problem structure is one of the key challenges in optimization. This is especially important for black-box optimization (BBO) where prior structural knowledge of a problem is not available. Existing model-based Evolutionary Algorithms (EAs) are very efficient at learning structure in both the discrete, and in the continuous domain. In this article, discrete and continuous model-building mechanisms are integrated for the Mixed-Integer (MI) domain, comprising discrete and continuous variables. We revisit a recently introduced model-based evolutionary algorithm for the MI domain, the Genetic Algorithm for Model-Based mixed-Integer opTimization (GAMBIT). We extend GAMBIT with a parameterless scheme that allows for practical use of the algorithm without the need to explicitly specify any parameters. We furthermore contrast GAMBIT with other model-based alternatives. The ultimate goal of processing mixed dependences explicitly in GAMBIT is also addressed by introducing a new mechanism for the explicit exploitation of mixed dependences. We find that processing mixed dependences with this novel mechanism allows for more efficient optimization. We further contrast the parameterless GAMBIT with Mixed-Integer Evolution Strategies (MIES) and other state-of-the-art MI optimization algorithms from the General Algebraic Modeling System (GAMS) commercial algorithm suite on problems with and without constraints, and show that GAMBIT is capable of solving problems where variable dependences prevent many algorithms from successfully optimizing them.

Southern Ocean Mixed-Layer Seasonal and Interannual Variations From Combined Satellite and In Situ Data

NASA Astrophysics Data System (ADS)

Buongiorno Nardelli, B.; Guinehut, S.; Verbrugge, N.; Cotroneo, Y.; Zambianchi, E.; Iudicone, D.

2017-12-01

The depth of the upper ocean mixed layer provides fundamental information on the amount of seawater that directly interacts with the atmosphere. Its space-time variability modulates water mass formation and carbon sequestration processes related to both the physical and biological pumps. These processes are particularly relevant in the Southern Ocean, where surface mixed-layer depth estimates are generally obtained either as climatological fields derived from in situ observations or through numerical simulations. Here we demonstrate that weekly observation-based reconstructions can be used to describe the variations of the mixed-layer depth in the upper ocean over a range of space and time scales. We compare and validate four different products obtained by combining satellite measurements of the sea surface temperature, salinity, and dynamic topography and in situ Argo profiles. We also compute an ensemble mean and use the corresponding spread to estimate mixed-layer depth uncertainties and to identify the more reliable products. The analysis points out the advantage of synergistic approaches that include in input the sea surface salinity observations obtained through a multivariate optimal interpolation. Corresponding data allow to assess mixed-layer depth seasonal and interannual variability. Specifically, the maximum correlations between mixed-layer anomalies and the Southern Annular Mode are found at different time lags, related to distinct summer/winter responses in the Antarctic Intermediate Water and Sub-Antarctic Mode Waters main formation areas.

Student Test Grades in College: A Study of Possible Predictors

ERIC Educational Resources Information Center

Hammonds, Frank; Mariano, Gina

2015-01-01

Research on variables related to test performance has produced mixed results. Typically, research of this type involves only a few variables. In an attempt to obtain a more complete picture, we investigated how test grades might be related to variables such as classification, student seating location, test completion time, predicted grade, time…

Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling

NASA Astrophysics Data System (ADS)

Abramov, R. V.

2011-12-01

Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger chaotic system would result in general increase of chaos at the slow variables.

MULTIVARIATE LINEAR MIXED MODELS FOR MULTIPLE OUTCOMES. (R824757)

EPA Science Inventory

We propose a multivariate linear mixed (MLMM) for the analysis of multiple outcomes, which generalizes the latent variable model of Sammel and Ryan. The proposed model assumes a flexible correlation structure among the multiple outcomes, and allows a global test of the impact of ...

Development and validation of a turbulent-mix model for variable-density and compressible flows.

PubMed

Banerjee, Arindam; Gore, Robert A; Andrews, Malcolm J

2010-10-01

The modeling of buoyancy driven turbulent flows is considered in conjunction with an advanced statistical turbulence model referred to as the BHR (Besnard-Harlow-Rauenzahn) k-S-a model. The BHR k-S-a model is focused on variable-density and compressible flows such as Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) driven mixing. The BHR k-S-a turbulence mix model has been implemented in the RAGE hydro-code, and model constants are evaluated based on analytical self-similar solutions of the model equations. The results are then compared with a large test database available from experiments and direct numerical simulations (DNS) of RT, RM, and KH driven mixing. Furthermore, we describe research to understand how the BHR k-S-a turbulence model operates over a range of moderate to high Reynolds number buoyancy driven flows, with a goal of placing the modeling of buoyancy driven turbulent flows at the same level of development as that of single phase shear flows.

A social-cognitive framework of multidisciplinary team innovation.

PubMed

Paletz, Susannah B F; Schunn, Christian D

2010-01-01

The psychology of science typically lacks integration between cognitive and social variables. We present a new framework of team innovation in multidisciplinary science and engineering groups that ties factors from both literatures together. We focus on the effects of a particularly challenging social factor, knowledge diversity, which has a history of mixed effects on creativity, most likely because those effects are mediated and moderated by cognitive and additional social variables. In addition, we highlight the distinction between team innovative processes that are primarily divergent versus convergent; we propose that the social and cognitive implications are different for each, providing a possible explanation for knowledge diversity's mixed results on team outcomes. Social variables mapped out include formal roles, communication norms, sufficient participation and information sharing, and task conflict; cognitive variables include analogy, information search, and evaluation. This framework provides a roadmap for research that aims to harness the power of multidisciplinary teams. Copyright © 2009 Cognitive Science Society, Inc.

Variables affecting learning in a simulation experience: a mixed methods study.

PubMed

Beischel, Kelly P

2013-02-01

The primary purpose of this study was to test a hypothesized model describing the direct effects of learning variables on anxiety and cognitive learning outcomes in a high-fidelity simulation (HFS) experience. The secondary purpose was to explain and explore student perceptions concerning the qualities and context of HFS affecting anxiety and learning. This study used a mixed methods quantitative-dominant explanatory design with concurrent qualitative data collection to examine variables affecting learning in undergraduate, beginning nursing students (N = 124). Being ready to learn, having a strong auditory-verbal learning style, and being prepared for simulation directly affected anxiety, whereas learning outcomes were directly affected by having strong auditory-verbal and hands-on learning styles. Anxiety did not quantitatively mediate cognitive learning outcomes as theorized, although students qualitatively reported debilitating levels of anxiety. This study advances nursing education science by providing evidence concerning variables affecting learning outcomes in HFS.

Spatial patterns of mixing in the Solomon Sea

NASA Astrophysics Data System (ADS)

Alberty, M. S.; Sprintall, J.; MacKinnon, J.; Ganachaud, A.; Cravatte, S.; Eldin, G.; Germineaud, C.; Melet, A.

2017-05-01

The Solomon Sea is a marginal sea in the southwest Pacific that connects subtropical and equatorial circulation, constricting transport of South Pacific Subtropical Mode Water and Antarctic Intermediate Water through its deep, narrow channels. Marginal sea topography inhibits internal waves from propagating out and into the open ocean, making these regions hot spots for energy dissipation and mixing. Data from two hydrographic cruises and from Argo profiles are employed to indirectly infer mixing from observations for the first time in the Solomon Sea. Thorpe and finescale methods indirectly estimate the rate of dissipation of kinetic energy (ɛ) and indicate that it is maximum in the surface and thermocline layers and decreases by 2-3 orders of magnitude by 2000 m depth. Estimates of diapycnal diffusivity from the observations and a simple diffusive model agree in magnitude but have different depth structures, likely reflecting the combined influence of both diapycnal mixing and isopycnal stirring. Spatial variability of ɛ is large, spanning at least 2 orders of magnitude within isopycnal layers. Seasonal variability of ɛ reflects regional monsoonal changes in large-scale oceanic and atmospheric conditions with ɛ increased in July and decreased in March. Finally, tide power input and topographic roughness are well correlated with mean spatial patterns of mixing within intermediate and deep isopycnals but are not clearly correlated with thermocline mixing patterns.

Mixed-strain housing for female C57BL/6, DBA/2, and BALB/c mice: validating a split-plot design that promotes refinement and reduction.

PubMed

Walker, Michael; Fureix, Carole; Palme, Rupert; Newman, Jonathan A; Ahloy Dallaire, Jamie; Mason, Georgia

2016-01-27

Inefficient experimental designs are common in animal-based biomedical research, wasting resources and potentially leading to unreplicable results. Here we illustrate the intrinsic statistical power of split-plot designs, wherein three or more sub-units (e.g. individual subjects) differing in a variable of interest (e.g. genotype) share an experimental unit (e.g. a cage or litter) to which a treatment is applied (e.g. a drug, diet, or cage manipulation). We also empirically validate one example of such a design, mixing different mouse strains -- C57BL/6, DBA/2, and BALB/c -- within cages varying in degree of enrichment. As well as boosting statistical power, no other manipulations are needed for individual identification if co-housed strains are differentially pigmented, so also sparing mice from stressful marking procedures. The validation involved housing 240 females from weaning to 5 months of age in single- or mixed- strain trios, in cages allocated to enriched or standard treatments. Mice were screened for a range of 26 commonly-measured behavioural, physiological and haematological variables. Living in mixed-strain trios did not compromise mouse welfare (assessed via corticosterone metabolite output, stereotypic behaviour, signs of aggression, and other variables). It also did not alter the direction or magnitude of any strain- or enrichment-typical difference across the 26 measured variables, or increase variance in the data: indeed variance was significantly decreased by mixed- strain housing. Furthermore, using Monte Carlo simulations to quantify the statistical power benefits of this approach over a conventional design demonstrated that for our effect sizes, the split- plot design would require significantly fewer mice (under half in most cases) to achieve a power of 80%. Mixed-strain housing allows several strains to be tested at once, and potentially refines traditional marking practices for research mice. Furthermore, it dramatically illustrates the enhanced statistical power of split-plot designs, allowing many fewer animals to be used. More powerful designs can also increase the chances of replicable findings, and increase the ability of small-scale studies to yield significant results. Using mixed-strain housing for female C57BL/6, DBA/2 and BALB/c mice is therefore an effective, efficient way to promote both refinement and the reduction of animal-use in research.

The link between eddy-driven jet variability and weather regimes in the North Atlantic-European sector

NASA Astrophysics Data System (ADS)

Madonna, E.; Li, C.; Grams, C. M.; Woollings, T.

2017-12-01

Understanding the variability of the North Atlantic eddy-driven jet is key to unravelling the dynamics, predictability and climate change response of extratropical weather in the region. This study aims to 1) reconcile two perspectives on wintertime variability in the North Atlantic-European sector and 2) clarify their link to atmospheric blocking. Two common views of wintertime variability in the North Atlantic are the zonal-mean framework comprising three preferred locations of the eddy-driven jet (southern, central, northern), and the weather regime framework comprising four classical North Atlantic-European regimes (Atlantic ridge AR, zonal ZO, European/Scandinavian blocking BL, Greenland anticyclone GA). We use a k-means clustering algorithm to characterize the two-dimensional variability of the eddy-driven jet stream, defined by the lower tropospheric zonal wind in the ERA-Interim reanalysis. The first three clusters capture the central jet and northern jet, along with a new mixed jet configuration; a fourth cluster is needed to recover the southern jet. The mixed cluster represents a split or strongly tilted jet, neither of which is well described in the zonal-mean framework, and has a persistence of about one week, similar to the other clusters. Connections between the preferred jet locations and weather regimes are corroborated - southern to GA, central to ZO, and northern to AR. In addition, the new mixed cluster is found to be linked to European/Scandinavian blocking, whose relation to the eddy-driven jet was previously unclear. The results highlight the necessity of bridging from weather to climate scales for a deeper understanding of atmospheric circulation variability.

Evaluation of the heat balance constituents of the upper mixed layer in the North Atlantic

NASA Astrophysics Data System (ADS)

Polonsky, A. B.; Sukhonos, P. A.

2016-11-01

Different physical mechanisms which cause interannual and interdecadal temperature anomalies in the upper mixed layer (UML) of the North Atlantic are investigated using the data of ORA-S3 reanalysis for the period of 1959-2011. It is shown that the annual mean heat budget in UML is mainly caused by the balance between advective heat transfer and horizontal turbulent mixing (estimated as a residual term in the equation of thermal balance). The local UML temperature change and contribution from the heat fluxes on the lower boundary of the UML to the heat budget of the upper layer are insignificant for the time scale under consideration. The contribution of the heat fluxes on the upper UML boundary to the low-frequency variability of the upper layer temperature in the whole North Atlantic area is substantially less than 30%. Areas like the northwestern part of the Northern Subtropical Anticyclonic Gyre (NSAG), where their contribution exceeds 30-60%, are exceptions. The typical time scales of advective heat transfer variability are revealed. In the NSAG area, an interannual variability associated with the North Atlantic Oscillation dominates, while in the North Atlantic subpolar gyre, an interdecadal variability of advective transfers with periods of more than 30 years prevails.

One hundred years of Arctic ice cover variations as simulated by a one-dimensional, ice-ocean model

NASA Astrophysics Data System (ADS)

Hakkinen, S.; Mellor, G. L.

1990-09-01

A one-dimensional ice-ocean model consisting of a second moment, turbulent closure, mixed layer model and a three-layer snow-ice model has been applied to the simulation of Arctic ice mass and mixed layer properties. The results for the climatological seasonal cycle are discussed first and include the salt and heat balance in the upper ocean. The coupled model is then applied to the period 1880-1985, using the surface air temperature fluctuations from Hansen et al. (1983) and from Wigley et al. (1981). The analysis of the simulated large variations of the Arctic ice mass during this period (with similar changes in the mixed layer salinity) shows that the variability in the summer melt determines to a high degree the variability in the average ice thickness. The annual oceanic heat flux from the deep ocean and the maximum freezing rate and associated nearly constant minimum surface salinity flux did not vary significantly interannually. This also implies that the oceanic influence on the Arctic ice mass is minimal for the range of atmospheric variability tested.

The osmotic virial formulation of the free energy of polymer mixing.

PubMed

Bosse, August W; Douglas, Jack F

2015-09-14

We derive an alternative formulation of the free energy of polymer mixing in terms of an osmotic virial expansion. Starting from a generalized free energy of mixing, and the assumption that the internal energy of mixing is analytic in the polymer composition variable, we demonstrate that the free energy of mixing can be represented as an infinite series in the osmotic virial coefficients. This osmotic virial formulation is consistent with, but more general than, a relationship derived for polymer blends with structured monomers by Dudowicz, Freed, and Douglas [J. Chem. Phys. 116, 9983 (2002)] and Douglas, Dudowicz, and Freed [J. Chem. Phys. 127, 224901 (2007)].

Detailed study of precipitation of a poorly water soluble test compound using methodologies as in activity and solubility screening - mixing and automation effects.

PubMed

Gillespie, Cheska; Kennedy, Alan R; Edwards, Darren; Dowden, Lee; Daublain, Pierre; Halling, Peter

2013-09-01

Storage of pharmaceutical discovery compounds dissolved in dimethylsulfoxide (DMSO) is commonplace within industry. Often, the DMSO stock solution is added to an aqueous system (e.g. in bioassay or kinetic solubility testing)- since most test compounds are hydrophobic, precipitation could occur. Little is known about the factors affecting this precipitation process at the low (µM) concentrations used in screening analyses. Here, a poorly water soluble test compound (tolnaftate) was used to compare manual and automated pipetting, and explore the effect of mixing variables on precipitation. The amount of drug present in the supernatant after precipitation and centrifugation of the samples was quantified. An unusual result was obtained in three different laboratories: results of experiments performed initially were statistically significantly higher than those performed after a few days in the same lab. No significant differences were found between automated and manual pipetting, including in variability. Vortex mixing was found to give significantly lower supernatant amounts compared to milder mixing types. The mixing employed affects the particle growth of the precipitate. These findings are of relevance to discovery stage bioassay and kinetic solubility analyses.

A Simple Model of Cirrus Horizontal Inhomogeneity and Cloud Fraction

NASA Technical Reports Server (NTRS)

Smith, Samantha A.; DelGenio, Anthony D.

1998-01-01

A simple model of horizontal inhomogeneity and cloud fraction in cirrus clouds has been formulated on the basis that all internal horizontal inhomogeneity in the ice mixing ratio is due to variations in the cloud depth, which are assumed to be Gaussian. The use of such a model was justified by the observed relationship between the normalized variability of the ice water mixing ratio (and extinction) and the normalized variability of cloud depth. Using radar cloud depth data as input, the model reproduced well the in-cloud ice water mixing ratio histograms obtained from horizontal runs during the FIRE2 cirrus campaign. For totally overcast cases the histograms were almost Gaussian, but changed as cloud fraction decreased to exponential distributions which peaked at the lowest nonzero ice value for cloud fractions below 90%. Cloud fractions predicted by the model were always within 28% of the observed value. The predicted average ice water mixing ratios were within 34% of the observed values. This model could be used in a GCM to produce the ice mixing ratio probability distribution function and to estimate cloud fraction. It only requires basic meteorological parameters, the depth of the saturated layer and the standard deviation of cloud depth as input.

Mesoscale mixing of the Denmark Strait Overflow in the Irminger Basin

NASA Astrophysics Data System (ADS)

Koszalka, Inga M.; Haine, Thomas W. N.; Magaldi, Marcello G.

2017-04-01

The Denmark Strait Overflow (DSO) is a major export route for dense waters from the Nordic Seas forming the lower limb of the Atlantic Meridional Overturning Circulation, an important element of the climate system. Mixing processes along the DSO pathway influence its volume transport and properties contributing to the variability of the deep overturning circulation. They are poorly sampled by observations, however, which hinders development of a proper DSO representation in global circulation models. We employ a high resolution regional ocean model of the Irminger Basin to quantify impact of the mesoscale flows on DSO mixing focusing on geographical localization and the time-modulation of water property changes. The model reproduces the observed bulk warming of the DSO plume 100-200 km downstream of the Denmark Strait sill. It also reveals that mesoscale variability of the overflow ('DSO-eddies', of 20-30 km extent and a time scale of 2-5 day) modulates water property changes and turbulent mixing, diagnosed with the vertical shear of horizontal velocity and the eddy heat flux divergence. The space-time localization of the DSO mixing and warming and the role of coherent mesoscale structures should be explored by turbulence measurements and factored into the coarse circulation models.

TSOS and TSOS-FK hybrid methods for modelling the propagation of seismic waves

NASA Astrophysics Data System (ADS)

Ma, Jian; Yang, Dinghui; Tong, Ping; Ma, Xiao

2018-05-01

We develop a new time-space optimized symplectic (TSOS) method for numerically solving elastic wave equations in heterogeneous isotropic media. We use the phase-preserving symplectic partitioned Runge-Kutta method to evaluate the time derivatives and optimized explicit finite-difference (FD) schemes to discretize the space derivatives. We introduce the averaged medium scheme into the TSOS method to further increase its capability of dealing with heterogeneous media and match the boundary-modified scheme for implementing free-surface boundary conditions and the auxiliary differential equation complex frequency-shifted perfectly matched layer (ADE CFS-PML) non-reflecting boundaries with the TSOS method. A comparison of the TSOS method with analytical solutions and standard FD schemes indicates that the waveform generated by the TSOS method is more similar to the analytic solution and has a smaller error than other FD methods, which illustrates the efficiency and accuracy of the TSOS method. Subsequently, we focus on the calculation of synthetic seismograms for teleseismic P- or S-waves entering and propagating in the local heterogeneous region of interest. To improve the computational efficiency, we successfully combine the TSOS method with the frequency-wavenumber (FK) method and apply the ADE CFS-PML to absorb the scattered waves caused by the regional heterogeneity. The TSOS-FK hybrid method is benchmarked against semi-analytical solutions provided by the FK method for a 1-D layered model. Several numerical experiments, including a vertical cross-section of the Chinese capital area crustal model, illustrate that the TSOS-FK hybrid method works well for modelling waves propagating in complex heterogeneous media and remains stable for long-time computation. These numerical examples also show that the TSOS-FK method can tackle the converted and scattered waves of the teleseismic plane waves caused by local heterogeneity. Thus, the TSOS and TSOS-FK methods proposed in this study present an essential tool for the joint inversion of local, regional, and teleseismic waveform data.

Metamorphic P-T-t path retrieved from metapelites in the southeastern Taihua metamorphic complex, and the Paleoproterozoic tectonic evolution of the southern North China Craton

NASA Astrophysics Data System (ADS)

Lu, Jun-Sheng; Zhai, Ming-Guo; Lu, Lin-Sheng; Wang, Hao Y. C.; Chen, Hong-Xu; Peng, Tao; Wu, Chun-Ming; Zhao, Tai-Ping

2017-02-01

The Taihua metamorphic complex in the southern part of the North China Craton is composed of tonalite-trondhjemite-granodiorite (TTG) gneisses, amphibolites, metapelitic gneisses, marbles, quartzites, and banded iron formations (BIFs). The protoliths of the complex have ages ranging from ∼2.1 to ∼2.9 Ga and was metamorphosed under the upper amphibolite to granulite facies conditions with NWW-SEE-striking gneissosity. Metapelitites from the Wugang area have three stages of metamorphic mineral assemblages. The prograde metamorphic mineral assemblage (M1) includes biotite + plagioclase + quartz + ilmenite preserved as inclusions in garnet porphyroblasts. The peak mineral assemblage (M2) consists of garnet porphyroblasts and matrix minerals of sillimanite + biotite + plagioclase + quartz + K-feldspar + ilmenite + rutile + pyrite. The retrograde mineral assemblage (M3), biotite + plagioclase + quartz, occurs as symplectic assemblages surrounding embayed garnet porphyroblasts. Garnet porphyroblasts are chemically zoned. Pseudosection calculated in the NCKFMASHTO model system suggests that mantles of garnet porphyroblasts define high-pressure granulites facies P-T conditions of 12.2 kbar and 830 °C, whereas garnet rims record P-T conditions of 10.2 kbar and 840 °C. Integrating the prograde mineral assemblages, zoning of garnet porphyroblasts with symplectic assemblages, a clockwise metamorphic P-T path can be retrieved. High resolution SIMS U-Pb dating and LA-ICP-MS trace element measurements of the metamorphic zircons demonstrate that metapelites in Wugang possibly record the peak or near peak metamorphic ages of ∼1.92 Ga. Furthermore, 40Ar/39Ar dating of biotite in metapelites suggests that the cooling of the Taihua complex may have lasted until ∼1.83 Ga. Therefore, a long-lived Palaeoproterozoic metamorphic event may define a slow exhumation process. Field relationship and new metamorphic data for the Taihua metamorphic complex does not support the previous model in which the Tran-North China Craton (TNCO) was formed through the collision between the East and West blocks.

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

PubMed

Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

2015-05-01

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

Mixing of multiple jets with a confined subsonic crossflow - Summary of NASA-supported experiments and modeling

NASA Technical Reports Server (NTRS)

Holdeman, James D.

1991-01-01

Experimental and computational results on the mixing of single, double, and opposed rows of jets with an isothermal or variable temperature mainstream in a confined subsonic crossflow are summarized. The studies were performed to investigate flow and geometric variations typical of the complex 3D flowfield in the dilution zone of combustion chambers in gas turbine engines. The principal observations from the experiments were that the momentum-flux ratio was the most significant flow variable, and that temperature distributions were similar (independent of orifice diameter) when the orifice spacing and the square-root of the momentum-flux ratio were inversely proportional. The experiments and empirical model for the mixing of a single row of jets from round holes were extended to include several variations typical of gas turbine combustors.

Using Mixed-Effects Structural Equation Models to Study Student Academic Development.

ERIC Educational Resources Information Center

Pike, Gary R.

1992-01-01

A study at the University of Tennessee Knoxville used mixed-effect structural equation models incorporating latent variables as an alternative to conventional methods of analyzing college students' (n=722) first-year-to-senior academic gains. Results indicate, contrary to previous analysis, that coursework and student characteristics interact to…

Mix and Switch Effects in Bilingual Language Processing

ERIC Educational Resources Information Center

Koeth, Joel T.

2012-01-01

This study utilized a novel task design in an effort to identify the source of the second language processing advantage commonly reported in mixed language conditions, investigate switch cost asymmetry in non-balanced bilinguals, and identify task-related variables that potentially contribute to inconsistent results across studies with similar…

Laboratory evaluation of influence of operational tolerance (acceptance criterion) on performance of hot-mix asphalt concrete.

DOT National Transportation Integrated Search

2010-06-01

The performance of flexible pavements relies heavily on the final quality of the hot-mix asphalt concrete (HMAC) as it : is produced and placed in the field. To account for production and construction variability while ensuring the quality of the : H...

Analysis of diurnal variability of atmospheric halocarbons and CFC replacements to imply emission strength and sources at an urban site of Lukang in central Taiwan

NASA Astrophysics Data System (ADS)

Lee, Bing-Sun; Chiou, Chung-Biau; Lin, Chung-Yi

2014-12-01

Hourly atmospheric measurements of halocarbons and chlorofluorocarbon (CFC) replacements were conducted at an urban site of Lukang, Changhua, in central Taiwan from May to August, 2013. The temporal distribution of different groups of halocarbons in the Lukang urban atmosphere, including chlorofluorocarbons (CFCs), Chlorodifluoromethane (HCFC-22), Bromochlorodifluoromethane (Halon-1211), and other chlorinated compounds, is presented and discussed. The concentrations (mixing ratios) of HCFC-22, Dichlorodifluoromethane (CFC-12), Halon-1211, Trichlorofluoromethane (CFC-11), Dichloromethane (CH2Cl2), and Trichloroethylene (TCE) were enhanced with respect to the local background levels; the atmospheric mixing ratio of carbon tetrachloride (CCl4) was slightly higher than its local background level; on the other hand, 1,1,2-Trichlorotrifluoroethane (CFC-113) was relatively uniform and not very different from background atmospheric level in non-urban areas. Among these compounds, HCFC-22, Halon-1211 and the halogenated compounds, CH2Cl2 and TCE, used as solvents were strongly enhanced. The average mixing ratio of Halon-1211 was higher than the local background of ∼4.5 ppt by ∼60% although Halon-1211 production had been phased out by 1996. Hourly average mixing ratios of halocarbons (HCFC-22, CFC-12, Halon-1211, CFC-11, CH2Cl2, and TCE) illustrated a distinct diurnal cycle characterized with a pattern of elevated mixing ratio and large mixing ratio variability amplitude at night relative to that in daytime. Although emission sources of these halocarbons were complex, hourly average mixing ratios for most of these high variability halocarbons peaked at ∼5:00 AM when the hourly average wind speed reached the minimum value of the day; by contrast, the hourly average mixing ratio of CO peaked at ∼8:30 AM when the ambient atmospheric wind condition was strongly influenced by sea breezes during the traffic rush hours. This phenomenon revealed that meteorological factors predominated the distribution of halocarbon mixing ratio in the urban atmosphere and the traffic emission of CFC-12 derived from old vehicles manufactured before 1994 was insignificant to the CFC-12 mixing ratio in the urban atmosphere. The meteorological condition of nighttime atmospheric temperature inversion and low wind speed facilitated the accumulation of terrestrial airborne pollutants near the ground; consequently the hourly average mixing ratios at night were higher than those in daytime by up to ∼2% (CFC-11), ∼7% (CFC-12), ∼75% (HCFC-22), ∼72% (Halon-1211), ∼280% (CH2Cl2), and ∼155% (TCE).

DETERMINANTS OF TEMPORAL VARIABILITY IN NHEXAS-MARYLAND ENVIRONMENTAL CONCENTRATIONS, EXPOSURES, AND BIOMARKERS

EPA Science Inventory

The longitudinal NHEXAS-Maryland study measured metals, PAHs, and pesticides in several media to capture temporal variability. Questionnaires were concurrently administered to identify factors that influenced changes in contaminant levels over time. We constructed mixed-effects...

Synoptic-to-planetary scale wind variability enhances phytoplankton biomass at ocean fronts

NASA Astrophysics Data System (ADS)

Whitt, D. B.; Taylor, J. R.; Lévy, M.

2017-06-01

In nutrient-limited conditions, phytoplankton growth at fronts is enhanced by winds, which drive upward nutrient fluxes via enhanced turbulent mixing and upwelling. Hence, depth-integrated phytoplankton biomass can be 10 times greater at isolated fronts. Using theory and two-dimensional simulations with a coupled physical-biogeochemical ocean model, this paper builds conceptual understanding of the physical processes driving upward nutrient fluxes at fronts forced by unsteady winds with timescales of 4-16 days. The largest vertical nutrient fluxes occur when the surface mixing layer penetrates the nutricline, which fuels phytoplankton in the mixed layer. At a front, mixed layer deepening depends on the magnitude and direction of the wind stress, cross-front variations in buoyancy and velocity at the surface, and potential vorticity at the base of the mixed layer, which itself depends on past wind events. Consequently, mixing layers are deeper and more intermittent in time at fronts than outside fronts. Moreover, mixing can decouple in time from the wind stress, even without other sources of physical variability. Wind-driven upwelling also enhances depth-integrated phytoplankton biomass at fronts; when the mixed layer remains shallower than the nutricline, this results in enhanced subsurface phytoplankton. Oscillatory along-front winds induce both oscillatory and mean upwelling. The mean effect of oscillatory vertical motion is to transiently increase subsurface phytoplankton over days to weeks, whereas slower mean upwelling sustains this increase over weeks to months. Taken together, these results emphasize that wind-driven phytoplankton growth is both spatially and temporally intermittent and depends on a diverse combination of physical processes.

Variability of activity patterns across mood disorders and time of day.

PubMed

Krane-Gartiser, Karoline; Vaaler, Arne E; Fasmer, Ole Bernt; Sørensen, Kjetil; Morken, Gunnar; Scott, Jan

2017-12-19

Few actigraphy studies in mood disorders have simultaneously included unipolar (UP) and bipolar (BD) depression or BD mixed states as a separate subgroup from mania. This study compared objectively measured activity in UP, BD depression, mania and mixed states and examined if patterns differed according to time of day and/or diagnostic group. Eighty -eight acutely admitted inpatients with mood disorders (52 UP; 18 mania; 12 BD depression; 6 mixed states) underwent 24 hours of actigraphy monitoring. Non-parametric analyses were used to compare median activity level over 24 h (counts per minute), two time series (64-min periods of continuous motor activity) in the morning and evening, and variability in activity across and within groups. There was no between-group difference in 24-h median level of activity, but significant differences emerged between BD depression compared to mania in the active morning period, and between UP and mania and mixed states in the active evening period. Within-group analyses revealed that UP cases showed several significant changes between morning and evening activity, with fewer changes in the BD groups. Mean activity over 24 hours has limited utility in differentiating UP and BD. In contrast, analysis of non-linear variability measures of activity at different times of day could help objectively distinguish between mood disorder subgroups. ClinicalTrials.gov Identifier: NCT01415323 , first registration July 6, 2011.

Mixed layer modeling in the East Pacific warm pool during 2002

NASA Astrophysics Data System (ADS)

Van Roekel, Luke P.; Maloney, Eric D.

2012-06-01

Two vertical mixing models (the modified dynamic instability model of Price et al.; PWP, and K-Profile Parameterizaton; KPP) are used to analyze intraseasonal sea surface temperature (SST) variability in the northeast tropical Pacific near the Costa Rica Dome during boreal summer of 2002. Anomalies in surface latent heat flux and shortwave radiation are the root cause of the three intraseasonal SST oscillations of order 1°C amplitude that occur during this time, although surface stress variations have a significant impact on the third event. A slab ocean model that uses observed monthly varying mixed layer depths and accounts for penetrating shortwave radiation appears to well-simulate the first two SST oscillations, but not the third. The third oscillation is associated with small mixed layer depths (<5 m) forced by, and acting with, weak surface stresses and a stabilizing heat flux that cause a transient spike in SST of 2°C. Intraseasonal variations in freshwater flux due to precipitation and diurnal flux variability do not significantly impact these intraseasonal oscillations. These results suggest that a slab ocean coupled to an atmospheric general circulation model, as used in previous studies of east Pacific intraseasonal variability, may not be entirely adequate to realistically simulate SST variations. Further, while most of the results from the PWP and KPP models are similar, some important differences that emerge are discussed.

Angiotensin II and CRF receptors in the central nucleus of the amygdala mediate hemodynamic response variability to cocaine in conscious rats.

PubMed

Watanabe, Mari A; Kucenas, Sarah; Bowman, Tamara A; Ruhlman, Melissa; Knuepfer, Mark M

2010-01-14

Stress or cocaine evokes either a large increase in systemic vascular resistance (SVR) or a smaller increase in SVR accompanied by an increase in cardiac output (designated vascular and mixed responders, respectively) in Sprague-Dawley rats. We hypothesized that the central nucleus of the amygdala (CeA) mediates this variability. Conscious, freely-moving rats, instrumented for measurement of arterial pressure and cardiac output and for drug delivery into the CeA, were given cocaine (5 mg/kg, iv, 4-6 times) and characterized as vascular (n=15) or mixed responders (n=10). Subsequently, we administered cocaine after bilateral microinjections (100 nl) of saline or selective agents in the CeA. Muscimol (80 pmol), a GABA(A) agonist, or losartan (43.4 pmol), an AT(1) receptor antagonist, attenuated the cocaine-induced increase in SVR in vascular responders, selectively, such that vascular responders were no longer different from mixed responders. The corticotropin releasing factor (CRF) antagonist, alpha-helical CRF(9-41) (15.7 pmol), abolished the difference between cardiac output and SVR in mixed and vascular responders. We conclude that greater increases in SVR observed in vascular responders are dependent on AT(1) receptor activation and, to a lesser extent on CRF receptors. Therefore, AT(1) and CRF receptors in the CeA contribute to hemodynamic response variability to intravenous cocaine.

Angiotensin II and CRF Receptors in the Central Nucleus of the Amygdala Mediate Hemodynamic Response Variability to Cocaine in Conscious Rats

PubMed Central

Watanabe, Mari A.; Kucenas, Sarah; Bowman, Tamara A.; Ruhlman, Melissa; Knuepfer, Mark M.

2009-01-01

Stress or cocaine evokes either a large increase in systemic vascular resistance (SVR) or a smaller increase in SVR accompanied by an increase in cardiac output (designated vascular and mixed responders, respectively) in Sprague-Dawley rats. We hypothesized that the central nucleus of the amygdala (CeA) mediates this variability. Conscious, freely-moving rats, instrumented for measurement of arterial pressure and cardiac output and for drug delivery into the CeA, were given cocaine (5 mg/kg, iv, 4-6 times) and characterized as vascular (n=15) or mixed responders (n=10). Subsequently, we administered cocaine after bilateral microinjections (100 nl) of saline or selective agents in the CeA. Muscimol (80 pmol), a GABAA agonist, or losartan (43.4 pmol), an AT1 receptor antagonist, attenuated the cocaine-induced increase in SVR in vascular responders, selectively, such that vascular responders were no longer different from mixed responders. The corticotropin releasing factor (CRF) antagonist, α-helical CRF9-41 (15.7 pmol), abolished the difference between cardiac output and SVR in mixed and vascular responders. We conclude that greater increases in SVR observed in vascular responders are dependent on AT1 receptor activation and, to a lesser extent on CRF receptors. Therefore, AT1 and CRF receptors in the CeA contribute to hemodynamic response variability to intravenous cocaine. PMID:19879859

CGBayesNets: Conditional Gaussian Bayesian Network Learning and Inference with Mixed Discrete and Continuous Data

PubMed Central

Weiss, Scott T.

2014-01-01

Bayesian Networks (BN) have been a popular predictive modeling formalism in bioinformatics, but their application in modern genomics has been slowed by an inability to cleanly handle domains with mixed discrete and continuous variables. Existing free BN software packages either discretize continuous variables, which can lead to information loss, or do not include inference routines, which makes prediction with the BN impossible. We present CGBayesNets, a BN package focused around prediction of a clinical phenotype from mixed discrete and continuous variables, which fills these gaps. CGBayesNets implements Bayesian likelihood and inference algorithms for the conditional Gaussian Bayesian network (CGBNs) formalism, one appropriate for predicting an outcome of interest from, e.g., multimodal genomic data. We provide four different network learning algorithms, each making a different tradeoff between computational cost and network likelihood. CGBayesNets provides a full suite of functions for model exploration and verification, including cross validation, bootstrapping, and AUC manipulation. We highlight several results obtained previously with CGBayesNets, including predictive models of wood properties from tree genomics, leukemia subtype classification from mixed genomic data, and robust prediction of intensive care unit mortality outcomes from metabolomic profiles. We also provide detailed example analysis on public metabolomic and gene expression datasets. CGBayesNets is implemented in MATLAB and available as MATLAB source code, under an Open Source license and anonymous download at http://www.cgbayesnets.com. PMID:24922310

CGBayesNets: conditional Gaussian Bayesian network learning and inference with mixed discrete and continuous data.

PubMed

McGeachie, Michael J; Chang, Hsun-Hsien; Weiss, Scott T

2014-06-01

Bayesian Networks (BN) have been a popular predictive modeling formalism in bioinformatics, but their application in modern genomics has been slowed by an inability to cleanly handle domains with mixed discrete and continuous variables. Existing free BN software packages either discretize continuous variables, which can lead to information loss, or do not include inference routines, which makes prediction with the BN impossible. We present CGBayesNets, a BN package focused around prediction of a clinical phenotype from mixed discrete and continuous variables, which fills these gaps. CGBayesNets implements Bayesian likelihood and inference algorithms for the conditional Gaussian Bayesian network (CGBNs) formalism, one appropriate for predicting an outcome of interest from, e.g., multimodal genomic data. We provide four different network learning algorithms, each making a different tradeoff between computational cost and network likelihood. CGBayesNets provides a full suite of functions for model exploration and verification, including cross validation, bootstrapping, and AUC manipulation. We highlight several results obtained previously with CGBayesNets, including predictive models of wood properties from tree genomics, leukemia subtype classification from mixed genomic data, and robust prediction of intensive care unit mortality outcomes from metabolomic profiles. We also provide detailed example analysis on public metabolomic and gene expression datasets. CGBayesNets is implemented in MATLAB and available as MATLAB source code, under an Open Source license and anonymous download at http://www.cgbayesnets.com.

Variability of the Mixed-Layer Height Over Mexico City

NASA Astrophysics Data System (ADS)

García-Franco, J. L.; Stremme, W.; Bezanilla, A.; Ruiz-Angulo, A.; Grutter, M.

2018-02-01

The diurnal and seasonal variability of the mixed-layer height in urban areas has implications for ground-level air pollution and the meteorological conditions. Measurements of the backscatter of light pulses with a commercial lidar system were performed for a continuous period of almost six years between 2011 and 2016 in the southern part of Mexico City. The profiles were temporally and vertically smoothed, clouds were filtered out, and the mixed-layer height was determined with an ad hoc treatment of both the filtered and unfiltered profiles. The results are in agreement when compared with values of mixed-layer height reconstructed from, (i) radiosonde data, and (ii) surface and vertical column densities of a trace gas. The daily maxima of the mean mixed-layer height reach values > 3 km above ground level in the months of March-April, and are clearly lower (< 2.7 km ) during the colder months from September-December. Mean daily minima are typically observed at 0700 local time (UTC - 6h), and are lowest during the winter months with values on average below 500 m. The data presented here show an anti-correlation between high-pollution episodes and the height of the mixed layer. The growth rate of the convective mixed-layer height has a seasonal behaviour, which is characterized together with the mixed-layer-height anomalies. A clear residual layer is evident from the backscattered signals recorded in days with specific atmospheric conditions, but also from the cloud-filtered mean diurnal profiles. The occasional presence of a residual layer results in an overestimation of the reported mixed-layer height during the night and early morning hours.

Variability of the Mixed-Layer Height Over Mexico City

NASA Astrophysics Data System (ADS)

García-Franco, J. L.; Stremme, W.; Bezanilla, A.; Ruiz-Angulo, A.; Grutter, M.

2018-06-01

The diurnal and seasonal variability of the mixed-layer height in urban areas has implications for ground-level air pollution and the meteorological conditions. Measurements of the backscatter of light pulses with a commercial lidar system were performed for a continuous period of almost six years between 2011 and 2016 in the southern part of Mexico City. The profiles were temporally and vertically smoothed, clouds were filtered out, and the mixed-layer height was determined with an ad hoc treatment of both the filtered and unfiltered profiles. The results are in agreement when compared with values of mixed-layer height reconstructed from, (i) radiosonde data, and (ii) surface and vertical column densities of a trace gas. The daily maxima of the mean mixed-layer height reach values > 3 km above ground level in the months of March-April, and are clearly lower (< 2.7 km) during the colder months from September-December. Mean daily minima are typically observed at 0700 local time (UTC - 6h), and are lowest during the winter months with values on average below 500 m. The data presented here show an anti-correlation between high-pollution episodes and the height of the mixed layer. The growth rate of the convective mixed-layer height has a seasonal behaviour, which is characterized together with the mixed-layer-height anomalies. A clear residual layer is evident from the backscattered signals recorded in days with specific atmospheric conditions, but also from the cloud-filtered mean diurnal profiles. The occasional presence of a residual layer results in an overestimation of the reported mixed-layer height during the night and early morning hours.

International comparisons of the associations between objective measures of the built environment and transport-related walking and cycling: IPEN Adult Study.

PubMed

Christiansen, Lars B; Cerin, Ester; Badland, Hannah; Kerr, Jacqueline; Davey, Rachel; Troelsen, Jens; van Dyck, Delfien; Mitáš, Josef; Schofield, Grant; Sugiyama, Takemi; Salvo, Deborah; Sarmiento, Olga L; Reis, Rodrigo; Adams, Marc; Frank, Larry; Sallis, James F

2016-12-01

Mounting evidence documents the importance of urban form for active travel, but international studies could strengthen the evidence. The aim of the study was to document the strength, shape, and generalizability of relations of objectively measured built environment variables with transport-related walking and cycling. This cross-sectional study maximized variation of environments and demographics by including multiple countries and by selecting adult participants living in neighborhoods based on higher and lower classifications of objectively measured walkability and socioeconomic status. Analyses were conducted on 12,181 adults aged 18-66 years, drawn from 14 cities across 10 countries worldwide. Frequency of transport-related walking and cycling over the last seven days was assessed by questionnaire and four objectively measured built environment variables were calculated. Associations of built environment variables with transport-related walking and cycling variables were estimated using generalized additive mixed models, and were tested for curvilinearity and study site moderation. We found positive associations of walking for transport with all the environmental attributes, but also found that the relationships was only linear for land use mix, but not for residential density, intersection density, and the number of parks. Our findings suggest that there may be optimum values in these attributes, beyond which higher densities or number of parks could have minor or even negative impact. Cycling for transport was associated linearly with residential density, intersection density (only for any cycling), and land use mix, but not with the number of parks. Across 14 diverse cities and countries, living in more densely populated areas, having a well-connected street network, more diverse land uses, and having more parks were positively associated with transport-related walking and/or cycling. Except for land-use-mix, all built environment variables had curvilinear relationships with walking, with a plateau in the relationship at higher levels of the scales.

European transition to a low carbon electricity system using a mix of variable renewable energies: carbon saving trajectories as functions of production and storage capacity.

NASA Astrophysics Data System (ADS)

Francois, Baptiste; Creutin, Jean-Dominique

2016-04-01

Today, most of the produced energy is generated from fossil energy sources (i.e. coal, petroleum). As a result, the energy sector is still the main source of greenhouse gas in the atmosphere. For limiting greenhouse gas emission, a transition from fossil to renewable energy is required, increasing gradually the fraction energy coming from variable renewable energy (i.e. solar power, wind power and run-of-the river hydropower, hereafter denoted as VRE). VRE penetration, i.e. the percentage of demand satisfied by variable renewables assuming no storage capacity, is hampered by their variable and un-controllable features. Many studies show that combining different VRE over space smoothes their variability and increases their global penetration by a better match of demand fluctuations. When the demand is not fully supplied by the VRE generation, backup generation is required from stored energy (mostly from dams) or fossil sources, the latter being associated with high greenhouse gas emission. Thus the VRE penetration is a direct indicator of carbon savings and basically depends on the VRE installed capacity, its mix features, and on the installed storage capacity. In this study we analyze the European transition to a low carbon electricity system. Over a selection of representative regions we analyze carbon saving trajectories as functions of VRE production and storage capacities for different scenarios mixing one to three VRE with non-renewables. We show substantial differences between trajectories when the mix of sources is far from the local optimums, when the storage capacity evolves. We bring new elements of reflection about the effect of transport grid features from local independent systems to a European "copper plate". This work is part of the FP7 project COMPLEX (Knowledge based climate mitigation systems for a low carbon economy; Project FP7-ENV-2012 number: 308601; http://www.complex.ac.uk/).

International comparisons of the associations between objective measures of the built environment and transport-related walking and cycling: IPEN Adult Study

PubMed Central

Christiansen, Lars B.; Cerin, Ester; Badland, Hannah; Kerr, Jacqueline; Davey, Rachel; Troelsen, Jens; van Dyck, Delfien; Mitáš, Josef; Schofield, Grant; Sugiyama, Takemi; Salvo, Deborah; Sarmiento, Olga L.; Reis, Rodrigo; Adams, Marc; Frank, Larry; Sallis, James F.

2016-01-01

Introduction Mounting evidence documents the importance of urban form for active travel, but international studies could strengthen the evidence. The aim of the study was to document the strength, shape, and generalizability of relations of objectively measured built environment variables with transport-related walking and cycling. Methods This cross-sectional study maximized variation of environments and demographics by including multiple countries and by selecting adult participants living in neighborhoods based on higher and lower classifications of objectively measured walkability and socioeconomic status. Analyses were conducted on 12,181 adults aged 18–66 years, drawn from 14 cities across 10 countries worldwide. Frequency of transport-related walking and cycling over the last seven days was assessed by questionnaire and four objectively measured built environment variables were calculated. Associations of built environment variables with transport-related walking and cycling variables were estimated using generalized additive mixed models, and were tested for curvilinearity and study site moderation. Results We found positive associations of walking for transport with all the environmental attributes, but also found that the relationships was only linear for land use mix, but not for residential density, intersection density, and the number of parks. Our findings suggest that there may be optimum values in these attributes, beyond which higher densities or number of parks could have minor or even negative impact. Cycling for transport was associated linearly with residential density, intersection density (only for any cycling), and land use mix, but not with the number of parks. Conclusion Across 14 diverse cities and countries, living in more densely populated areas, having a well-connected street network, more diverse land uses, and having more parks were positively associated with transport-related walking and/or cycling. Except for land-use-mix, all built environment variables had curvilinear relationships with walking, with a plateau in the relationship at higher levels of the scales. PMID:28111613

Slowing down of North Pacific climate variability and its implications for abrupt ecosystem change.

PubMed

Boulton, Chris A; Lenton, Timothy M

2015-09-15

Marine ecosystems are sensitive to stochastic environmental variability, with higher-amplitude, lower-frequency--i.e., "redder"--variability posing a greater threat of triggering large ecosystem changes. Here we show that fluctuations in the Pacific Decadal Oscillation (PDO) index have slowed down markedly over the observational record (1900-present), as indicated by a robust increase in autocorrelation. This "reddening" of the spectrum of climate variability is also found in regionally averaged North Pacific sea surface temperatures (SSTs), and can be at least partly explained by observed deepening of the ocean mixed layer. The progressive reddening of North Pacific climate variability has important implications for marine ecosystems. Ecosystem variables that respond linearly to climate forcing will have become prone to much larger variations over the observational record, whereas ecosystem variables that respond nonlinearly to climate forcing will have become prone to more frequent "regime shifts." Thus, slowing down of North Pacific climate variability can help explain the large magnitude and potentially the quick succession of well-known abrupt changes in North Pacific ecosystems in 1977 and 1989. When looking ahead, despite model limitations in simulating mixed layer depth (MLD) in the North Pacific, global warming is robustly expected to decrease MLD. This could potentially reverse the observed trend of slowing down of North Pacific climate variability and its effects on marine ecosystems.

Detecting Non-Gaussian and Lognormal Characteristics of Temperature and Water Vapor Mixing Ratio

NASA Astrophysics Data System (ADS)

Kliewer, A.; Fletcher, S. J.; Jones, A. S.; Forsythe, J. M.

2017-12-01

Many operational data assimilation and retrieval systems assume that the errors and variables come from a Gaussian distribution. This study builds upon previous results that shows that positive definite variables, specifically water vapor mixing ratio and temperature, can follow a non-Gaussian distribution and moreover a lognormal distribution. Previously, statistical testing procedures which included the Jarque-Bera test, the Shapiro-Wilk test, the Chi-squared goodness-of-fit test, and a composite test which incorporated the results of the former tests were employed to determine locations and time spans where atmospheric variables assume a non-Gaussian distribution. These tests are now investigated in a "sliding window" fashion in order to extend the testing procedure to near real-time. The analyzed 1-degree resolution data comes from the National Oceanic and Atmospheric Administration (NOAA) Global Forecast System (GFS) six hour forecast from the 0Z analysis. These results indicate the necessity of a Data Assimilation (DA) system to be able to properly use the lognormally-distributed variables in an appropriate Bayesian analysis that does not assume the variables are Gaussian.

Variability of particle number emissions from diesel and hybrid diesel-electric buses in real driving conditions.

PubMed

Sonntag, Darrell B; Gao, H Oliver; Holmén, Britt A

2008-08-01

A linear mixed model was developed to quantify the variability of particle number emissions from transit buses tested in real-world driving conditions. Two conventional diesel buses and two hybrid diesel-electric buses were tested throughout 2004 under different aftertreatments, fuels, drivers, and bus routes. The mixed model controlled the confounding influence of factors inherent to on-board testing. Statistical tests showed that particle number emissions varied significantly according to the after treatment, bus route, driver, bus type, and daily temperature, with only minor variability attributable to differences between fuel types. The daily setup and operation of the sampling equipment (electrical low pressure impactor) and mini-dilution system contributed to 30-84% of the total random variability of particle measurements among tests with diesel oxidation catalysts. By controlling for the sampling day variability, the model better defined the differences in particle emissions among bus routes. In contrast, the low particle number emissions measured with diesel particle filters (decreased by over 99%) did not vary according to operating conditions or bus type but did vary substantially with ambient temperature.

Case mix, quality, and cost relationships in Colorado nursing homes.

PubMed

Schlenker, R E; Shaughessy, P W

1984-01-01

The analyses reported in this article assessed the cost, case mix, and quality interrelationships among Colorado nursing homes. A unique set of patient-level data was collected specifically to measure case mix and quality. Case mix was found to be strongly associated with cost, accounting for up to 45 percent of the variation in cost per patient day. The relationship between quality and cost was weaker; quality variables accounted for only about 10 percent of the cost per day variation. Case mix was also associated with several facility characteristics found to be significant in other cost studies, suggesting that such facility characteristics serve as partial proxy measures for case mix. The cost-case mix relationships appear to be strong enough to justify incorporating case mix directly in nursing home reimbursement systems. In contrast, the weaker cost-quality association implies that it may not (yet) be appropriate to incorporate quality directly in reimbursement.

Basin-scale variability in plankton biomass and community metabolism in the sub-tropical North Atlantic Ocean

NASA Astrophysics Data System (ADS)

Harrison, W. G.; Arístegui, J.; Head, E. J. H.; Li, W. K. W.; Longhurst, A. R.; Sameoto, D. D.

Three trans-Atlantic oceanographic surveys (Nova Scotia to Canary Islands) were carried out during fall 1992 and spring 1993 to describe the large-scale variability in hydrographic, chemical and biological properties of the upper water column of the subtropical gyre and adjacent waters. Significant spatial and temporal variability characterized a number of the biological pools and rate processes whereas others were relatively invariant. Systematic patterns were observed in the zonal distribution of some properties. Most notable were increases (eastward) in mixed-layer temperature and salinity, depths of the nitracline and chlorophyll- a maximum, regenerated production (NH 4 uptake) and bacterial production. Dissolved inorganic carbon (DIC) concentrations, phytoplankton biomass, mesozooplankton biomass and new production (NO 3 uptake) decreased (eastward). Bacterial biomass, primary production, and community respiration exhibited no discernible zonal distribution patterns. Seasonal variability was most evident in hydrography (cooler/fresher mixed-layer in spring), and chemistry (mixed-layer DIC concentration higher and nitracline shallower in spring) although primary production and bacterial production were significantly higher in spring than in fall. In general, seasonal variability was greater in the west than in the east; seasonality in most properties was absent west of Canary Islands (˜20°W). The distribution of autotrophs could be reasonably well explained by hydrography and nutrient structure, independent of location or season. Processes underlying the distribution of the microheterophs, however, were less clear. Heterotrophic biomass and metabolism was less variable than autotrophs and appeared to dominate the upper ocean carbon balance of the subtropical North Atlantic in both fall and spring. Geographical patterns in distribution are considered in the light of recent efforts to partition the ocean into distinct "biogeochemical provinces".

Higher-order methods for simulations on quantum computers

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

Sornborger, A.T.; Stewart, E.D.

1999-09-01

To implement many-qubit gates for use in quantum simulations on quantum computers efficiently, we develop and present methods reexpressing exp[[minus]i(H[sub 1]+H[sub 2]+[center dot][center dot][center dot])[Delta]t] as a product of factors exp[[minus]iH[sub 1][Delta]t], exp[[minus]iH[sub 2][Delta]t],[hor ellipsis], which is accurate to third or fourth order in [Delta]t. The methods we derive are an extended form of the symplectic method, and can also be used for an integration of classical Hamiltonians on classical computers. We derive both integral and irrational methods, and find the most efficient methods in both cases. [copyright] [ital 1999] [ital The American Physical Society

Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket

NASA Astrophysics Data System (ADS)

Sharapov, A. A.

2015-09-01

We introduce the concept of a variational tricomplex, which is applicable both to variational and nonvariational gauge systems. Assigning this tricomplex with an appropriate symplectic structure and a Cauchy foliation, we establish a general correspondence between the Lagrangian and Hamiltonian pictures of one and the same (not necessarily variational) dynamics. In practical terms, this correspondence allows one to construct the generating functional of a weak Poisson structure starting from that of a Lagrange structure. As a byproduct, a covariant procedure is proposed for deriving the classical BRST charge of the BFV formalism by a given BV master action. The general approach is illustrated by the examples of Maxwell’s electrodynamics and chiral bosons in two dimensions.

LEGO: A modular accelerator design code

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

Cai, Y.; Donald, M.; Irwin, J.

1997-08-01

An object-oriented accelerator design code has been designed and implemented in a simple and modular fashion. It contains all major features of its predecessors: TRACY and DESPOT. All physics of single-particle dynamics is implemented based on the Hamiltonian in the local frame of the component. Components can be moved arbitrarily in the three dimensional space. Several symplectic integrators are used to approximate the integration of the Hamiltonian. A differential algebra class is introduced to extract a Taylor map up to arbitrary order. Analysis of optics is done in the same way both for the linear and nonlinear case. Currently, themore » code is used to design and simulate the lattices of the PEP-II. It will also be used for the commissioning.« less

Power and limitation of soil properties as predictors of rangeland health and ecosystem functioning in a Northern mixed-grass prairie[Abstract

USDA-ARS?s Scientific Manuscript database

Soil properties are thought to affect rangeland ecosystem functioning (e.g. primary productivity, hydrology), and thus soil variables that are consistently correlated with key ecosystem functions may be general indicators of rangeland health. We summarize results from several studies in mixed-grass...

Mixing Methods in Randomized Controlled Trials (RCTs): Validation, Contextualization, Triangulation, and Control

ERIC Educational Resources Information Center

Spillane, James P.; Pareja, Amber Stitziel; Dorner, Lisa; Barnes, Carol; May, Henry; Huff, Jason; Camburn, Eric

2010-01-01

In this paper we described how we mixed research approaches in a Randomized Control Trial (RCT) of a school principal professional development program. Using examples from our study we illustrate how combining qualitative and quantitative data can address some key challenges from validating instruments and measures of mediator variables to…

Identity Formation in Adolescents from Italian, Mixed, and Migrant Families

ERIC Educational Resources Information Center

Crocetti, Elisabetta; Fermani, Alessandra; Pojaghi, Barbara; Meeus, Wim

2011-01-01

The purpose of this study was to compare identity formation in adolescents from Italian (n = 261), mixed (n = 100), and migrant families (n =148). Participants completed the Italian version of the Utrecht-Management of Identity Commitments Scale that assesses identity processes in educational and relational domains. Within a variable-centered…

One Strategy for Controlling Costs in University Teaching Hospitals

ERIC Educational Resources Information Center

Thompson, John D.; And Others

1978-01-01

A methodology is outlined that can be used by teaching hospitals in determining their costs of treating patients with a complex mix of diagnoses. It is not held that case mix alone explains all cost differences between teaching and nonteaching hospitals, but that factor must be isolated before examining other variables. (Author/LBH)

Integrating Micro-Macro Organizational Communication Research: Rationale, Issues, and Mechanisms.

ERIC Educational Resources Information Center

Miller, Vernon; And Others

The integration of micro-macro variables is critical to the development of organizational communication as an academic field. Mixed-level analysis is inherent in organizational phenomena, and its neglect perpetuates the gap in and fragmentation of organizational communication theories. Three of the many ways to design mixed-level analyses are…

Tidal and atmospheric forcing of the upper ocean in the Gulf of California. I - Sea surface temperature variability

NASA Technical Reports Server (NTRS)

Paden, Cynthia A.; Winant, Clinton D.; Abbott, Mark R.

1991-01-01

SST variability in the northern Gulf of California is examined on the basis of findings of two years of satellite infrared imagery (1984-1986). Empirical orthogonal functions of the temporal and spatial SST variance for 20 monthly mean images show that the dominant SST patterns are generated by spatially varying tidal mixing in the presence of seasonal heating and cooling. Atmospheric forcing of the northern gulf appears to occur over large spatial scales. Area-averaged SSTs for the Guaymas Basin, island region, and northern basin exhibit significant fluctuations which are highly correlated. These fluctuations in SST correspond to similar fluctuations in the air temperature which are related to synoptic weather events over the gulf. A regression analysis of the SST relative to the fortnightly tidal range shows that tidal mixing occurs over the sills in the island region as well as on the shallow northern shelf. Mixing over the sills occurs as a result of large breaking internal waves of internal hydraulic jumps which mix over water in the upper 300-500 m.

Evidence for magma mixing within the Laacher See magma chamber (East Eifel, Germany)

USGS Publications Warehouse

Worner, G.; Wright, T.L.

1984-01-01

The final pyroclastic products of the late Quaternary phonolitic Laacher See volcano (East Eifel, W.-Germany) range from feldspar-rich gray phonolite to dark olivine-bearing rocks with variable amounts of feldspar and Al-augite megacrysts. Petrographically and chemically homogeneous clasts occur along with composite lapilli spanning the compositional range from phonolite (MgO 0.9%) to mafic hybrid rock (MgO 7.0%) for all major and trace elements. Both a basanitic and a phonolitic phenocryst paragenesis occur within individual clasts. The phonolite-derived phenocrysts are characterized by glass inclusions of evolved composition, rare inverse zoning and strong resorption indicating disequilibrium with the mafic hybrid matrix. Basanitic (magnesian) clinopyroxene and olivine, in contrast, show skeletal (normally zoned) overgrowths indicative of post-mixing crystallization. In accord with petrographical and other chemical evidence, mass balance calculations suggest mixing of an evolved Laacher See phonolite containing variable amounts of mineral cumulates and a megacryst-bearing basanite magma. Magma mixing occurred just prior to eruption (hours) of the lowermost magma layer of the Laacher See magma chamber but did not trigger the volcanic activity. ?? 1984.

Favre-Averaged Turbulence Statistics in Variable Density Mixing of Buoyant Jets

NASA Astrophysics Data System (ADS)

Charonko, John; Prestridge, Kathy

2014-11-01

Variable density mixing of a heavy fluid jet with lower density ambient fluid in a subsonic wind tunnel was experimentally studied using Particle Image Velocimetry and Planar Laser Induced Fluorescence to simultaneously measure velocity and density. Flows involving the mixing of fluids with large density ratios are important in a range of physical problems including atmospheric and oceanic flows, industrial processes, and inertial confinement fusion. Here we focus on buoyant jets with coflow. Results from two different Atwood numbers, 0.1 (Boussinesq limit) and 0.6 (non-Boussinesq case), reveal that buoyancy is important for most of the turbulent quantities measured. Statistical characteristics of the mixing important for modeling these flows such as the PDFs of density and density gradients, turbulent kinetic energy, Favre averaged Reynolds stress, turbulent mass flux velocity, density-specific volume correlation, and density power spectra were also examined and compared with previous direct numerical simulations. Additionally, a method for directly estimating Reynolds-averaged velocity statistics on a per-pixel basis is extended to Favre-averages, yielding improved accuracy and spatial resolution as compared to traditional post-processing of velocity and density fields.

Effects of temporal averaging on short-term irradiance variability under mixed sky conditions

NASA Astrophysics Data System (ADS)

Lohmann, Gerald M.; Monahan, Adam H.

2018-05-01

Characterizations of short-term variability in solar radiation are required to successfully integrate large numbers of photovoltaic power systems into the electrical grid. Previous studies have used ground-based irradiance observations with a range of different temporal resolutions and a systematic analysis of the effects of temporal averaging on the representation of variability is lacking. Using high-resolution surface irradiance data with original temporal resolutions between 0.01 and 1 s from six different locations in the Northern Hemisphere, we characterize the changes in representation of temporal variability resulting from time averaging. In this analysis, we condition all data to states of mixed skies, which are the most potentially problematic in terms of local PV power volatility. Statistics of clear-sky index k* and its increments Δk*τ (i.e., normalized surface irradiance and changes therein over specified intervals of time) are considered separately. Our results indicate that a temporal averaging time scale of around 1 s marks a transition in representing single-point irradiance variability, such that longer averages result in substantial underestimates of variability. Higher-resolution data increase the complexity of data management and quality control without appreciably improving the representation of variability. The results do not show any substantial discrepancies between locations or seasons.

Measuring the surgical 'learning curve': methods, variables and competency.

PubMed

Khan, Nuzhath; Abboudi, Hamid; Khan, Mohammed Shamim; Dasgupta, Prokar; Ahmed, Kamran

2014-03-01

To describe how learning curves are measured and what procedural variables are used to establish a 'learning curve' (LC). To assess whether LCs are a valuable measure of competency. A review of the surgical literature pertaining to LCs was conducted using the Medline and OVID databases. Variables should be fully defined and when possible, patient-specific variables should be used. Trainee's prior experience and level of supervision should be quantified; the case mix and complexity should ideally be constant. Logistic regression may be used to control for confounding variables. Ideally, a learning plateau should reach a predefined/expert-derived competency level, which should be fully defined. When the group splitting method is used, smaller cohorts should be used in order to narrow the range of the LC. Simulation technology and competence-based objective assessments may be used in training and assessment in LC studies. Measuring the surgical LC has potential benefits for patient safety and surgical education. However, standardisation in the methods and variables used to measure LCs is required. Confounding variables, such as participant's prior experience, case mix, difficulty of procedures and level of supervision, should be controlled. Competency and expert performance should be fully defined. © 2013 The Authors. BJU International © 2013 BJU International.

Logit-normal mixed model for Indian Monsoon rainfall extremes

NASA Astrophysics Data System (ADS)

Dietz, L. R.; Chatterjee, S.

2014-03-01

Describing the nature and variability of Indian monsoon rainfall extremes is a topic of much debate in the current literature. We suggest the use of a generalized linear mixed model (GLMM), specifically, the logit-normal mixed model, to describe the underlying structure of this complex climatic event. Several GLMM algorithms are described and simulations are performed to vet these algorithms before applying them to the Indian precipitation data procured from the National Climatic Data Center. The logit-normal model was applied with fixed covariates of latitude, longitude, elevation, daily minimum and maximum temperatures with a random intercept by weather station. In general, the estimation methods concurred in their suggestion of a relationship between the El Niño Southern Oscillation (ENSO) and extreme rainfall variability estimates. This work provides a valuable starting point for extending GLMM to incorporate the intricate dependencies in extreme climate events.

Distillation of mixed-state continuous-variable entanglement by photon subtraction

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

Zhang Shengli; Loock, Peter van

2010-12-15

We present a detailed theoretical analysis for the distillation of one copy of a mixed two-mode continuous-variable entangled state using beam splitters and coherent photon-detection techniques, including conventional on-off detectors and photon-number-resolving detectors. The initial Gaussian mixed-entangled states are generated by transmitting a two-mode squeezed state through a lossy bosonic channel, corresponding to the primary source of errors in current approaches to optical quantum communication. We provide explicit formulas to calculate the entanglement in terms of logarithmic negativity before and after distillation, including losses in the channel and the photon detection, and show that one-copy distillation is still possible evenmore » for losses near the typical fiber channel attenuation length. A lower bound for the transmission coefficient of the photon-subtraction beam splitter is derived, representing the minimal value that still allows to enhance the entanglement.« less

MILP model for integrated balancing and sequencing mixed-model two-sided assembly line with variable launching interval and assignment restrictions

NASA Astrophysics Data System (ADS)

Azmi, N. I. L. Mohd; Ahmad, R.; Zainuddin, Z. M.

2017-09-01

This research explores the Mixed-Model Two-Sided Assembly Line (MMTSAL). There are two interrelated problems in MMTSAL which are line balancing and model sequencing. In previous studies, many researchers considered these problems separately and only few studied them simultaneously for one-sided line. However in this study, these two problems are solved simultaneously to obtain more efficient solution. The Mixed Integer Linear Programming (MILP) model with objectives of minimizing total utility work and idle time is generated by considering variable launching interval and assignment restriction constraint. The problem is analysed using small-size test cases to validate the integrated model. Throughout this paper, numerical experiment was conducted by using General Algebraic Modelling System (GAMS) with the solver CPLEX. Experimental results indicate that integrating the problems of model sequencing and line balancing help to minimise the proposed objectives function.

Impacts of sea-surface salinity in an eddy-resolving semi-global OGCM

NASA Astrophysics Data System (ADS)

Furue, Ryo; Takatama, Kohei; Sasaki, Hideharu; Schneider, Niklas; Nonaka, Masami; Taguchi, Bunmei

2018-02-01

To explore the impacts of sea-surface salinity (SSS) on the interannual variability of upper-ocean state, we compare two 10-year runs of an eddy-resolving ocean general circulation model (OGCM): in one, SSS is strongly restored toward a monthly climatology (World Ocean Atlas '98) and in the other, toward the SSS of a monthly gridded Argo product. The inclusion of the Argo SSS generally improves the interannual variability of the mixed layer depth; particularly so in the western tropical Pacific, where so-called "barrier layers" are reproduced when the Argo SSS is included. The upper-ocean subsurface salinity variability is also improved in the tropics and subtropics even below the mixed layer. To understand the reason for the latter improvement, we separate the salinity difference between the two runs into its "dynamical" and "spiciness" components. The dynamical component is dominated by small-scale noise due to the chaotic nature of mesoscale eddies. The spiciness difference indicates that as expected from the upper-ocean general circulation, SSS variability in the mixed layer is subducted into the thermocline in subtropics; this signal is generally advected downward, equatorward, and westward in the equator-side of the subtropical gyre. The SSS signal subducted in the subtropical North Pacific appears to enter the Indian Ocean through the Indonesian Throughflow, although this signal is weak and probably insignificant in our model.

Surgical outcomes of laparoscopic hysterectomy with concomitant endometriosis without bowel or bladder dissection: a cohort analysis to define a case-mix variable.

PubMed

Sandberg, Evelien M; Driessen, Sara R C; Bak, Evelien A T; van Geloven, Nan; Berger, Judith P; Smeets, Mathilde J G H; Rhemrev, Johann P T; Jansen, Frank Willem

2018-01-01

Pelvic endometriosis is often mentioned as one of the variables influencing surgical outcomes of laparoscopic hysterectomy (LH). However, its additional surgical risks have not been well established. The aim of this study was to analyze to what extent concomitant endometriosis influences surgical outcomes of LH and to determine if it should be considered as case-mix variable. A total of 2655 LH's were analyzed, of which 397 (15.0%) with concomitant endometriosis. For blood loss and operative time, no measurable association was found for stages I ( n  = 106) and II ( n  = 103) endometriosis compared to LH without endometriosis. LH with stages III ( n  = 93) and IV ( n  = 95) endometriosis were associated with more intra-operative blood loss ( p  = < .001) and a prolonged operative time ( p  = < .001) compared to LH without endometriosis. No significant association was found between endometriosis (all stages) and complications ( p  = .62). The findings of our study have provided numeric support for the influence of concomitant endometriosis on surgical outcomes of LH, without bowel or bladder dissection. Only stages III and IV were associated with a longer operative time and more blood loss and should thus be considered as case-mix variables in future quality measurement tools.

Numerical investigation of the variable nozzle effect on the mixed flow turbine performance characteristics

NASA Astrophysics Data System (ADS)

Meziri, B.; Hamel, M.; Hireche, O.; Hamidou, K.

2016-09-01

There are various matching ways between turbocharger and engine, the variable nozzle turbine is the most significant method. The turbine design must be economic with high efficiency and large capacity over a wide range of operational conditions. These design intents are used in order to decrease thermal load and improve thermal efficiency of the engine. This paper presents an original design method of a variable nozzle vane for mixed flow turbines developed from previous experimental and numerical studies. The new device is evaluated with a numerical simulation over a wide range of rotational speeds, pressure ratios, and different vane angles. The compressible turbulent steady flow is solved using the ANSYS CFX software. The numerical results agree well with experimental data in the nozzleless configuration. In the variable nozzle case, the results show that the turbine performance characteristics are well accepted in different open positions and improved significantly in low speed regime and at low pressure ratio.

Impacts of cattle grazing on spatio-temporal variability of soil moisture and above-ground live plant biomass in mixed grasslands

NASA Astrophysics Data System (ADS)

Virk, Ravinder

Areas with relatively high spatial heterogeneity generally have more biodiversity than spatially homogeneous areas due to increased potential habitat. Management practices such as controlled grazing also affect the biodiversity in grasslands, but the nature of this impact is not well understood. Therefore this thesis studies the impacts of variation in grazing on soil moisture and biomass heterogeneity. These are not only important in terms of management of protected grasslands, but also for designing an effective grazing system from a livestock management point of view. This research is a part of the cattle grazing experiment underway in Grasslands National Park (GNP) of Canada since 2006, as part of the adaptive management process for restoring ecological integrity of the northern mixed-grass prairie region. An experimental approach using field measurements and remote sensing (Landsat) was combined with modelling (CENTURY) to examine and predict the impacts of grazing intensity on the spatial heterogeneity and patterns of above-ground live plant biomass (ALB) in experimental pastures in a mixed grassland ecosystem. The field-based research quantified the temporal patterns and spatial variability in both soil moisture (SM) and ALB, and the influence of local intra-seasonal weather variability and slope location on the spatio-temporal variability of SM and ALB at field plot scales. Significant impacts of intra-seasonal weather variability, slope position and grazing pressure on SM and ALB across a range of scales (plot and local (within pasture)) were found. Grazing intensity significantly affected the ALB even after controlling for the effect of slope position. Satellite-based analysis extended the scale of interest to full pastures and the surrounding region to assess the effects of grazing intensity on the spatio-temporal pattern of ALB in mixed grasslands. Overall, low to moderate grazing intensity showed increase in ALB heterogeneity whereas no change in ALB heterogeneity over time was observed for heavy grazing intensity. All grazing intensities showed decrease in spatial range (patch size) over time indicating that grazing is a patchy process. The study demonstrates that cattle grazing with variable intensity can maintain and change the spatial patterns of vegetation in the studied region. Using a modelling approach, the relative degrees to which grazing intensity and soil properties affect grassland productivity and carbon dynamics at longer time-periods were investigated. Both grass productivity and carbon dynamics are sensitive to variability in soil texture and grazing intensity. Moderate grazing is predicted to be the best option in terms of maintaining sufficient heterogeneity to support species diversity, as well as for carbon management in the mixed grassland ecosystem.

Finite-g Strings

NASA Astrophysics Data System (ADS)

Vicedo, Benoit

2008-10-01

In view of one day proving the AdS/CFT correspondence, a deeper understanding of string theory on certain curved backgrounds such as AdS_5xS^5 is required. In this dissertation we make a step in this direction by focusing on RxS^3. It was discovered in recent years that string theory on AdS_5xS^5 admits a Lax formulation. However, the complete statement of integrability requires not only the existence of a Lax formulation, but also that the resulting integrals of motion are in pairwise involution. This idea is central to the first part of this thesis. Exploiting this integrability we apply algebro-geometric methods to string theory on RxS^3 and obtain the general finite-gap solution. The construction is based on an invariant algebraic curve previously found in the AdS_5xS^5 case. However, encoding the dynamics of the solution requires specification of additional marked points. By restricting the symplectic structure of the string to this algebro-geometric data we derive the action-angle variables of the system. We then perform a first-principle semiclassical quantisation of string theory on RxS^3 as a toy model for strings on AdS_5xS^5. The result is exactly what one expects from the dual gauge theory perspective, namely the underlying algebraic curve discretises in a natural way. We also derive a general formula for the fluctuation energies around the generic finite-gap solution. The ideas used can be generalised to AdS_5xS^5.

Bayesian Optimization Under Mixed Constraints with A Slack-Variable Augmented Lagrangian

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

Picheny, Victor; Gramacy, Robert B.; Wild, Stefan M.

An augmented Lagrangian (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global search in the presence of inequality constraints; however, a drawback was that expected improvement (EI) evaluations relied on Monte Carlo. Here we introduce an alternative slack variable AL, and show that in this formulation the EI may be evaluated with library routines. The slack variables furthermore facilitate equality as well as inequality constraints, and mixtures thereof.more » We show our new slack “ALBO” compares favorably to the original. Its superiority over conventional alternatives is reinforced on several mixed constraint examples.« less

Monitoring mixed venous oxygen saturation in patients with obstructive shock after massive pulmonary embolism.

PubMed

Krivec, Bojan; Voga, Gorazd; Podbregar, Matej

2004-05-31

Patients with massive pulmonary embolism and obstructive shock usually require hemodynamic stabilization and thrombolysis. Little is known about the optimal and proper use of volume infusion and vasoactive drugs, or about the titration of thrombolytic agents in patients with relative contraindication for such treatment. The aim of the study was to find the most rapidly changing hemodynamic variable to monitor and optimize the treatment of patients with obstructive shock following massive pulmonary embolism. Ten consecutive patients hospitalized in the medical intensive care unit in the community General Hospital with obstructive shock following massive pulmonary embolism were included in the prospective observational study. Heart rate, systolic arterial pressure, central venous pressure, mean pulmonary-artery pressure, cardiac index, total pulmonary vascular-resistance index, mixed venous oxygen saturation, and urine output were measured on admission and at 1, 2, 3, 4, 8, 12, and 16 hours. Patients were treated with urokinase through the distal port of a pulmonary-artery catheter. At 1 hour, mixed venous oxygen saturation, systolic arterial pressure and cardiac index were higher than their admission values (31+/-10 vs. 49+/-12%, p<0.0001; 86+/-12 vs. 105+/-17 mmHg, p<0.01; 1.5+/-0.4 vs. 1.9+/-0.7 L/min/m2, p<0.05; respectively), whereas heart rate, central venous pressure, mean pulmonary-artery pressure and urine output remained unchanged. Total pulmonary vascular-resistance index was lower than at admission (29+/-10 vs. 21+/-12 mmHg/L/min/m2, p<0.05). The relative change of mixed venous oxygen saturation at hour 1 was higher than the relative changes of all other studied variables (p<0.05). Serum lactate on admission and at 12 hours correlated to mixed venous oxygen saturation (r=-0.855, p<0.001). In obstructive shock after massive pulmonary embolism, mixed venous oxygen saturation changes more rapidly than other standard hemodynamic variables.

An Assessment of Southern Ocean Water Masses and Sea Ice During 1988-2007 in a Suite of Interannual CORE-II Simulations

NASA Technical Reports Server (NTRS)

Downes, Stephanie M.; Farneti, Riccardo; Uotila, Petteri; Griffies, Stephen M.; Marsland, Simon J.; Bailey, David; Behrens, Erik; Bentsen, Mats; Bi, Daohua; Biastoch, Arne;

Resource utilization in home health care: results of a prospective study.

PubMed

Trisolini, M G; Thomas, C P; Cashman, S B; Payne, S M

1994-01-01

Resource utilization in home health care has become an issue of concern due to rising costs and recent initiatives to develop prospective payment systems for home health care. A number of issues remain unresolved for the development of prospective reimbursement in this sector, including the types of variables to be included as payment variables and appropriate measures of resource use. This study supplements previous work on home health case-mix by analyzing the factors affecting one aspect of resource use for skilled nursing visits--visit length--and explores the usefulness of several specially collected variables which are not routinely available in administrative records. A data collection instrument was developed with a focus group of skilled nurses, identifying a range of variables hypothesized to affect visit length. Five categories of variables were studied using multiple regression analysis: provider-related; patient's socio-economic status; patient's clinical status; patient's support services; and visit-specific. The final regression model identifies 9 variables which significantly affect visit time. Five of the 9 are visit-specific variables, a significant finding since these are not routinely collected. Case-mix systems which include visit time as a measure of resource use will need to investigate visit-specific variables, as this study indicates they could have the largest influence on visit time. Two other types of resources used in home health care, supplies and security drivers, were also investigated in less detail.

Perspectives on dilution jet mixing

NASA Technical Reports Server (NTRS)

Holdeman, J. D.

1986-01-01

A microcomputer code which displays 3-D oblique and 2-D plots of the temperature distribution downstream of jets mixing with a confined crossflow has been used to investigate the effects of varying the several independent flow and geometric parameters on the mixing. Temperature profiles calculated with this empirical model are presented to show the effects of orifice size and spacing, momentum flux ratio, density ratio, variable temperature mainstream, flow area convergence, orifice aspect ratio, and opposed and axially staged rows of jets.

Investigation of micromixing by acoustically oscillated sharp-edges

PubMed Central

Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco

2016-01-01

Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel. PMID:27158292

Dispersion in deep polar firn driven by synoptic-scale surface pressure variability

NASA Astrophysics Data System (ADS)

Buizert, Christo; Severinghaus, Jeffrey P.

2016-09-01

Commonly, three mechanisms of firn air transport are distinguished: molecular diffusion, advection, and near-surface convective mixing. Here we identify and describe a fourth mechanism, namely dispersion driven by synoptic-scale surface pressure variability (or barometric pumping). We use published gas chromatography experiments on firn samples to derive the along-flow dispersivity of firn, and combine this dispersivity with a dynamical air pressure propagation model forced by surface air pressure time series to estimate the magnitude of dispersive mixing in the firn. We show that dispersion dominates mixing within the firn lock-in zone. Trace gas concentrations measured in firn air samples from various polar sites confirm that dispersive mixing occurs. Including dispersive mixing in a firn air transport model suggests that our theoretical estimates have the correct order of magnitude, yet may overestimate the true dispersion. We further show that strong barometric pumping, such as at the Law Dome site, may reduce the gravitational enrichment of δ15N-N2 and other tracers below gravitational equilibrium, questioning the traditional definition of the lock-in depth as the depth where δ15N enrichment ceases. Last, we propose that 86Kr excess may act as a proxy for past synoptic activity (or paleo-storminess) at the site.

Replica exchange and expanded ensemble simulations as Gibbs sampling: simple improvements for enhanced mixing.

PubMed

Chodera, John D; Shirts, Michael R

2011-11-21

The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in discovering new ways to enhance the phase space mixing of these protocols in order to improve sampling of uncorrelated configurations. Here, we demonstrate how both of these classes of algorithms can be considered as special cases of Gibbs sampling within a Markov chain Monte Carlo framework. Gibbs sampling is a well-studied scheme in the field of statistical inference in which different random variables are alternately updated from conditional distributions. While the update of the conformational degrees of freedom by Metropolis Monte Carlo or molecular dynamics unavoidably generates correlated samples, we show how judicious updating of the thermodynamic state indices--corresponding to thermodynamic parameters such as temperature or alchemical coupling variables--can substantially increase mixing while still sampling from the desired distributions. We show how state update methods in common use can lead to suboptimal mixing, and present some simple, inexpensive alternatives that can increase mixing of the overall Markov chain, reducing simulation times necessary to obtain estimates of the desired precision. These improved schemes are demonstrated for several common applications, including an alchemical expanded ensemble simulation, parallel tempering, and multidimensional replica exchange umbrella sampling.

Investigation of micromixing by acoustically oscillated sharp-edges.

PubMed

Nama, Nitesh; Huang, Po-Hsun; Huang, Tony Jun; Costanzo, Francesco

2016-03-01

Recently, acoustically oscillated sharp-edges have been utilized to achieve rapid and homogeneous mixing in microchannels. Here, we present a numerical model to investigate acoustic mixing inside a sharp-edge-based micromixer in the presence of a background flow. We extend our previously reported numerical model to include the mixing phenomena by using perturbation analysis and the Generalized Lagrangian Mean (GLM) theory in conjunction with the convection-diffusion equation. We divide the flow variables into zeroth-order, first-order, and second-order variables. This results in three sets of equations representing the background flow, acoustic response, and the time-averaged streaming flow, respectively. These equations are then solved successively to obtain the mean Lagrangian velocity which is combined with the convection-diffusion equation to predict the concentration profile. We validate our numerical model via a comparison of the numerical results with the experimentally obtained values of the mixing index for different flow rates. Further, we employ our model to study the effect of the applied input power and the background flow on the mixing performance of the sharp-edge-based micromixer. We also suggest potential design changes to the previously reported sharp-edge-based micromixer to improve its performance. Finally, we investigate the generation of a tunable concentration gradient by a linear arrangement of the sharp-edge structures inside the microchannel.

Durability of an inorganic polymer concrete coating

NASA Astrophysics Data System (ADS)

Wasserman, Kenneth

The objective of the research program reported in this thesis is to evaluate the durability of an inorganic polymer composite coating exposed to freeze/thaw cycling and wet-dry cycling. Freeze/thaw cycling is performed following ASTM D6944-09 Standard Practice for Resistance of Cured Coatings to Thermal Cycling and wet/dry cycling is performed following guidelines set forth in a thesis written by Ronald Garon at Rutgers University. For both sets of experiments, four coating mixture proportions were evaluated. The variables were: silica/alumina ratio, mixing protocol using high shear and normal shear mixing, curing temperatures of 70 and 120 degrees Fahrenheit and use of nano size constituent materials. The mix with highest silica/alumina ratio was designated as Mix 1 and mixes with lower ratios were designated as Mix 2 and Mix 3. Mix 4 had nano silica particles. Four prisms were used for each variable including control that had no coating. The performance of the coating was evaluated using adhesion strength measured using: ASTM D7234 Test Method for Pull-Off Strength of Coatings on Concrete Using Portable Adhesion Testers. Tests were performed after every five consecutive cycles of thermal conditioning and six consecutive cycles of wet-dry exposure. Results from the thermal cycling and wet-dry testing demonstrate that all coating formulations are durable. The minimum adhesion strength was 300 psi even though a relatively weak base concrete surface was chosen for the study. The weak surface was chosen to simulate aged concrete surfaces present in actual field conditions. Due to the inherent nature of the test procedure the variation in test results is high. However, based on the test results, high shear mixer and high temperature curing are not recommended. As expected nano size constituent materials provide better performance.

Is recurrence in major depressive disorder related to bipolarity and mixed features? Results from the BRIDGE-II-Mix study.

PubMed

Mazzarini, Lorenzo; Kotzalidis, Georgios D; Piacentino, Daria; Rizzato, Salvatore; Angst, Jules; Azorin, Jean-Michel; Bowden, Charles L; Mosolov, Sergey; Young, Allan H; Vieta, Eduard; Girardi, Paolo; Perugi, Giulio

2018-03-15

Current classifications separate Bipolar (BD) from Major Depressive Disorder (MDD) based on polarity rather than recurrence. We aimed to determine bipolar/mixed feature frequency in a large MDD multinational sample with (High-Rec) and without (Low-Rec) >3 recurrences, comparing the two subsamples. We measured frequency of bipolarity/hypomanic features during current depressive episodes (MDEs) in 2347 MDD patients from the BRIDGE-II-mix database, comparing High-Rec with Low-Rec. We used Bonferroni-corrected Student's t-test for continuous, and chi-squared test, for categorical variables. Logistic regression estimated the size of the association between clinical characteristics and High-Rec MDD. Compared to Low-Rec (n = 1084, 46.2%), High-Rec patients (n = 1263, 53.8%) were older, with earlier depressive onset, had more family history of BD, more atypical features, suicide attempts, hospitalisations, and treatment resistance and (hypo)manic switches when treated with antidepressants, higher comorbidity with borderline personality disorder, and more hypomanic symptoms during current MDE, resulting in higher rates of mixed depression according to both DSM-5 and research-based diagnostic (RBDC) criteria. Logistic regression showed age at first symptoms < 30 years, current MDE duration ≤ 1 month, hypomania/mania among first-degree relatives, past suicide attempts, treatment-resistance, antidepressant-induced swings, and atypical, mixed, or psychotic features during MDE to associate with High-Rec. Number of MDEs for defining recurrence was arbitrary; cross-sectionality did not allow assessment of conversion from MDD to BD. High-Rec MDD differed from Low-Rec group for several clinical/epidemiological variables, including bipolar/mixed features. Bipolarity specifier and RBDC were more sensitive than DSM-5 criteria in detecting bipolar and mixed features in MDD. Copyright © 2017. Published by Elsevier B.V.

Characterisation and modelling of mixing processes in groundwaters of a potential geological repository for nuclear wastes in crystalline rocks of Sweden.

PubMed

Gómez, Javier B; Gimeno, María J; Auqué, Luis F; Acero, Patricia

2014-01-15

This paper presents the mixing modelling results for the hydrogeochemical characterisation of groundwaters in the Laxemar area (Sweden). This area is one of the two sites that have been investigated, under the financial patronage of the Swedish Nuclear Waste and Management Co. (SKB), as possible candidates for hosting the proposed repository for the long-term storage of spent nuclear fuel. The classical geochemical modelling, interpreted in the light of the palaeohydrogeological history of the system, has shown that the driving process in the geochemical evolution of this groundwater system is the mixing between four end-member waters: a deep and old saline water, a glacial meltwater, an old marine water, and a meteoric water. In this paper we put the focus on mixing and its effects on the final chemical composition of the groundwaters using a comprehensive methodology that combines principal component analysis with mass balance calculations. This methodology allows us to test several combinations of end member waters and several combinations of compositional variables in order to find optimal solutions in terms of mixing proportions. We have applied this methodology to a dataset of 287 groundwater samples from the Laxemar area collected and analysed by SKB. The best model found uses four conservative elements (Cl, Br, oxygen-18 and deuterium), and computes mixing proportions with respect to three end member waters (saline, glacial and meteoric). Once the first order effect of mixing has been taken into account, water-rock interaction can be used to explain the remaining variability. In this way, the chemistry of each water sample can be obtained by using the mixing proportions for the conservative elements, only affected by mixing, or combining the mixing proportions and the chemical reactions for the non-conservative elements in the system, establishing the basis for predictive calculations. © 2013 Elsevier B.V. All rights reserved.

Microphysical and macrophysical characteristics of ice and mixed-phase clouds compared between in-situ observations from the NSF ORCAS campaign and the NCAR Community Atmospheric Model

NASA Astrophysics Data System (ADS)

Diao, M.; D'Alessandro, J.; Wu, C.; Liu, X.; Jensen, J. B.

2016-12-01

Large spatial coverage of ice and mixed-phase clouds is frequently observed in the higher latitudinal regions, especially over the Arctic and Antarctica. However, because the microphysical properties in the ice and mixed-phase clouds are highly variable in space, major challenges still remain in understanding the characteristics of ice and mixed-phase clouds on the microscale, as well as representing the sub-grid scale variabilities of relative humidity in the General Circulation Models. In this work, we use the in-situ, airborne observations from the NSF O2/N2 Ratio and CO2 Airborne Southern Ocean (ORCAS) Study (January - February 2016) to analyze the microphysical and macrophysical characteristics of ice and mixed-phase clouds over the Southern Ocean. A total of 18 flights onboard the NSF Gulfstream-V research aircraft are used to quantify the cloud properties and relative humidity distributions at various temperatures, pressures and aerosol background. New QC/QA water vapor data of the Vertical Cavity Surface Emitting Laser based on the laboratory calibration in summer 2016 will be presented. The statistical distributions of cloud microphysical properties and relative humidity with respect to ice (RHi) derived from in-situ observations will be compared with the NCAR Community Atmospheric Model Version 5 (CAM5). The horizontal extent of ice and mixed-phase clouds, and their formation and evolution will be derived based on the method of Diao et al. (2013). The occurrence frequency of ice supersaturation (i.e., RHi > 100%) will be examined in relation to various chemical tracers (i.e., O3 and CO) and total aerosol number concentrations (e.g., aerosols > 0.1 μm and > 0.5 μm) at clear-sky and in-cloud conditions. We will quantify whether these characteristics of ISS are scale-dependent from the microscale to the mesoscale. Overall, our work will evaluate the spatial variabilities of RHi inside/outside of ice and mixed-phase clouds, the frequency and magnitude of ice supersaturation, as well as the correlations between ice water content and liquid water content in the CAM5 simulations.

Main processes of the Atlantic cold tongue interannual variability

NASA Astrophysics Data System (ADS)

Planton, Yann; Voldoire, Aurore; Giordani, Hervé; Caniaux, Guy

2018-03-01

The interannual variability of the Atlantic cold tongue (ACT) is studied by means of a mixed-layer heat budget analysis. A method to classify extreme cold and warm ACT events is proposed and applied to ten various analysis and reanalysis products. This classification allows 5 cold and 5 warm ACT events to be selected over the period 1982-2007. Cold (warm) ACT events are defined by the presence of negative (positive) sea surface temperature (SST) anomalies at the center of the equatorial Atlantic in late boreal spring, preceded by negative (positive) zonal wind stress anomalies in the western equatorial Atlantic. An ocean general circulation model capable of reconstructing the interannual variability of the ACT correctly is used to demonstrate that cold ACT events develop rapidly from May to June mainly due to intense cooling by vertical mixing and horizontal advection. The simulated cooling at the center of the basin is the result of the combined effects of non-local and local processes. The non-local process is an upwelling associated with an eastward-propagating Kelvin wave, which makes the mixed-layer more shallow and preconditions the upper layers to be cooled by an intense heat loss at the base of the mixed-layer, which is amplified by a stronger local injection of energy from the atmosphere. The early cooling by vertical mixing in March is also shown to be a good predictor of June cooling. In July, horizontal advection starts to warm the mixed-layer abnormally and damps SST anomalies. The advection anomalies, which result from changes in the horizontal temperature gradient, are associated in some cases with the propagation of Rossby waves along the equator. During warm ACT events, processes are reversed, generating positive SST anomalies: a downwelling Kelvin wave triggers stratification anomalies and mixed-layer depth anomalies, amplified by a weaker injection of energy from the atmosphere in May-June. In July, warm ACT events are abnormally cooled due to negative horizontal advection anomalies resulting from processes similar to those that occur during cold ACT events. This additional cooling process extends the period of cooling of the ACT, reducing SST anomalies.

High prevalence of Mycobacterium tuberculosis mixed infection in the capital of moderate tuberculosis incidence country.

PubMed

Hajimiri, Elahe Sadat; Masoomi, Morteza; Ebrahimzadeh, Nayereh; Fateh, Abolfazl; Hadizadeh Tasbiti, Alireza; Rahimi Jamnani, Fatemeh; Bahrmand, Ahmad Reza; Mirsaeidi, Mehdi; Vaziri, Farzam; Siadat, Seyed Davar

2016-04-01

Recent studies using molecular epidemiological techniques have demonstrated mixed infection with multiple strains of Mycobacterium tuberculosis especially in countries with high tuberculosis (TB) burden. We aimed to determine the prevalence of mixed infection among patients with TB in the capital of Iran as a country with moderate incidence rate. Samples were collected randomly from January 2011 to December 2013 in Tehran, capital of Iran. A total of 75 M. tuberculosis isolates were genotyped by 24 loci mycobacterial interspersed repetitive unit-variable number tandem repeat typing (MIRU-VNTR) for screening the mixed infection. Twenty patients (20/75) were identified with mixed infection, and the estimated rate of mixed infection was 26.6%. Thirteen out of the 24 loci were able to detect the mixed infection in our study. Mixed infections occur at high prevalence among studied Iranian TB patients. Further research is inevitable to evaluate the association of mixed infection and disease progression and treatment. Copyright © 2016 Elsevier Ltd. All rights reserved.

Preliminary evaluation of environmental variables affecting diameter growth of individual hardwoods in the Southern Appalachian Mountains

Treesearch

W. Henry McNab; F. Thomas Lloyd

2001-01-01

The value of environmental variables as measures of site quality for individual tree growth models was determined for 12 common species of eastern hardwoods in the Southern Appalachian Mountains. Periodic diameter increment was modeled as a function of size, competition and environmental variables for 1,381 trees in even-aged stands of mixed-species. Resulting species...

Considerations when using variable frequency drive technology for pond aquculture

USDA-ARS?s Scientific Manuscript database

Some farmers have decided to use variable frequency drives (VFDs) to control pump speed and water flow rate to reduce operational cost and costs associated with repairs and maintenance. Mixed performance issues with VFDs and electric motors have been reported. Examples include frequent drive failure...

Comparative biology and population mixing among local, coastal and offshore Atlantic herring (Clupea harengus) in the North Sea, Skagerrak, Kattegat and western Baltic

PubMed Central

Slotte, Aril; Johannessen, Arne; Kvamme, Cecilie; Clausen, Lotte Worsøe; Nash, Richard D. M.

2017-01-01

The population structure of Atlantic herring (Clupea harengus) from 13 local, coastal and offshore areas of the North Sea, Skagerrak, Kattegat and western Baltic (northeast Atlantic) was studied using biological and environmental data from 1970–2015. The objective was to identify distinct populations by comparing variability in the temporal and spatial phenotypic characteristics and evaluate the potential for mixing of populations in time and space. The populations varied in biological characteristics such as mean vertebral counts (VS), growth and maturity ogives. Generalized additive models indicated temporally stable VS in the North Sea and western Baltic, whereas intra-annual temporal variation of VS occurred in other areas. High variability of VS within a population was not affected by environmental factors such as temperature and salinity. Consequently, seasonal VS variability can be explained by the presence or absence of herring populations as they migrate between areas. The three main populations identified in this paper correspond to the three managed stocks in this area: Norwegian spring spawners (NSS), western Baltic spring spawners (WBSS) and North Sea autumn spawners (NSAS). In addition, several local populations were identified in fjords or lakes along the coast, but our analyses could not detect direct mixing of local populations with the three main populations. Our results highlight the importance of recognizing herring dynamics and understanding the mixing of populations as a challenge for management of herring. PMID:29084258

The Association between Tax Structure and Cigarette Price Variability: Findings from the International Tobacco Control Policy Evaluation (ITC) Project

PubMed Central

Shang, Ce; Chaloupka, Frank J.; Fong, Geoffrey T; Thompson, Mary; O’Connor, Richard J

2015-01-01

Background Recent studies have shown that more opportunities exist for tax avoidance when cigarette excise tax structure departs from a uniform specific structure. However, the association between tax structure and cigarette price variability has not been thoroughly studied in the existing literature. Objective To examine how cigarette tax structure is associated with price variability. The variability of self-reported prices is measured using the ratios of differences between higher and lower prices to the median price such as the IQR-to-median ratio. Methods We used survey data taken from the International Tobacco Control Policy Evaluation (ITC) Project in 17 countries to conduct the analysis. Cigarette prices were derived using individual purchase information and aggregated to price variability measures for each surveyed country and wave. The effect of tax structures on price variability was estimated using Generalised Estimating Equations after adjusting for year and country attributes. Findings Our study provides empirical evidence of a relationship between tax structure and cigarette price variability. We find that, compared to the specific uniform tax structure, mixed uniform and tiered (specific, ad valorem or mixed) structures are associated with greater price variability (p≤0.01). Moreover, while a greater share of the specific component in total excise taxes is associated with lower price variability (p≤0.05), a tiered tax structure is associated with greater price variability (p≤0.01). The results suggest that a uniform and specific tax structure is the most effective tax structure for reducing tobacco consumption and prevalence by limiting price variability and decreasing opportunities for tax avoidance. PMID:25855641

Wood volume increment in thinned, 50- to 55-year-old, mixed-species Allegheny hardwoods

Treesearch

Christopher A. Nowak

1996-01-01

A thinning study in 50- to 55-year-old, even-aged, mixed species Allegheny hardwoods produced highly variable merchantable stemwood volume increment responses. Regression equations relating parameters of stand growth (ingrowth, mortality, survivor growth, net growth, and gross growth) to relative stand density had R2 values ranging from 0.07 to 0...

Ground cover, erosion risk and production implications of targeted management practices in Australian mixed farming systems: lessons from the Grain and Graze program

USDA-ARS?s Scientific Manuscript database

Maintaining the productive capacity of the agricultural soils of Australia's broadacre cropping zone requires careful management, given a highly variable climate and soils that are susceptible to degradation. Mixed croplivestock farming systems are the predominant land use across these regions and m...

A Mixed-Methods Study Investigating the Relationship between Media Multitasking Orientation and Grade Point Average

ERIC Educational Resources Information Center

Lee, Jennifer

2012-01-01

The intent of this study was to examine the relationship between media multitasking orientation and grade point average. The study utilized a mixed-methods approach to investigate the research questions. In the quantitative section of the study, the primary method of statistical analyses was multiple regression. The independent variables for the…

Evaluating potential trade-offs among fuel treatment strategies in mixed-conifer forests of the Sierra Nevada

Treesearch

Jens T. Stevens; Brandon M. Collins; Jonathan W. Long; Malcolm P. North; Susan J. Prichard; Leland W. Tarnay; Angela M. White

2016-01-01

Fuel treatments in fire-suppressed mixed-conifer forests are designed to moderate potential wildfire behavior and effects. However, the objectives for modifying potential fire effects can vary widely, from improving fire suppression efforts and protecting infrastructure, to reintroducing low-severity fire, to restoring and maintaining variable forest structure and...

Generalized Path Analysis and Generalized Simultaneous Equations Model for Recursive Systems with Responses of Mixed Types

ERIC Educational Resources Information Center

Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang

2006-01-01

This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…

On the Relationship between EFL Teachers' Classroom Management Approaches and the Dominant Teaching Style: A Mixed Method Study

ERIC Educational Resources Information Center

Kazemi, Ali; Soleimani, Neda

2016-01-01

As a factor contributing to a successful teaching career, classroom management can be affected by many latent and explicit variables. In this mixed method study, the researchers sought to scrutinize the possible connections among EFL teachers' classroom management approaches at two dimensions of behavior management and instructional management and…