Collective symplectic integrators

International Nuclear Information System (INIS)

McLachlan, Robert I; Modin, Klas; Verdier, Olivier

2014-01-01

We construct symplectic integrators for Lie–Poisson systems. The integrators are standard symplectic (partitioned) Runge–Kutta methods. Their phase space is a symplectic vector space equipped with a Hamiltonian action with momentum map J whose range is the target Lie–Poisson manifold, and their Hamiltonian is collective, that is, it is the target Hamiltonian pulled back by J. The method yields, for example, a symplectic midpoint rule expressed in 4 variables for arbitrary Hamiltonians on so(3) ∗ . The method specializes in the case that a sufficiently large symmetry group acts on the fibres of J, and generalizes to the case that the vector space carries a bifoliation. Examples involving many classical groups are presented. (paper)

A differential algebraic integration algorithm for symplectic mappings in systems with three-dimensional magnetic field

International Nuclear Information System (INIS)

Chang, P.; Lee, S.Y.; Yan, Y.T.

2006-01-01

A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders

A Differential Algebraic Integration Algorithm for Symplectic Mappings in Systems with Three-Dimensional Magnetic Field

International Nuclear Information System (INIS)

Chang, P

2004-01-01

A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders

Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics

Science.gov (United States)

Webb, G. M.; Anco, S. C.

2016-02-01

The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.

Symplecticity in Beam Dynamics: An Introduction

Energy Technology Data Exchange (ETDEWEB)

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.

Lectures on Symplectic Geometry

CERN Document Server

Silva, Ana Cannas

2001-01-01

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...

Reduction of symplectic principal R-bundles

International Nuclear Information System (INIS)

Lacirasella, Ignazio; Marrero, Juan Carlos; Padrón, Edith

2012-01-01

We describe a reduction process for symplectic principal R-bundles in the presence of a momentum map. These types of structures play an important role in the geometric formulation of non-autonomous Hamiltonian systems. We apply this procedure to the standard symplectic principal R-bundle associated with a fibration π:M→R. Moreover, we show a reduction process for non-autonomous Hamiltonian systems on symplectic principal R-bundles. We apply these reduction processes to several examples. (paper)

An optimized formulation for Deprit-type Lie transformations of Taylor maps for symplectic systems

International Nuclear Information System (INIS)

Shi, Jicong

1993-01-01

An optimized iterative formulation is presented for directly transforming a Taylor map of a symplectic system into a Deprit-type Lie transformation, which is a composition of a linear transfer matrix and a single Lie transformation, to an arbitrary order

Symmetries of the Space of Linear Symplectic Connections

Science.gov (United States)

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.

Associated symplectic and co-symplectic structures

International Nuclear Information System (INIS)

Frescura, F.A.M.; Lubczonok, G.

1991-01-01

In a recent article, the authors introduced a new geometric structure which they proposed to call co-symplectic geometry. This structure is based on a symmetric bilinear form of signature zero and leads to a geometry that is, in many respects, analogous to the symplectic geometry. Its usefulness lies principally in the fact that it provides scope for the geometrization of a number of familiar structures in physics which are not so easily amenable by the methods of symplectic geometry. These include the angular momentum operators of quantum theory, the Dirac operators in relativistic quantum field theory. It is anticipated that, in conjunction with the more familiar symplectic geometry, the co-symplectic geometry will go some way to providing the tools necessary for a full geometrization of physics. In this paper, a co-symplectic structure on the cotangent bundle T * X of an arbitrary manifold X is defined, and the notion of associated symplectic and co-symplectic structures is introduced. By way of example, the two-dimensional case is considered in some detail. The general case is investigated, and some implications of these results for polarizations in geometric quantization are considered

Infinitesimal deformations of a formal symplectic groupoid

OpenAIRE

Karabegov, Alexander

2010-01-01

Given a formal symplectic groupoid $G$ over a Poisson manifold $(M, \\pi_0)$, we define a new object, an infinitesimal deformation of $G$, which can be thought of as a formal symplectic groupoid over the manifold $M$ equipped with an infinitesimal deformation $\\pi_0 + \\epsilon \\pi_1$ of the Poisson bivector field $\\pi_0$. The source and target mappings of a deformation of $G$ are deformations of the source and target mappings of $G$. To any pair of natural star products $(\\ast, \\tilde\\ast)$ ha...

A general symplectic method for the response analysis of infinitely periodic structures subjected to random excitations

Directory of Open Access Journals (Sweden)

You-Wei Zhang

Full Text Available A general symplectic method for the random response analysis of infinitely periodic structures subjected to stationary/non-stationary random excitations is developed using symplectic mathematics in conjunction with variable separation and the pseudo-excitation method (PEM. Starting from the equation of motion for a single loaded substructure, symplectic analysis is firstly used to eliminate the dependent degrees of the freedom through condensation. A Fourier expansion of the condensed equation of motion is then applied to separate the variables of time and wave number, thus enabling the necessary recurrence scheme to be developed. The random response is finally determined by implementing PEM. The proposed method is justified by comparison with results available in the literature and is then applied to a more complicated time-dependent coupled system.

Transversity results and computations in symplectic field theory

International Nuclear Information System (INIS)

Fabert, Oliver

2008-01-01

Although the definition of symplectic field theory suggests that one has to count holomorphic curves in cylindrical manifolds R x V equipped with a cylindrical almost complex structure J, it is already well-known from Gromov-Witten theory that, due to the presence of multiply-covered curves, we in general cannot achieve transversality for all moduli spaces even for generic choices of J. In this thesis we treat the transversality problem of symplectic field theory in two important cases. In the first part of this thesis we are concerned with the rational symplectic field theory of Hamiltonian mapping tori, which is also called the Floer case. For this observe that in the general geometric setup for symplectic field theory, the contact manifolds can be replaced by mapping tori M φ of symplectic manifolds (M,ω M ) with symplectomorphisms φ. While the cylindrical contact homology of M φ is given by the Floer homologies of powers of φ, the other algebraic invariants of symplectic field theory for M φ provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian φ we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer, Wysocki and Zehnder and allows us to compute the full contact homology of M φ ≅ S 1 x M. The second part of this thesis is devoted to the branched covers of trivial cylinders over closed Reeb orbits, which are the trivial examples of punctured holomorphic curves studied in rational symplectic field theory. Since all moduli spaces of trivial curves with virtual dimension one cannot be regular, we use obstruction bundles in order to find compact perturbations making the Cauchy-Riemann operator transversal to the zero section and show that the algebraic count of elements in the resulting regular moduli spaces is zero. Once the analytical foundations of symplectic field theory are established, our result implies that the

Construction of nonlinear symplectic six-dimensional thin-lens maps by exponentiation

CERN Document Server

Heinemann, K; Schmidt, F

1995-01-01

The aim of this paper is to construct six-dimensional symplectic thin-lens transport maps for the tracking program SIXTRACK, continuing an earlier report by using another method which consistes in applying Lie series and exponentiation as described by W. Groebner and for canonical systems by A.J. Dragt. We firstly use an approximate Hamiltonian obtained by a series expansion of the square root. Furthermore, nonlinear crossing terms due to the curvature in bending magnets are neglected. An improved Hamiltonian, excluding solenoids, is introduced in Appendix A by using the unexpanded square root mentioned above, but neglecting again nonlinear crossing terms...

Transversity results and computations in symplectic field theory

Energy Technology Data Exchange (ETDEWEB)

Fabert, Oliver

2008-02-21

Although the definition of symplectic field theory suggests that one has to count holomorphic curves in cylindrical manifolds R x V equipped with a cylindrical almost complex structure J, it is already well-known from Gromov-Witten theory that, due to the presence of multiply-covered curves, we in general cannot achieve transversality for all moduli spaces even for generic choices of J. In this thesis we treat the transversality problem of symplectic field theory in two important cases. In the first part of this thesis we are concerned with the rational symplectic field theory of Hamiltonian mapping tori, which is also called the Floer case. For this observe that in the general geometric setup for symplectic field theory, the contact manifolds can be replaced by mapping tori M{sub {phi}} of symplectic manifolds (M,{omega}{sub M}) with symplectomorphisms {phi}. While the cylindrical contact homology of M{sub {phi}} is given by the Floer homologies of powers of {phi}, the other algebraic invariants of symplectic field theory for M{sub {phi}} provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian {phi} we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer, Wysocki and Zehnder and allows us to compute the full contact homology of M{sub {phi}} {approx_equal} S{sup 1} x M. The second part of this thesis is devoted to the branched covers of trivial cylinders over closed Reeb orbits, which are the trivial examples of punctured holomorphic curves studied in rational symplectic field theory. Since all moduli spaces of trivial curves with virtual dimension one cannot be regular, we use obstruction bundles in order to find compact perturbations making the Cauchy-Riemann operator transversal to the zero section and show that the algebraic count of elements in the resulting regular moduli spaces is zero. Once the analytical foundations of symplectic

Construction of symplectic full-turn maps by application of an arbitrary tracking code

International Nuclear Information System (INIS)

Warnock, R.L.

1989-03-01

A map to describe propagation of particles through any section of a nonlinear lattice may be represented as a Taylor expansion about the origin in phase space. Although the technique to compute the Taylor coefficients has been improved recently, the expansion may fail to provide adequate accuracy in regions where nonlinear effects are substantial. A representation of the map in angle-action coordinates, with the angle dependence given by a Fourier series, and the action dependence by polynomials in I/sup 1/2/, may be more successful. Maps of this form are easily constructed by taking Fourier transforms of results from an arbitrary symplectic tracking code. Examples are given of one-turn and two turn maps for the SLC North Damping Ring in a strongly nonlinear region. Results for accuracy and speed of evaluation of the maps are quite encouraging. It seems feasible to make accurate maps for the SSC by this method. 9 refs., 1 tab

Symplectic and trigonometrically fitted symplectic methods of second and third order

International Nuclear Information System (INIS)

Monovasilis, Th.; Simos, T.E.

2006-01-01

The numerical integration of Hamiltonian systems by symplectic and trigonometrically symplectic method is considered in this Letter. We construct new symplectic and trigonometrically symplectic methods of second and third order. We apply our new methods as well as other existing methods to the numerical integration of the harmonic oscillator, the 2D harmonic oscillator with an integer frequency ratio and an orbit problem studied by Stiefel and Bettis

A Symplectic Beam-Beam Interaction with Energy Change

International Nuclear Information System (INIS)

Moshammer, Herbert

2003-01-01

The performance of many colliding storage rings is limited by the beam-beam interaction. A particle feels a nonlinear force produced by the encountering bunch at the collision. This beam-beam force acts mainly in the transverse directions so that the longitudinal effects have scarcely been studied, except for the cases of a collision with a crossing angle. Recently, however, high luminosity machines are being considered where the beams are focused extensively at the interaction point (IP) so that the beam sizes can vary significantly within the bunch length. Krishnagopal and Siemann have shown that they should not neglect the bunch length effect in this case. The transverse kick depends on the longitudinal position as well as on the transverse position. If they include this effect, however, from the action-reaction principle, they should expect, at the same time, an energy change which depends on the transverse coordinates. Such an effect is reasonably understood from the fact that the beam-beam force is partly due to the electric field, which can change the energy. The action-reaction principle comes from the symplecticity of the reaction: the electromagnetic influence on a particle is described by a Hamiltonian. The symplecticity is one of the most fundamental requirements when studying the beam dynamics. A nonsymplectic approximation can easily lead to unphysical results. In this paper, they propose a simple, approximately but symplectic mapping for the beam-beam interaction which includes the energy change as well as the bunch-length effect. In the next section, they propose the mapping in a Hamiltonian form, which directly assures its symplecticity. Then in section 3, they study the nature of the mapping by interpreting its consequences. The mapping itself is quite general and can be applied to any distribution function. They show in Section 4 how it appears when the distribution function is a Gaussian in transverse directions. The mapping is applied to the

Symplectic entropy

International Nuclear Information System (INIS)

De Nicola, Sergio; Fedele, Renato; Man'ko, Margarita A; Man'ko, Vladimir I

2007-01-01

The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation

Symplectic S5 action on symplectic homotopy K3 surfaces

Indian Academy of Sciences (India)

HONGXIA LI

Let X be a symplectic homotopy K3 surface and G = S5 act on X symplectically. In this paper, we give a weak classification of the G action on X by discussing the fixed-point set structure. Besides, we analyse the exoticness of smooth structures of X under the action of G. Keywords. K3 surfaces; symplectic actions; exotic ...

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

Science.gov (United States)

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.

Modeling of stochastic broadening in a poloidally diverted discharge with piecewise analytic symplectic mapping flux functions

International Nuclear Information System (INIS)

Punjabi, Alkesh; Ali, Halima; Evans, Todd; Boozer, Allen

2008-01-01

A highly accurate calculation of the magnetic field line Hamiltonian in DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)] is made from piecewise analytic equilibrium fit data for shot 115467 3000 ms. The safety factor calculated from this Hamiltonian has a logarithmic singularity at an ideal separatrix. The logarithmic region inside the ideal separatrix contains 2.5% of toroidal flux inside the separatrix. The logarithmic region is symmetric about the separatrix. An area-preserving map for the field line trajectories is obtained in magnetic coordinates from the Hamiltonian equations of motion for the lines and a canonical transformation. This map is used to calculate trajectories of magnetic field lines in DIII-D. The field line Hamiltonian in DIII-D is used as the generating function for the map and to calculate stochastic broadening from field-errors and spatial noise near the separatrix. A very negligible amount (0.03%) of magnetic flux is lost from inside the separatrix due to these nonaxisymmetric fields. It is quite easy to add magnetic perturbations to generating functions and calculate trajectories for maps in magnetic coordinates. However, it is not possible to integrate across the separatrix. It is also difficult to find the physical position corresponding to magnetic coordinates. For open field lines, periodicity in the poloidal angle is assumed, which is not satisfactory. The goal of this paper is to demonstrate the efficacy of the symplectic mapping approach rather than using realistic DIII-D parameters or modeling specific experimental results

Classical Mechanics and Symplectic Integration

DEFF Research Database (Denmark)

Nordkvist, Nikolaj; Hjorth, Poul G.

2005-01-01

Content: Classical mechanics: Calculus of variations, Lagrange’s equations, Symmetries and Noether’s theorem, Hamilton’s equations, cannonical transformations, integrable systems, pertubation theory. Symplectic integration: Numerical integrators, symplectic integrators, main theorem on symplectic...

Weakly nonlocal symplectic structures, Whitham method and weakly nonlocal symplectic structures of hydrodynamic type

International Nuclear Information System (INIS)

Maltsev, A Ya

2005-01-01

We consider the special type of field-theoretical symplectic structures called weakly nonlocal. The structures of this type are, in particular, very common for integrable systems such as KdV or NLS. We introduce here the special class of weakly nonlocal symplectic structures which we call weakly nonlocal symplectic structures of hydrodynamic type. We investigate then the connection of such structures with the Whitham averaging method and propose the procedure of 'averaging' the weakly nonlocal symplectic structures. The averaging procedure gives the weakly nonlocal symplectic structure of hydrodynamic type for the corresponding Whitham system. The procedure also gives 'action variables' corresponding to the wave numbers of m-phase solutions of the initial system which give the additional conservation laws for the Whitham system

Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion

Energy Technology Data Exchange (ETDEWEB)

Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Zhou, Weien, E-mail: weienzhou@nudt.edu.cn [College of Science, National University of Defense Technology, Changsha 410073 (China)

2017-08-01

We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.

Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion

International Nuclear Information System (INIS)

Cui, Jianbo; Hong, Jialin; Liu, Zhihui; Zhou, Weien

2017-01-01

We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.

Symplectic and Hamiltonian structures of nonlinear evolution equations

International Nuclear Information System (INIS)

Dorfman, I.Y.

1993-01-01

A Hamiltonian structure on a finite-dimensional manifold can be introduced either by endowing it with a (pre)symplectic structure, or by describing the Poisson bracket with the help of a tensor with two upper indices named the Poisson structure. Under the assumption of nondegeneracy, the Poisson structure is nothing else than the inverse of the symplectic structure. Also in the degenerate case the distinction between the two approaches is almost insignificant, because both presymplectic and Poisson structures split into symplectic structures on leaves of appropriately chosen foliations. Hamiltonian structures that arise in the theory of evolution equations demonstrate something new in this respect: trying to operate in local terms, one is induced to develop both approaches independently. Hamiltonian operators, being the infinite-dimensional counterparts of Poisson structures, were the first to become the subject of investigations. A considerable period of time passed before the papers initiated research in the theory of symplectic operators, being the counterparts of presymplectic structures. In what follows, we focus on the main achievements in this field

Symplectic methods in circular accelerators

International Nuclear Information System (INIS)

Forest, E.

1994-01-01

By now symplectic integration has been applied to many problems in classical mechanics. It is my conviction that the field of particle simulation in circular rings is ideally suited for the application of symplectic integration. In this paper, I present a short description symplectic tools in circular storage rings

A survey of open problems in symplectic integration

Energy Technology Data Exchange (ETDEWEB)

McLachlan, R.I. [Univ. of Colorado, Boulder, CO (United States); Scovel, C. [Los Alamos National Lab., NM (United States)

1993-10-15

In the past few years there has been a substantial amount of research on symplectic integration. The subject is only part of a program concerned with numerically preserving a system`s inherent geometrical structures. Volume preservation, reversibility, local conservation laws for elliptic equations, and systems with integral invariants are but a few examples of such invariant structures. In many cases one requires a numerical method to stay in the smallest possible appropriate group of phase space maps. It is not the authors` opinion that symplecticity, for example, automatically makes a numerical method superior to all others, but it is their opinion that it should be taken seriously and that a conscious, informed decision be made in that regard. The authors present here a survey of open problems in symplectic integration, including other problems from the larger program. This is not intended as a review of symplectic integration and is naturally derived from the authors` own research interests. At present, this survey is incomplete, but the authors hope the help of the colleagues to be able to include in the proceedings of this conference a more comprehensive survey. Many of the problems mentioned here call for numerical experimentation, some for application of suggested but untested methods, some for new methods, and some for theorems, Some envisage large research programs.

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

Punjabi, Alkesh; Ali, Halima

2008-01-01

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.

Complex and symplectic geometry

CERN Document Server

Medori, Costantino; Tomassini, Adriano

2017-01-01

This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Symplectic Tracking of Multi-Isotopic Heavy-Ion Beams in SixTrack

CERN Document Server

Hermes, Pascal; De Maria, Riccardo

2016-01-01

The software SixTrack provides symplectic proton tracking over a large number of turns. The code is used for the tracking of beam halo particles and the simulation of their interaction with the collimators to study the efficiency of the LHC collimation system. Tracking simulations for heavy-ion beams require taking into account the mass to charge ratio of each particle because heavy ions can be subject to fragmentation at their passage through the collimators. In this paper we present the derivation of a Hamiltonian for multi-isotopic heavy-ion beams and symplectic tracking maps derived from it. The resulting tracking maps were implemented in the tracking software SixTrack. With this modification, SixTrack can be used to natively track heavy-ion beams of multiple isotopes through a magnetic accelerator lattice.

Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology & Symplectic Geometry, Noncommutative Geometry and Physics

CERN Document Server

Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry

2014-01-01

Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...

Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems

International Nuclear Information System (INIS)

Struckmeier, Juergen

2005-01-01

We will present a consistent description of Hamiltonian dynamics on the 'symplectic extended phase space' that is analogous to that of a time-independent Hamiltonian system on the conventional symplectic phase space. The extended Hamiltonian H 1 and the pertaining extended symplectic structure that establish the proper canonical extension of a conventional Hamiltonian H will be derived from a generalized formulation of Hamilton's variational principle. The extended canonical transformation theory then naturally permits transformations that also map the time scales of the original and destination system, while preserving the extended Hamiltonian H 1 , and hence the form of the canonical equations derived from H 1 . The Lorentz transformation, as well as time scaling transformations in celestial mechanics, will be shown to represent particular canonical transformations in the symplectic extended phase space. Furthermore, the generalized canonical transformation approach allows us to directly map explicitly time-dependent Hamiltonians into time-independent ones. An 'extended' generating function that defines transformations of this kind will be presented for the time-dependent damped harmonic oscillator and for a general class of explicitly time-dependent potentials. In the appendix, we will re-establish the proper form of the extended Hamiltonian H 1 by means of a Legendre transformation of the extended Lagrangian L 1

Function theory on symplectic manifolds

CERN Document Server

Polterovich, Leonid

2014-01-01

This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards. I like the spirit of this book. It formulates concepts clearly and explains the relationship between them. The subject matter is i...

Wigner functions on non-standard symplectic vector spaces

Science.gov (United States)

Dias, Nuno Costa; Prata, João Nuno

2018-01-01

We consider the Weyl quantization on a flat non-standard symplectic vector space. We focus mainly on the properties of the Wigner functions defined therein. In particular we show that the sets of Wigner functions on distinct symplectic spaces are different but have non-empty intersections. This extends previous results to arbitrary dimension and arbitrary (constant) symplectic structure. As a by-product we introduce and prove several concepts and results on non-standard symplectic spaces which generalize those on the standard symplectic space, namely, the symplectic spectrum, Williamson's theorem, and Narcowich-Wigner spectra. We also show how Wigner functions on non-standard symplectic spaces behave under the action of an arbitrary linear coordinate transformation.

Symplectic geometry and Fourier analysis

CERN Document Server

Wallach, Nolan R

2018-01-01

Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.

EXPLICIT SYMPLECTIC-LIKE INTEGRATORS WITH MIDPOINT PERMUTATIONS FOR SPINNING COMPACT BINARIES

Energy Technology Data Exchange (ETDEWEB)

Luo, Junjie; Wu, Xin; Huang, Guoqing [Department of Physics and Institute of Astronomy, Nanchang University, Nanchang 330031 (China); Liu, Fuyao, E-mail: xwu@ncu.edu.cn [School of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620 (China)

2017-01-01

We refine the recently developed fourth-order extended phase space explicit symplectic-like methods for inseparable Hamiltonians using Yoshida’s triple product combined with a midpoint permuted map. The midpoint between the original variables and their corresponding extended variables at every integration step is readjusted as the initial values of the original variables and their corresponding extended ones at the next step integration. The triple-product construction is apparently superior to the composition of two triple products in computational efficiency. Above all, the new midpoint permutations are more effective in restraining the equality of the original variables and their corresponding extended ones at each integration step than the existing sequent permutations of momenta and coordinates. As a result, our new construction shares the benefit of implicit symplectic integrators in the conservation of the second post-Newtonian Hamiltonian of spinning compact binaries. Especially for the chaotic case, it can work well, but the existing sequent permuted algorithm cannot. When dissipative effects from the gravitational radiation reaction are included, the new symplectic-like method has a secular drift in the energy error of the dissipative system for the orbits that are regular in the absence of radiation, as an implicit symplectic integrator does. In spite of this, it is superior to the same-order implicit symplectic integrator in accuracy and efficiency. The new method is particularly useful in discussing the long-term evolution of inseparable Hamiltonian problems.

Multi-symplectic Birkhoffian structure for PDEs with dissipation terms

International Nuclear Information System (INIS)

Su Hongling; Qin Mengzhao; Wang Yushun; Scherer, Rudolf

2010-01-01

A generalization of the multi-symplectic form for Hamiltonian systems to self-adjoint systems with dissipation terms is studied. These systems can be expressed as multi-symplectic Birkhoffian equations, which leads to a natural definition of Birkhoffian multi-symplectic structure. The concept of Birkhoffian multi-symplectic integrators for Birkhoffian PDEs is investigated. The Birkhoffian multi-symplectic structure is constructed by the continuous variational principle, and the Birkhoffian multi-symplectic integrator by the discrete variational principle. As an example, two Birkhoffian multi-symplectic integrators for the equation describing a linear damped string are given.

Complex/Symplectic Mirrors

Energy Technology Data Exchange (ETDEWEB)

Chuang, Wu-yen; Kachru, Shamit; /Stanford U., ITP /SLAC; Tomasiello, Alessandro; /Stanford U., ITP

2005-10-28

We construct a class of symplectic non-Kaehler and complex non-Kaehler string theory vacua, extending and providing evidence for an earlier suggestion by Polchinski and Strominger. The class admits a mirror pairing by construction. Comparing hints from a variety of sources, including ten-dimensional supergravity and KK reduction on SU(3)-structure manifolds, suggests a picture in which string theory extends Reid's fantasy to connect classes of both complex non-Kaehler and symplectic non-Kaehler manifolds.

Symplectic quantum structure

Energy Technology Data Exchange (ETDEWEB)

Voit, Kay-Michael

2008-06-16

In the first part we considered the quantum phase space in terms of noncommutative differential geometry. Following relevant literature, a short introduction to vector fields and differential forms on the differential vector space M{sub N}(C) was given. Special emphasis has been laid on the construction of a canonical symplectic form analogous to the one known from classical mechanics. The canonical choice of this form has been shown to be just the (scaled) commutator of two matrices. Using the Schwinger basis, the symplectic form derived in the first sections has been further examined by calculating concrete expressions for products of general matrices and their commutators which are, as we remember, just the symplectic form. Subsequently, a discrete analog to the continuous theory has been developed, in which the lattice of the quantum phase space forms the base space, and the Heisenberg group including the Schwinger elements is identified with the fiber space. In the continuum limit it could be shown that the discrete theory seamlessly passed into the commonly known continuous theory of connection forms on fiber bundles. The connection form and its exterior covariant derivation, the curvature form, have been calculated. It has been found that the curvature form can even be pulled back to the symplectic form by the section defined by the Schwinger elements. (orig.)

On local invariants of singular symplectic forms

Science.gov (United States)

Domitrz, Wojciech

2017-04-01

We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.

Formal Symplectic Groupoid of a Deformation Quantization

Science.gov (United States)

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.

Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems

DEFF Research Database (Denmark)

Nest, Ryszard; Tsygan, Boris

2001-01-01

Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely the Poisson structures coming from symplectic Lie algebroids......, as well as holomorphic symplectic structures. For deformations of these structures we prove the classification theorems and a general a general index theorem....

Symplectic Geometric Algorithms for Hamiltonian Systems

CERN Document Server

Feng, Kang

2010-01-01

"Symplectic Geometry Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development

Orthogonal and symplectic

CERN Document Server

Mason, A M

2018-01-01

In this paper the authors apply to the zeros of families of L-functions with orthogonal or symplectic symmetry the method that Conrey and Snaith (Correlations of eigenvalues and Riemann zeros, 2008) used to calculate the n-correlation of the zeros of the Riemann zeta function. This method uses the Ratios Conjectures (Conrey, Farmer, and Zimbauer, 2008) for averages of ratios of zeta or L-functions. Katz and Sarnak (Zeroes of zeta functions and symmetry, 1999) conjecture that the zero statistics of families of L-functions have an underlying symmetry relating to one of the classical compact groups U(N), O(N) and USp(2N). Here the authors complete the work already done with U(N) (Conrey and Snaith, Correlations of eigenvalues and Riemann zeros, 2008) to show how new methods for calculating the n-level densities of eigenangles of random orthogonal or symplectic matrices can be used to create explicit conjectures for the n-level densities of zeros of L-functions with orthogonal or symplectic symmetry, including al...

The Maslov index in symplectic Banach spaces

CERN Document Server

Booss-Bavnbek, Bernhelm

2018-01-01

The authors consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index. As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral f...

The Maslov index in symplectic Banach spaces

DEFF Research Database (Denmark)

Booss-Bavnbek, Bernhelm; Zhu, Chaofeng

. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all...... for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds....

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

Science.gov (United States)

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.

Contact and symplectic topology

CERN Document Server

Colin, Vincent; Stipsicz, András

2014-01-01

Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.

Multi-symplectic Preissmann methods for generalized Zakharov-Kuznetsov equation

International Nuclear Information System (INIS)

Wang Junjie; Yang Kuande; Wang Liantang

2012-01-01

Generalized Zakharov-Kuznetsov equation, a typical nonlinear wave equation, was studied based on the multi-symplectic theory in Hamilton space. The multi-symplectic formulations of generalized Zakharov-Kuznetsov equation with several conservation laws are presented. The multi-symplectic Preissmann method is used to discretize the formulations. The numerical experiment is given, and the results verify the efficiency of the multi-symplectic scheme. (authors)

Coherent State Projection Operator Representation of Symplectic Transformations as a Loyal Representation of Symplectic Group

Science.gov (United States)

Fan, Hong-Yi; Chen, Jun-Hua

2002-08-01

We find that the coherent state projection operator representation of symplectic transformation constitutes a loyal group representation of symplectic group. The result of successively applying squeezing operators on number state can be easily derived. The project supported by National Natural Science Foundation of China under Grant No. 10575057 and the President Foundation of the Chinese Academy of Sciences

Relative symplectic caps, 4-genus and fibered knots

Indian Academy of Sciences (India)

We prove relative versions of the symplectic capping theorem and sufficiency of Giroux's criterion for Stein fillability and use these to study the 4-genus of knots. More precisely, suppose we have a symplectic 4-manifold with convex boundary and a symplectic surface in such that is a transverse knot in .

Poisson traces, D-modules, and symplectic resolutions.

Science.gov (United States)

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Poisson traces, D-modules, and symplectic resolutions

Science.gov (United States)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Generalized reciprocity principle for discrete symplectic systems

Directory of Open Access Journals (Sweden)

Julia Elyseeva

2015-12-01

Full Text Available This paper studies transformations for conjoined bases of symplectic difference systems $Y_{i+1}=\\mathcal S_{i}Y_{i}$ with the symplectic coefficient matrices $\\mathcal S_i.$ For an arbitrary symplectic transformation matrix $P_{i}$ we formulate most general sufficient conditions for $\\mathcal S_{i},\\, P_{i}$ which guarantee that $P_{i}$ preserves oscillatory properties of conjoined bases $Y_{i}.$ We present examples which show that our new results extend the applicability of the discrete transformation theory.

A modified symplectic PRK scheme for seismic wave modeling

Science.gov (United States)

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.

Elementary symplectic topology and mechanics

CERN Document Server

Cardin, Franco

2015-01-01

This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in...

On orbifold criteria for symplectic toric quotients

DEFF Research Database (Denmark)

Farsi, Carla; Herbig, Hans-Christian; Seaton, Christopher

2013-01-01

We introduce the notion of regular symplectomorphism and graded regular symplectomorphism between singular phase spaces. Our main concern is to exhibit examples of unitary torus representations whose symplectic quotients cannot be graded regularly symplectomorphic to the quotient of a symplectic...

Examples of integrable and non-integrable systems on singular symplectic manifolds

Science.gov (United States)

Delshams, Amadeu; Kiesenhofer, Anna; Miranda, Eva

2017-05-01

We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell's transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lowering its rank at certain points. The resulting geometrical structures that model these examples are no longer symplectic but symplectic with singularities which are mainly of two types: bm-symplectic and m-folded symplectic structures. These examples comprise the three body problem as non-integrable exponent and some integrable reincarnations such as the two fixed-center problem. Given that the geometrical and dynamical properties of bm-symplectic manifolds and folded symplectic manifolds are well-understood [10-12,9,15,13,14,24,20,22,25,28], we envisage that this new point of view in this collection of examples can shed some light on classical long-standing problems concerning the study of dynamical properties of these systems seen from the Poisson viewpoint.

Translating solitons to symplectic and Lagrangian mean curvature flows

International Nuclear Information System (INIS)

Han Xiaoli; Li Jiayu

2007-05-01

In this paper, we construct finite blow-up examples for symplectic mean curvature flows and we study symplectic translating solitons. We prove that there is no translating solitons with vertical bar α vertical bar ≤ α 0 to the symplectic mean curvature flow or to the almost calibrated Lagrangian mean curvature flow for some α 0 . (author)

Quantum symplectic geometry. 1. The matrix Hamiltonian formalism

International Nuclear Information System (INIS)

Djemai, A.E.F.

1994-07-01

The main purpose of this work is to describe the quantum analogue of the usual classical symplectic geometry and then to formulate the quantum mechanics as a (quantum) non-commutative symplectic geometry. In this first part, we define the quantum symplectic structure in the context of the matrix differential geometry by using the discrete Weyl-Schwinger realization of the Heisenberg group. We also discuss the continuous limit and give an expression of the quantum structure constants. (author). 42 refs

Note on Symplectic SVD-Like Decomposition

Directory of Open Access Journals (Sweden)

AGOUJIL Said

2016-02-01

Full Text Available The aim of this study was to introduce a constructive method to compute a symplectic singular value decomposition (SVD-like decomposition of a 2n-by-m rectangular real matrix A, based on symplectic refectors.This approach used a canonical Schur form of skew-symmetric matrix and it allowed us to compute eigenvalues for the structured matrices as Hamiltonian matrix JAA^T.

Explicit symplectic algorithms based on generating functions for charged particle dynamics

Science.gov (United States)

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.

Symplectic topology of integrable Hamiltonian systems

International Nuclear Information System (INIS)

Nguyen Tien Zung.

1993-08-01

We study the topology of integrable Hamiltonian systems, giving the main attention to the affine structure of their orbit spaces. In particular, we develop some aspects of Fomenko's theory about topological classification of integrable non-degenerate systems, and consider some relations between such systems and ''pure'' contact and symplectic geometry. We give a notion of integrable surgery and use it to obtain some interesting symplectic structures. (author). Refs, 10 figs

Symplectic integrators with adaptive time steps

Science.gov (United States)

Richardson, A. S.; Finn, J. M.

2012-01-01

In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper, we identify the causes for this lack of performance, and find that they fall into two categories. In the first, the time step is considered a function of time alone, Δ = Δ(t). In this case, backward error analysis shows that while the algorithms remain symplectic, parametric instabilities may arise because of resonance between oscillations of Δ(t) and the orbital motion. In the second category the time step is a function of phase space variables Δ = Δ(q, p). In this case, the system of equations to be solved is analyzed by introducing a new time variable τ with dt = Δ(q, p) dτ. The transformed equations are no longer in Hamiltonian form, and thus do not benefit from integration methods which would be symplectic for Hamiltonian systems. We analyze two methods for integrating the transformed equations which do, however, preserve the structure of the original equations. The first is an extended phase space method, which has been successfully used in previous studies of adaptive time step symplectic integrators. The second, novel, method is based on a non-canonical mixed-variable generating function. Numerical trials for both of these methods show good results, without parametric instabilities or spurious growth or damping. It is then shown how to adapt the time step to an error estimate found by backward error analysis, in order to optimize the time-stepping scheme. Numerical results are obtained using this formulation and compared with other time-stepping schemes for the extended phase space symplectic method.

The GL(1 vertical stroke 1)-symplectic fermion correspondence

International Nuclear Information System (INIS)

Creutzig, Thomas; Roenne, Peter B.

2008-12-01

In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1 vertical stroke 1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1 vertical stroke 1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1 vertical stroke 1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition. (orig.)

The GL(1 vertical stroke 1)-symplectic fermion correspondence

Energy Technology Data Exchange (ETDEWEB)

Creutzig, Thomas; Roenne, Peter B.

2008-12-15

In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1 vertical stroke 1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1 vertical stroke 1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1 vertical stroke 1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition. (orig.)

Symplectic discretization for spectral element solution of Maxwell's equations

International Nuclear Information System (INIS)

Zhao Yanmin; Dai Guidong; Tang Yifa; Liu Qinghuo

2009-01-01

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.

Symplectic invariants, entropic measures and correlations of Gaussian states

Energy Technology Data Exchange (ETDEWEB)

Serafini, Alessio; Illuminati, Fabrizio; Siena, Silvio De [Dipartimento di Fisica ' E R Caianiello' , Universita di Salerno, INFM UdR Salerno, INFN Sezione di Napoli, Gruppo Collegato di Salerno, Via S Allende, 84081 Baronissi, SA (Italy)

2004-01-28

We present a derivation of the Von Neumann entropy and mutual information of arbitrary two-mode Gaussian states, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different hierarchies of mixed Gaussian states. A comparison between mutual information and entanglement of formation for symmetric states is considered, taking note of the crucial role of the symplectic eigenvalues in qualifying and quantifying the correlations present in a generic state. (letter to the editor)

Symplectic invariants, entropic measures and correlations of Gaussian states

International Nuclear Information System (INIS)

Serafini, Alessio; Illuminati, Fabrizio; Siena, Silvio De

2004-01-01

We present a derivation of the Von Neumann entropy and mutual information of arbitrary two-mode Gaussian states, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different hierarchies of mixed Gaussian states. A comparison between mutual information and entanglement of formation for symmetric states is considered, taking note of the crucial role of the symplectic eigenvalues in qualifying and quantifying the correlations present in a generic state. (letter to the editor)

The Maslov index in weak symplectic functional analysis

DEFF Research Database (Denmark)

Booss-Bavnbek, Bernhelm; Zhu, Chaofeng

2013-01-01

We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach...

Lorentz covariant canonical symplectic algorithms for dynamics of charged particles

Science.gov (United States)

Wang, Yulei; Liu, Jian; Qin, Hong

2016-12-01

In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz covariance, a general procedure for constructing Lorentz covariant canonical symplectic algorithms (LCCSAs) is provided, based on which an explicit LCCSA for dynamics of relativistic charged particles is built. LCCSA possesses Lorentz invariance as well as long-term numerical accuracy and stability, due to the preservation of a discrete symplectic structure and the Lorentz symmetry of the system. For situations with time-dependent electromagnetic fields, which are difficult to handle in traditional construction procedures of symplectic algorithms, LCCSA provides a perfect explicit canonical symplectic solution by implementing the discretization in 4-spacetime. We also show that LCCSA has built-in energy-based adaptive time steps, which can optimize the computation performance when the Lorentz factor varies.

The difficulty of symplectic analysis with second class systems

International Nuclear Information System (INIS)

Shirzad, A.; Mojiri, M.

2005-01-01

Using the basic concepts of the chain by chain method we show that the symplectic analysis, which was claimed to be equivalent to the usual Dirac method, fails when second class constraints are present. We propose a modification in symplectic analysis that solves the problem

Symplectic multi-particle tracking on GPUs

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Derivation of the dipole map

International Nuclear Information System (INIS)

Ali, Halima; Punjabi, Alkesh; Boozer, Allen

2004-01-01

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

Fedosov’s formal symplectic groupoids and contravariant connections

Science.gov (United States)

Karabegov, Alexander V.

2006-10-01

Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kähler-Poisson manifolds this construction provides, in particular, the formal symplectic groupoids with separation of variables. We show that the dual of a semisimple Lie algebra does not admit torsion-free Poisson contravariant connections.

Free and constrained symplectic integrators for numerical general relativity

International Nuclear Information System (INIS)

Richter, Ronny; Lubich, Christian

2008-01-01

We consider symplectic time integrators in numerical general relativity and discuss both free and constrained evolution schemes. For free evolution of ADM-like equations we propose the use of the Stoermer-Verlet method, a standard symplectic integrator which here is explicit in the computationally expensive curvature terms. For the constrained evolution we give a formulation of the evolution equations that enforces the momentum constraints in a holonomically constrained Hamiltonian system and turns the Hamilton constraint function from a weak to a strong invariant of the system. This formulation permits the use of the constraint-preserving symplectic RATTLE integrator, a constrained version of the Stoermer-Verlet method. The behavior of the methods is illustrated on two effectively (1+1)-dimensional versions of Einstein's equations, which allow us to investigate a perturbed Minkowski problem and the Schwarzschild spacetime. We compare symplectic and non-symplectic integrators for free evolution, showing very different numerical behavior for nearly-conserved quantities in the perturbed Minkowski problem. Further we compare free and constrained evolution, demonstrating in our examples that enforcing the momentum constraints can turn an unstable free evolution into a stable constrained evolution. This is demonstrated in the stabilization of a perturbed Minkowski problem with Dirac gauge, and in the suppression of the propagation of boundary instabilities into the interior of the domain in Schwarzschild spacetime

Infinitesimal Deformations of a Formal Symplectic Groupoid

Science.gov (United States)

Karabegov, Alexander

2011-09-01

Given a formal symplectic groupoid G over a Poisson manifold ( M, π 0), we define a new object, an infinitesimal deformation of G, which can be thought of as a formal symplectic groupoid over the manifold M equipped with an infinitesimal deformation {π_0 + \\varepsilon π_1} of the Poisson bivector field π 0. To any pair of natural star products {(ast,tildeast)} having the same formal symplectic groupoid G we relate an infinitesimal deformation of G. We call it the deformation groupoid of the pair {(ast,tildeast)} . To each star product with separation of variables {ast} on a Kähler-Poisson manifold M we relate another star product with separation of variables {hatast} on M. We build an algorithm for calculating the principal symbols of the components of the logarithm of the formal Berezin transform of a star product with separation of variables {ast} . This algorithm is based upon the deformation groupoid of the pair {(ast,hatast)}.

Method to render second order beam optics programs symplectic

International Nuclear Information System (INIS)

Douglas, D.; Servranckx, R.V.

1984-10-01

We present evidence that second order matrix-based beam optics programs violate the symplectic condition. A simple method to avoid this difficulty, based on a generating function approach to evaluating transfer maps, is described. A simple example illustrating the non-symplectricity of second order matrix methods, and the effectiveness of our solution to the problem, is provided. We conclude that it is in fact possible to bring second order matrix optics methods to a canonical form. The procedure for doing so has been implemented in the program DIMAT, and could be implemented in programs such as TRANSPORT and TURTLE, making them useful in multiturn applications. 15 refs

Construction and uniqueness of the C*-Weyl algebra over a general pre-symplectic space

International Nuclear Information System (INIS)

Binz, Ernst; Honegger, Reinhard; Rieckers, Alfred

2004-01-01

A systematic approach to the C*-Weyl algebra W(E,σ) over a possibly degenerate pre-symplectic form σ on a real vector space E of possibly infinite dimension is elaborated in an almost self-contained manner. The construction is based on the theory of Kolmogorov decompositions for σ-positive-definite functions on involutive semigroups and their associated projective unitary group representations. The σ-positive-definite functions provide also the C*-norm of W(E,σ), the latter being shown to be *-isomorphic to the twisted group C*-algebra of the discrete vector group E. The connections to related constructions are indicated. The treatment of the fundamental symmetries is outlined for arbitrary pre-symplectic σ. The construction method is especially applied to the trivial symplectic form σ=0, leading to the commutative Weyl algebra over E, which is shown to be isomorphic to the C*-algebra of the almost periodic continuous function on the topological dual E τ ' of E with respect to an arbitrary locally convex Hausdorff topology τ on E. It is demonstrated that the almost periodic compactification aE τ ' of E τ ' is independent of the chosen locally convex τ on E, and that aE τ ' is continuously group isomorphic to the character group E of E. Applications of the results to the procedures of strict and continuous deformation quantizations are mentioned in the outlook

Variational and symplectic integrators for satellite relative orbit propagation including drag

Science.gov (United States)

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.

Symplectic Synchronization of Lorenz-Stenflo System with Uncertain Chaotic Parameters via Adaptive Control

Directory of Open Access Journals (Sweden)

Cheng-Hsiung Yang

2013-01-01

Full Text Available A new symplectic chaos synchronization of chaotic systems with uncertain chaotic parameters is studied. The traditional chaos synchronizations are special cases of the symplectic chaos synchronization. A sufficient condition is given for the asymptotical stability of the null solution of error dynamics and a parameter difference. The symplectic chaos synchronization with uncertain chaotic parameters may be applied to the design of secure communication systems. Finally, numerical results are studied for symplectic chaos synchronized from two identical Lorenz-Stenflo systems in three different cases.

Symplectic and semiclassical aspects of the Schläfli identity

Science.gov (United States)

Hedeman, Austin; Kur, Eugene; Littlejohn, Robert G.; Haggard, Hal M.

2015-03-01

The Schläfli identity, which is important in Regge calculus and loop quantum gravity, is examined from a symplectic and semiclassical standpoint in the special case of flat, three-dimensional space. In this case a proof is given, based on symplectic geometry. A series of symplectic and Lagrangian manifolds related to the Schläfli identity, including several versions of a Lagrangian manifold of tetrahedra, are discussed. Semiclassical interpretations of the various steps are provided. Possible generalizations to three-dimensional spaces of constant (nonzero) curvature, involving Poisson-Lie groups and q-deformed spin networks, are discussed.

Conformal transformation and symplectic structure of self-dual fields

International Nuclear Information System (INIS)

Yang Kongqing; Luo Yan

1996-01-01

Considered two dimensional self-dual fields, the symplectic structure on the space of solutions is given. It is shown that this structure is Poincare invariant. The Lagrangian of two dimensional self-dual field is invariant under infinite one component conformal group, then this symplectic structure is also invariant under this conformal group. The conserved currents in geometrical formalism are also obtained

Symplectic models for general insertion devices

International Nuclear Information System (INIS)

Wu, Y.; Forest, E.; Robin, D. S.; Nishimura, H.; Wolski, A.; Litvinenko, V. N.

2001-01-01

A variety of insertion devices (IDs), wigglers and undulators, linearly or elliptically polarized,are widely used as high brightness radiation sources at the modern light source rings. Long and high-field wigglers have also been proposed as the main source of radiation damping at next generation damping rings. As a result, it becomes increasingly important to understand the impact of IDs on the charged particle dynamics in the storage ring. In this paper, we report our recent development of a general explicit symplectic model for IDs with the paraxial ray approximation. High-order explicit symplectic integrators are developed to study real-world insertion devices with a number of wiggler harmonics and arbitrary polarizations

New results for time reversed symplectic dynamic systems and quadratic functionals

Directory of Open Access Journals (Sweden)

Roman Simon Hilscher

2012-05-01

Full Text Available In this paper, we examine time scale symplectic (or Hamiltonian systems and the associated quadratic functionals which contain a forward shift in the time variable. Such systems and functionals have a close connection to Jacobi systems for calculus of variations and optimal control problems on time scales. Our results, among which we consider the Reid roundabout theorem, generalize the corresponding classical theory for time reversed discrete symplectic systems, as well as they complete the recently developed theory of time scale symplectic systems.

Variational symplectic algorithm for guiding center dynamics and its application in tokamak geometry

International Nuclear Information System (INIS)

Qin Hong; Guan Xiaoyin; Tang, William M.

2009-01-01

A variational symplectic integrator for the guiding center motion of charged particles in general magnetic fields is developed to enable accurate long-time simulation studies of magnetized plasmas. 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 the dynamics. The variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure and globally bounds the numerical error in energy by a small number for all simulation time steps. Compared with standard integrators, such as the fourth order Runge-Kutta method, the variational symplectic integrator has superior numerical properties over long integration time. For example, in a two-dimensional tokamak geometry, the variational symplectic integrator is able to guarantee the accuracy for both the trapped and transit particle orbits for arbitrarily long simulation time. This is important for modern large-scale simulation studies of fusion plasmas where it is critical to use algorithms with long-term accuracy and fidelity. The variational symplectic integrator is expected to have a wide range of applications.

Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods

Directory of Open Access Journals (Sweden)

Tetsuya Misawa

2010-01-01

Full Text Available “Symplectic” schemes for stochastic Hamiltonian dynamical systems are formulated through “composition methods (or operator splitting methods” proposed by Misawa (2001. In the proposed methods, a symplectic map, which is given by the solution of a stochastic Hamiltonian system, is approximated by composition of the stochastic flows derived from simpler Hamiltonian vector fields. The global error orders of the numerical schemes derived from the stochastic composition methods are provided. To examine the superiority of the new schemes, some illustrative numerical simulations on the basis of the proposed schemes are carried out for a stochastic harmonic oscillator system.

Collective coordinates on symplectic manifolds

International Nuclear Information System (INIS)

Razumov, A.V.; Taranov, A.Yu.

1981-01-01

For an arbitrary Lie group of canonical transformations on a symplectic manifold collective coordinates are introduced. They describe a motion of the dynamical system as a whole under the group transformations. Some properties of Lie group of canonical transformations are considered [ru

Explicit K-symplectic algorithms for charged particle dynamics

International Nuclear Information System (INIS)

He, Yang; Zhou, Zhaoqi; Sun, Yajuan; Liu, Jian; Qin, Hong

2017-01-01

We study the Lorentz force equation of charged particle dynamics by considering its K-symplectic structure. As the Hamiltonian of the system can be decomposed as four parts, we are able to construct the numerical methods that preserve the K-symplectic structure based on Hamiltonian splitting technique. The newly derived numerical methods are explicit, and are shown in numerical experiments to be stable over long-term simulation. The error convergency as well as the long term energy conservation of the numerical solutions is also analyzed by means of the Darboux transformation.

Explicit K-symplectic algorithms for charged particle dynamics

Energy Technology Data Exchange (ETDEWEB)

He, Yang [School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083 (China); Zhou, Zhaoqi [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190 (China); Sun, Yajuan, E-mail: sunyj@lsec.cc.ac.cn [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Liu, Jian [Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026 (China); Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026 (China); Qin, Hong [Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026 (China); Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States)

2017-02-12

We study the Lorentz force equation of charged particle dynamics by considering its K-symplectic structure. As the Hamiltonian of the system can be decomposed as four parts, we are able to construct the numerical methods that preserve the K-symplectic structure based on Hamiltonian splitting technique. The newly derived numerical methods are explicit, and are shown in numerical experiments to be stable over long-term simulation. The error convergency as well as the long term energy conservation of the numerical solutions is also analyzed by means of the Darboux transformation.

A Family of Trigonometrically-fitted Partitioned Runge-Kutta Symplectic Methods

International Nuclear Information System (INIS)

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

2007-01-01

We are presenting a family of trigonometrically fitted partitioned Runge-Kutta symplectic methods of fourth order with six stages. The solution of the one dimensional time independent Schroedinger equation is considered by trigonometrically fitted symplectic integrators. The Schroedinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential

Symplectic Attitude Estimation for Small Satellites

National Research Council Canada - National Science Library

Valpiani, James M; Palmer, Phillip L

2006-01-01

.... Symplectic numerical methods are applied to the Extended Kalman Filter (EKF) algorithm to give the SKF, which outperforms the standard EKF in the presence of nonlinearity and low measurement noise in the 1-D case...

A symplectic Poisson solver based on Fast Fourier Transformation. The first trial

International Nuclear Information System (INIS)

Vorobiev, L.G.; Hirata, Kohji.

1995-11-01

A symplectic Poisson solver calculates numerically a potential and fields due to a 2D distribution of particles in a way that the symplecticity and smoothness are assured automatically. Such a code, based on Fast Fourier Transformation combined with Bicubic Interpolation, is developed for the use in multi-turn particle simulation in circular accelerators. Beside that, it may have a number of applications, where computations of space charge forces should obey a symplecticity criterion. Detailed computational schemes of all algorithms will be outlined to facilitate practical programming. (author)

Precise iteration formulae of the Maslov-type index theory for symplectic paths

International Nuclear Information System (INIS)

Yiming Long

1998-10-01

In this paper, using homotopy components of symplectic matrices, and basic properties of the Maslov-type index theory, we establish precise iteration formulae of the Maslov-type index theory for any path in the symplectic group starting from the identity. (author)

Holonomic systems for period mappings

Energy Technology Data Exchange (ETDEWEB)

Chen, Jingyue, E-mail: jychen@brandeis.edu [Department of Mathematics, Brandeis University, Waltham, MA 02454 (United States); Huang, An, E-mail: anhuang@math.harvard.edu [Department of Mathematics, Harvard University, Cambridge, MA 02138 (United States); Lian, Bong H., E-mail: lian@brandeis.edu [Department of Mathematics, Brandeis University, Waltham, MA 02454 (United States)

2015-09-15

Period mappings were introduced in the sixties [4] to study variation of complex structures of families of algebraic varieties. The theory of tautological systems was introduced recently [7,8] to understand period integrals of algebraic manifolds. In this paper, we give an explicit construction of a tautological system for each component of a period mapping. We also show that the D-module associated with the tautological system gives rise to many interesting vanishing conditions for period integrals at certain special points of the parameter space.

Symplectic matrix, gauge invariance and Dirac brackets for super-QED

Energy Technology Data Exchange (ETDEWEB)

Alves, D.T. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Cheb-Terrab, E.S. [British Columbia Univ., Vancouver, BC (Canada). Dept. of Mathematics

1999-08-01

The calculation of Dirac brackets (DB) using a symplectic matrix approach but in a Hamiltonian framework is discussed, and the calculation of the DB for the supersymmetric extension of QED (super-QED) is shown. The relation between the zero-mode of the pre-symplectic matrix and the gauge transformations admitted by the model is verified. A general description to construct Lagrangians linear in the velocities is also presented. (author)

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

Science.gov (United States)

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.

Canonical and symplectic analysis for three dimensional gravity without dynamics

Energy Technology Data Exchange (ETDEWEB)

Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx [Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48 72570, Puebla, Pue. (Mexico); Osmart Ochoa-Gutiérrez, H. [Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado postal 1152, 72001 Puebla, Pue. (Mexico)

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–Jackiw 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.

Noncommutativity and Duality through the Symplectic Embedding Formalism

Directory of Open Access Journals (Sweden)

Everton M.C. Abreu

2010-07-01

Full Text Available This work is devoted to review the gauge embedding of either commutative and noncommutative (NC theories using the symplectic formalism framework. To sum up the main features of the method, during the process of embedding, the infinitesimal gauge generators of the gauge embedded theory are easily and directly chosen. Among other advantages, this enables a greater control over the final Lagrangian and brings some light on the so-called ''arbitrariness problem''. This alternative embedding formalism also presents a way to obtain a set of dynamically dual equivalent embedded Lagrangian densities which is obtained after a finite number of steps in the iterative symplectic process, oppositely to the result proposed using the BFFT formalism. On the other hand, we will see precisely that the symplectic embedding formalism can be seen as an alternative and an efficient procedure to the standard introduction of the Moyal product in order to produce in a natural way a NC theory. In order to construct a pedagogical explanation of the method to the nonspecialist we exemplify the formalism showing that the massive NC U(1 theory is embedded in a gauge theory using this alternative systematic path based on the symplectic framework. Further, as other applications of the method, we describe exactly how to obtain a Lagrangian description for the NC version of some systems reproducing well known theories. Naming some of them, we use the procedure in the Proca model, the irrotational fluid model and the noncommutative self-dual model in order to obtain dual equivalent actions for these theories. To illustrate the process of noncommutativity introduction we use the chiral oscillator and the nondegenerate mechanics.

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

Science.gov (United States)

Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang

2017-06-01

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

Major shell centroids in the symplectic collective model

International Nuclear Information System (INIS)

Draayer, J.P.; Rosensteel, G.; Tulane Univ., New Orleans, LA

1983-01-01

Analytic expressions are given for the major shell centroids of the collective potential V(#betta#, #betta#) and the shape observable #betta# 2 in the Sp(3,R) symplectic model. The tools of statistical spectroscopy are shown to be useful, firstly, in translating a requirement that the underlying shell structure be preserved into constraints on the parameters of the collective potential and, secondly, in giving a reasonable estimate for a truncation of the infinite dimensional symplectic model space from experimental B(E2) transition strengths. Results based on the centroid information are shown to compare favorably with results from exact calculations in the case of 20 Ne. (orig.)

Proton spin tracking with symplectic integration of orbit motion

Energy Technology Data Exchange (ETDEWEB)

Luo, Y. [Brookhaven National Lab. (BNL), Upton, NY (United States); Dutheil, Y. [Brookhaven National Lab. (BNL), Upton, NY (United States); Huang, H. [Brookhaven National Lab. (BNL), Upton, NY (United States); Meot, F. [Brookhaven National Lab. (BNL), Upton, NY (United States); Ranjbar, V. [Brookhaven National Lab. (BNL), Upton, NY (United States)

2015-05-03

Symplectic integration had been adopted for orbital motion tracking in code SimTrack. SimTrack has been extensively used for dynamic aperture calculation with beam-beam interaction for the Relativistic Heavy Ion Collider (RHIC). Recently proton spin tracking has been implemented on top of symplectic orbital motion in this code. In this article, we will explain the implementation of spin motion based on Thomas-BMT equation, and the benchmarking with other spin tracking codes currently used for RHIC. Examples to calculate spin closed orbit and spin tunes are presented too.

Bianchi type A hyper-symplectic and hyper-Kaehler metrics in 4D

International Nuclear Information System (INIS)

De Andrés, L C; Fernández, M; Ivanov, S; Santisteban, J A; Ugarte, L; Vassilev, D

2012-01-01

We present a simple explicit construction of hyper-Kaehler and hyper-symplectic (also known as neutral hyper-Kaehler or hyper-para-Kaehler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence between hyper-Kaehler and hyper-symplectic structures of dimension 4. (paper)

Reduction of a symplectic-like Lie algebroid with momentum map and its application to fiberwise linear Poisson structures

International Nuclear Information System (INIS)

Marrero, Juan Carlos; Padrón, Edith; Rodríguez-Olmos, Miguel

2012-01-01

This paper addresses the problem of developing an extension of the Marsden–Weinstein reduction process to symplectic-like Lie algebroids, and in particular to the case of the canonical cover of a fiberwise linear Poisson structure, whose reduction process is the analog to cotangent bundle reduction in the context of Lie algebroids. Dedicated to the memory of Jerrold E Marsden (paper)

Birkhoffian Symplectic Scheme for a Quantum System

International Nuclear Information System (INIS)

Su Hongling

2010-01-01

In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure-preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f. Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system. (general)

Bianchi type A hyper-symplectic and hyper-K\\"ahler metrics in 4D

OpenAIRE

de Andrés, Luis C.; Fernández, Marisa; Ivanov, Stefan; Santisteban, José A.; Ugarte, Luis; Vassilev, Dimiter

2011-01-01

We present a simple explicit construction of hyper-Kaehler and hyper-symplectic (also known as neutral hyper-Kaehler or hyper-parakaehler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence between hyper-Kaehler and hyper-symplectic structures in dimension four.

Spherical complexes attached to symplectic lattices

NARCIS (Netherlands)

van der Kallen, W.L.J.; Looijenga, E.J.N.

2011-01-01

To the integral symplectic group Sp(2g, Z) we associate two posets of which we prove that they have the Cohen-Macaulay property. As an application we show that the locus of marked decomposable principally polarized abelian varieties in the Siegel space of genus g has the homotopy type of a bouquet

Ordered and isomorphic mapping of periodic structures in the parametrically forced logistic map

Energy Technology Data Exchange (ETDEWEB)

Maranhão, Dariel M., E-mail: dariel@ifsp.edu.br [Departamento de Ciências e Matemática, Instituto Federal de Educação, Ciência e Tecnologia de São Paulo, São Paulo (Brazil); Diretoria de Informática, Universidade Nove de Julho, São Paulo (Brazil)

2016-09-23

Highlights: • A direct description of the internal structure of a periodic window in terms of winding numbers is proposed. • Periodic structures in parameter spaces are mapped in a recurrent and isomorphic way. • Sequences of winding numbers show global and local organization of periodic domains. - Abstract: We investigate the periodic domains found in the parametrically forced logistic map, the classical logistic map when its control parameter changes dynamically. Phase diagrams in two-parameter spaces reveal intricate periodic structures composed of patterns of intersecting superstable orbits curves, defining the cell of a periodic window. Cells appear multifoliated and ordered, and they are isomorphically mapped when one changes the map parameters. Also, we identify the characteristics of simplest cell and apply them to other more complex, discussing how the topography on parameter space is affected. By use of the winding number as defined in periodically forced oscillators, we show that the hierarchical organization of the periodic domains is manifested in global and local scales.

Super integrable four-dimensional autonomous mappings

International Nuclear Information System (INIS)

Capel, H W; Sahadevan, R; Rajakumar, S

2007-01-01

A systematic investigation of the complete integrability of a fourth-order autonomous difference equation of the type w(n + 4) = w(n)F(w(n + 1), w(n + 2), w(n + 3)) is presented. We identify seven distinct families of four-dimensional mappings which are super integrable and have three (independent) integrals via a duality relation as introduced in a recent paper by Quispel, Capel and Roberts (2005 J. Phys. A: Math. Gen. 38 3965-80). It is observed that these seven families can be related to the four-dimensional symplectic mappings with two integrals including all the four-dimensional periodic reductions of the integrable double-discrete modified Korteweg-deVries and sine-Gordon equations treated in an earlier paper by two of us (Capel and Sahadevan 2001 Physica A 289 86-106)

Symplectic dynamics of the nuclear mean-field

International Nuclear Information System (INIS)

Grigorescu, Marius

1996-01-01

Collective and microscopic pictures of the nuclear dynamics are related in the frame of time-dependent variational principle on symplectic trial manifolds. For symmetry braking systems such manifolds are constructed by cranking, and applied to study the nuclear isovector collective excitations. (author)

Symplectic geometry of field theories and covariant quantization of superstrings and superparticles

International Nuclear Information System (INIS)

Crnkovic, C.

1987-01-01

A detailed development of the symplectic geometry formalism for a general Lagrangian field theory is presented. Special attention is paid to the theories with constraints and/or gauge degrees of freedom. Special cases of Yang-Mills theory, general relativity and Witten's string field theory are studied and the generators of (super-) Poincare transformations are derived using their respective symplectic forms. The formalism extends naturally to theories formulated in the superspace. The second part of the thesis deals with issues in covariant quantization. By studying the symplectic geometry of the Green-Schwarz covariant superstring action, we elucidate some aspects of its covariant quantization. We derive the on-shell gauge-fixed action and the equations of motion for all the fields. Finally, turning to Siegel's version of the superparticle action, we perform its BRST quantization

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

International Nuclear Information System (INIS)

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

2008-01-01

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. (general)

Application of symplectic integrator to numerical fluid analysis

International Nuclear Information System (INIS)

Tanaka, Nobuatsu

2000-01-01

This paper focuses on application of the symplectic integrator to numerical fluid analysis. For the purpose, we introduce Hamiltonian particle dynamics to simulate fluid behavior. The method is based on both the Hamiltonian formulation of a system and the particle methods, and is therefore called Hamiltonian Particle Dynamics (HPD). In this paper, an example of HPD applications, namely the behavior of incompressible inviscid fluid, is solved. In order to improve accuracy of HPD with respect to space, CIVA, which is a highly accurate interpolation method, is combined, but the combined method is subject to problems in that the invariants of the system are not conserved in a long-time computation. For solving the problems, symplectic time integrators are introduced and the effectiveness is confirmed by numerical analyses. (author)

Symplectic integration for complex wigglers

International Nuclear Information System (INIS)

Forest, E.; Ohmi, K.

1992-01-01

Using the example of the helical wiggler proposed for the KEK photon factory, we show how to integrate the equation of motion through the wiggler. The integration is performed in cartesian coordinates. For the usual expanded Hamiltonian (without square root), we derive a first order symplectic integrator for the purpose of tracking through a wiggler in a ring. We also show how to include classical radiation for the computation of the damping decrement

Multi-symplectic variational integrators for nonlinear Schrödinger equations with variable coefficients

International Nuclear Information System (INIS)

Liao Cui-Cui; Cui Jin-Chao; Liang Jiu-Zhen; Ding Xiao-Hua

2016-01-01

In this paper, we propose a variational integrator for nonlinear Schrödinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrödinger equations with variable coefficients, cubic nonlinear Schrödinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space. (paper)

Canonicalization and symplectic simulation of the gyrocenter dynamics in time-independent magnetic fields

International Nuclear Information System (INIS)

Zhang, Ruili; Tang, Yifa; Zhu, Beibei; Liu, Jian; Xiao, Jianyuan; Qin, Hong

2014-01-01

The gyrocenter dynamics of charged particles in time-independent magnetic fields is a non-canonical Hamiltonian system. The canonical description of the gyrocenter has both theoretical and practical importance. We provide a general procedure of the gyrocenter canonicalization, which is expressed by the series of a small variable ϵ depending only on the parallel velocity u and can be expressed in a recursive manner. We prove that the truncation of the series to any given order generates a set of exact canonical coordinates for a system, whose Lagrangian approximates to that of the original gyrocenter system in the same order. If flux surfaces exist for the magnetic field, the series stops simply at the second order and an exact canonical form of the gyrocenter system is obtained. With the canonicalization schemes, the canonical symplectic simulation of gyrocenter dynamics is realized for the first time. The canonical symplectic algorithm has the advantage of good conservation properties and long-term numerical accuracy, while avoiding numerical instability. It is worth mentioning that explicitly expressing the canonical Hamiltonian in new coordinates is usually difficult and impractical. We give an iteration procedure that is easy to implement in the original coordinates associated with the coordinate transformation. This is crucial for modern large-scale simulation studies in plasma physics. The dynamics of gyrocenters in the dipole magnetic field and in the toroidal geometry are simulated using the canonical symplectic algorithm by comparison with the higher-order non symplectic Runge-Kutta scheme. The overwhelming superiorities of the symplectic method for the gyrocenter system are evidently exhibited

A symplectic framework for field theories

International Nuclear Information System (INIS)

Kijowski, J.; Tulczyjew, W.M.

1979-01-01

These notes are concerned with the formulation of a new conceptual framework for classical field theories. Although the formulation is based on fairly advanced concepts of symplectic geometry these notes cannot be viewed as a reformulation of known structures in more rigorous and elegant torns. Our intention is rather to communicate to theoretical physicists a set of new physical ideas. We have chosen for this purpose the language of local coordinates which is more elementary and more widely known than the abstract language of modern differntial geometry. Our emphasis is directed more to physical intentions than to mathematical vigour. We start with a symplectic analysis of staties. Both discrete and continuous systems are considered on a largely intuitive level. The notion of reciprocity and potentiality of the theory is discussed. Chapter II is a presentation of particle dynamics together with more rigorous definitions of the geometric structure. Lagrangian-Submanifolds and their generating function 3 are defined and the time evolution of particle states is studied. Chapter II form the main part of these notes. Here we describe the construction of canonical momenta and discuss the field dynamics in finite domains of space-time. We also establish the relation between our symplectic framework and the geometric formulation of the calculus of variations of multiple integrals. In the following chapter we give a few examples of field theories selected to illustrate various features of the new approach. A new formulation of the theory of gravity consists of using the affine connection in space-time as the field configuration. In the past section we present an analysis of hydrodynamics within our framework which reveals a formal analogy with electrodynamics. The discovery of potentials for hydrodynamics and the subsequent formulation of a variational principle provides an excellent example for the fruitfulness of the new approach to field theory. A short review of

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

Science.gov (United States)

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.

Local symplectic operators and structures related to them

International Nuclear Information System (INIS)

Dorfman, I.Y.; Mokhov, O.I.

1991-01-01

Matrices with entries being differential operators, that endow the phase space of an evolution system with a (pre)symplectic structure are considered. Special types of such structures are explicitly described. Links with integrability, geometry of loop spaces, and Baecklund transformations are traces

Pseudo-periodic maps and degeneration of Riemann surfaces

CERN Document Server

Matsumoto, Yukio

2011-01-01

The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen’s incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one-parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.

Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

International Nuclear Information System (INIS)

Geng Xianguo; Su Ting

2007-01-01

A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

A symplectic coherent beam-beam model

International Nuclear Information System (INIS)

Furman, M.A.

1989-05-01

We consider a simple one-dimensional model to study the effects of the beam-beam force on the coherent dynamics of colliding beams. The key ingredient is a linearized beam-beam kick. We study only the quadrupole modes, with the dynamical variables being the 2nd-order moments of the canonical variables q, p. Our model is self-consistent in the sense that no higher order moments are generated by the linearized beam-beam kicks, and that the only source of violation of symplecticity is the radiation. We discuss the round beam case only, in which vertical and horizontal quantities are assumed to be equal (though they may be different in the two beams). Depending on the values of the tune and beam intensity, we observe steady states in which otherwise identical bunches have sizes that are equal, or unequal, or periodic, or behave chaotically from turn to turn. Possible implications of luminosity saturation with increasing beam intensity are discussed. Finally, we present some preliminary applications to an asymmetric collider. 8 refs., 8 figs

Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds

OpenAIRE

Lehn, Christian

2011-01-01

We generalize Voisin's theorem on deformations of pairs of a symplectic manifold and a Lagrangian submanifold to the case of Lagrangian normal crossing subvarieties. Partial results are obtained for arbitrary Lagrangian subvarieties. We apply our results to the study of singular fibers of Lagrangian fibrations.

On the Faddeev-Jackiw symplectic framework for topologically massive gravity

Energy Technology Data Exchange (ETDEWEB)

Escalante, Alberto [Benemerita Universidad Autonoma de Puebla, Instituto de Fisica, Puebla (Mexico); Rodriguez-Tzompantzi, Omar [Benemerita Universidad Autonoma de Puebla, Facultad de Ciencias Fisico Matematicas, Puebla (Mexico)

2016-10-15

The dynamical structure of topologically massive gravity in the context of the Faddeev-Jackiw symplectic approach is studied. It is shown that this method allows us to avoid some ambiguities arising in the study of the gauge structure via the Dirac formalism. In particular, the complete set of constraints and the generators of the gauge symmetry of the theory are obtained straightforwardly via the zero modes of the symplectic matrix. In order to obtain the generalized Faddeev-Jackiw brackets and calculate the local physical degrees of freedom of this model, an appropriate gauge-fixing procedure is introduced. Finally, the similarities and relative advantages between the Faddeev-Jackiw method and Dirac's formalism are briefly discussed. (orig.)

On Non-Abelian Symplectic Cutting

DEFF Research Database (Denmark)

Martens, Johan; Thaddeus, Michael

2012-01-01

We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact groups. By using a degeneration based on the Vinberg monoid we give, in good cases, a global quotient description of a surgery construction introduced by Woodward and Meinrenken, and show it can be interpreted in algebro......-geometric terms. A key ingredient is the `universal cut' of the cotangent bundle of the group itself, which is identified with a moduli space of framed bundles on chains of projective lines recently introduced by the authors....

Relative symplectic caps, 4-genus and fibered knots

Indian Academy of Sciences (India)

convex boundary embeds in a closed symplectic 4-manifold. ... We shall apply Theorem 1.2 in particular to study the 4-genus of a link in S3 by proving ...... [13] Honda Ko, Factoring nonrotative T 2×I layers, Erratum: On the classification of tight.

Constrained dynamics of two interacting relativistic particles in the Faddeev-Jackiw symplectic framework

Science.gov (United States)

Rodríguez-Tzompantzi, Omar

2018-05-01

The Faddeev-Jackiw symplectic formalism for constrained systems is applied to analyze the dynamical content of a model describing two massive relativistic particles with interaction, which can also be interpreted as a bigravity model in one dimension. We systematically investigate the nature of the physical constraints, for which we also determine the zero-modes structure of the corresponding symplectic matrix. After identifying the whole set of constraints, we find out the transformation laws for all the set of dynamical variables corresponding to gauge symmetries, encoded in the remaining zero modes. In addition, we use an appropriate gauge-fixing procedure, the conformal gauge, to compute the quantization brackets (Faddeev-Jackiw brackets) and also obtain the number of physical degree of freedom. Finally, we argue that this symplectic approach can be helpful for assessing physical constraints and understanding the gauge structure of theories of interacting spin-2 fields.

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

Science.gov (United States)

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.

No division and the set of periods for tree maps

International Nuclear Information System (INIS)

Alseda, L.; Ye Xiangdong.

1992-06-01

We extend the notion of no division for star maps to tree maps. It is proved that the set of periods of a tree map is cofinite if there exists some periodic orbit of the given map with period larger than one having no division. Using this result we get some simple proofs of known results for tree maps and show that if X is a tree then a union of initial segments of some finite linear orderings which depend only on the given tree minus a finite set is the set of periods for arbitrary maps from X into itself. (author). 18 refs

Gauge properties of the guiding center variational symplectic integrator

International Nuclear Information System (INIS)

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

2012-01-01

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 for 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→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 φ 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)].

Global symplectic structure-preserving integrators for spinning compact binaries

Science.gov (United States)

Zhong, Shuang-Ying; Wu, Xin; Liu, San-Qiu; Deng, Xin-Fa

2010-12-01

This paper deals mainly with the application of the second-order symplectic implicit midpoint rule and its symmetric compositions to a post-Newtonian Hamiltonian formulation with canonical spin variables in relativistic compact binaries. The midpoint rule, as a basic algorithm, is directly used to integrate the completely canonical Hamiltonian system. On the other hand, there are symmetric composite methods based on a splitting of the Hamiltonian into two parts: the Newtonian part associated with a Kepler motion, and a perturbation part involving the orbital post-Newtonian and spin contributions, where the Kepler flow has an analytic solution and the perturbation can be calculated by the midpoint rule. An example is the second-order mixed leapfrog symplectic integrator with one stage integration of the perturbation flow and two semistage computations of the Kepler flow at every integration step. Also, higher-order composite methods such as the Forest-Ruth fourth-order symplectic integrator and its optimized algorithm are applicable. Various numerical tests including simulations of chaotic orbits show that the mixed leapfrog integrator is always superior to the midpoint rule in energy accuracy, while both of them are almost equivalent in computational efficiency. Particularly, the optimized fourth-order algorithm compared with the mixed leapfrog scheme provides good precision and needs no expensive additional computational time. As a result, it is worth performing a more detailed and careful examination of the dynamical structure of chaos and order in the parameter windows and phase space of the binary system.

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

Science.gov (United States)

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.

The complex Laguerre symplectic ensemble of non-Hermitian matrices

International Nuclear Information System (INIS)

Akemann, G.

2005-01-01

We solve the complex extension of the chiral Gaussian symplectic ensemble, defined as a Gaussian two-matrix model of chiral non-Hermitian quaternion real matrices. This leads to the appearance of Laguerre polynomials in the complex plane and we prove their orthogonality. Alternatively, a complex eigenvalue representation of this ensemble is given for general weight functions. All k-point correlation functions of complex eigenvalues are given in terms of the corresponding skew orthogonal polynomials in the complex plane for finite-N, where N is the matrix size or number of eigenvalues, respectively. We also allow for an arbitrary number of complex conjugate pairs of characteristic polynomials in the weight function, corresponding to massive quark flavours in applications to field theory. Explicit expressions are given in the large-N limit at both weak and strong non-Hermiticity for the weight of the Gaussian two-matrix model. This model can be mapped to the complex Dirac operator spectrum with non-vanishing chemical potential. It belongs to the symmetry class of either the adjoint representation or two colours in the fundamental representation using staggered lattice fermions

Stochastic deformation of a thermodynamic symplectic structure

OpenAIRE

Kazinski, P. O.

2008-01-01

A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transform...

Two new solutions to the third-order symplectic integration method

International Nuclear Information System (INIS)

Iwatsu, Reima

2009-01-01

Two new solutions are obtained for the symplecticity conditions of explicit third-order partitioned Runge-Kutta time integration method. One of them has larger stability limit and better dispersion property than the Ruth's method.

Orthogonal and symplectic Yangians and Yang–Baxter R-operators

International Nuclear Information System (INIS)

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

2016-01-01

Yang–Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalized L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.

Orthogonal and symplectic Yangians and Yang–Baxter R-operators

Energy Technology Data Exchange (ETDEWEB)

Isaev, A.P., E-mail: isaevap@theor.jinr.ru [Bogoliubov Lab., Joint Institute of Nuclear Research, Dubna (Russian Federation); Karakhanyan, D., E-mail: karakhan@yerphi.am [Yerevan Physics Institute, 2 Alikhanyan br., 0036 Yerevan (Armenia); Kirschner, R., E-mail: Roland.Kirschner@itp.uni-leipzig.de [Institut für Theoretische Physik, Universität Leipzig, PF 100 920, D-04009 Leipzig (Germany)

2016-03-15

Yang–Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalized L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.

Orthogonal and symplectic Yangians and Yang–Baxter R-operators

Directory of Open Access Journals (Sweden)

A.P. Isaev

2016-03-01

Full Text Available Yang–Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalized L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.

Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations

International Nuclear Information System (INIS)

Hong Jialin; Li Chun

2006-01-01

In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law

Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation

International Nuclear Information System (INIS)

Sha, Wei; Huang, Zhixiang; Wu, Xianliang; Chen, Mingsheng

2007-01-01

An explicit fourth-order finite-difference time-domain (FDTD) scheme using the symplectic integrator is applied to electromagnetic simulation. A feasible numerical implementation of the symplectic FDTD (SFDTD) scheme is specified. In particular, new strategies for the air-dielectric interface treatment and the near-to-far-field (NFF) transformation are presented. By using the SFDTD scheme, both the radiation and the scattering of three-dimensional objects are computed. Furthermore, the energy-conserving characteristic hold for the SFDTD scheme is verified under long-term simulation. Numerical results suggest that the SFDTD scheme is more efficient than the traditional FDTD method and other high-order methods, and can save computational resources

Wavelet approach to accelerator problems. 3: Melnikov functions and symplectic topology

International Nuclear Information System (INIS)

Fedorova, A.; Zeitlin, M.; Parsa, Z.

1997-05-01

This is the third part of a series of talks in which the authors present applications of methods of wavelet analysis to polynomial approximations for a number of accelerator physics problems. They consider the generalization of the variational wavelet approach to nonlinear polynomial problems to the case of Hamiltonian systems for which they need to preserve underlying symplectic or Poissonian or quasicomplex structures in any type of calculations. They use the approach for the problem of explicit calculations of Arnold-Weinstein curves via Floer variational approach from symplectic topology. The loop solutions are parameterized by the solutions of reduced algebraical problem--matrix Quadratic Mirror Filters equations. Also they consider wavelet approach to the calculations of Melnikov functions in the theory of homoclinic chaos in perturbed Hamiltonian systems

Variational Symplectic Integrator for Long-Time Simulations of the Guiding-Center Motion of Charged Particles in General Magnetic Fields

International Nuclear Information System (INIS)

Qin Hong; Guan Xiaoyin

2008-01-01

A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed for long-time simulation studies of magnetized plasmas. 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 the dynamics. The variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure, and has better numerical properties over long integration time, compared with standard integrators, such as the standard and variable time-step fourth order Runge-Kutta methods

Variational Symplectic Integrator for Long-Time Simulations of the Guiding-Center Motion of Charged Particles in General Magnetic Fields

International Nuclear Information System (INIS)

Qin, H.; Guan, X.

2008-01-01

A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed for long-time simulation studies of magnetized plasmas. 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 the dynamics. The variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure, and has better numerical properties over long integration time, compared with standard integrators, such as the standard and variable time-step fourth order Runge-Kutta methods.

Algebraic dynamics algorithm: Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

Institute of Scientific and Technical Information of China (English)

WANG ShunJin; ZHANG Hua

2007-01-01

Based on the exact analytical solution of ordinary differential equations,a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm.A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models.The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision,and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.

Algebraic dynamics algorithm:Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

Institute of Scientific and Technical Information of China (English)

2007-01-01

Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.

Renormalization of period doubling in symmetric four-dimensional volume-preserving maps

International Nuclear Information System (INIS)

Mao, J.; Greene, J.M.

1987-01-01

We have determined three maps (truncated at quadratic terms) that are fixed under the renormalization operator of pitchfork period doubling in symmetric four-dimensional volume-preserving maps. Each of these contains the previously known two-dimensional area-preserving map that is fixed under the period-doubling operator. One of these three fixed maps consists of two uncoupled two-dimensional (nonlinear) area-preserving fixed maps. The other two contain also the two-dimensional area-preserving fixed map coupled (in general) with a linear two-dimensional map. The renormalization calculation recovers all numerical results for the pitchfork period doubling in the symmetric four-dimensional volume-preserving maps, reported by Mao and Helleman [Phys. Rev. A 35, 1847 (1987)]. For a large class of nonsymmetric four-dimensional volume-preserving maps, we found that the fixed maps are the same as those for the symmetric maps

Explicit symplectic integrators of molecular dynamics algorithms for rigid-body molecules in the canonical, isobaric-isothermal, and related ensembles.

Science.gov (United States)

Okumura, Hisashi; Itoh, Satoru G; Okamoto, Yuko

2007-02-28

The authors propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isobaric-isothermal ensembles. They also present a symplectic algorithm in the constant normal pressure and lateral surface area ensemble and that combined with the Parrinello-Rahman algorithm. Employing the symplectic integrators for MD algorithms, there is a conserved quantity which is close to Hamiltonian. Therefore, they can perform a MD simulation more stably than by conventional nonsymplectic algorithms. They applied this algorithm to a TIP3P pure water system at 300 K and compared the time evolution of the Hamiltonian with those by the nonsymplectic algorithms. They found that the Hamiltonian was conserved well by the symplectic algorithm even for a time step of 4 fs. This time step is longer than typical values of 0.5-2 fs which are used by the conventional nonsymplectic algorithms.

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

Science.gov (United States)

Chen, Qiang; Qin, Hong; Liu, Jian; Xiao, Jianyuan; Zhang, Ruili; He, Yang; Wang, Yulei

2017-11-01

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. 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.

An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

KAUST Repository

Karlsson, Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

2015-01-01

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.

Bifurcation analysis of the logistic map via two periodic impulsive forces

International Nuclear Information System (INIS)

Jiang Hai-Bo; Li Tao; Zeng Xiao-Liang; Zhang Li-Ping

2014-01-01

The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincaré map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map. (general)

Symplectic tomography of nonclassical states of trapped ion

International Nuclear Information System (INIS)

Man'ko, O.

1996-03-01

The marginal distribution for two types of nonclassical states of trapped ion - for squeezed and correlated states and for squeezed even and odd coherent states (squeezed Schroedinger cat states) is studied. The obtained marginal distribution for the two types of states is shown to satisfy classical dynamical equation equivalent to standard quantum evolution equation for density matrix (wave function) derived in symplectic tomography scheme. (author). 20 refs

Symplectic tracking using point magnets in the presence of a longitudinal magnetic field

International Nuclear Information System (INIS)

Parzen, G.

1993-09-01

In the absence of a longitudinal magnetic field, symplectic tracking can be achieved by replacing the magnets by a series of point magnets and drift spaces. To treat the case when a longitudinal magnetic field is also present, this procedure is modified in this paper by replacing the drift space by a solenoidal drift, which is defined as the motion of a particle in a uniform longitudinal magnetic field. A symplectic integrator can be obtained by subdividing each magnet into pieces and replacing each magnet piece by point magnets, with only transverse fields, and solenoidal drift spaces. The reference orbit used here is made up of arcs of circles and straight lines which join smoothly with each other. For this choice of reference orbit, the required results are obtained to track particles, which are the transfer functions, and the transfer time for the different elements. It is shown that these results provide a symplectic integrator, and they are exact in the sense that as the number of magnet pieces is increased, the particle motion will converge to the particle motion of the exact equations of motion

An hp symplectic pseudospectral method for nonlinear optimal control

Science.gov (United States)

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.

The electromagnetic Dirac-Fock-Podolsky problem and symplectic properties of the Maxwell and Yang-Mills type dynamical systems

International Nuclear Information System (INIS)

Bogolubov, N.N. Jr.; Prykarpatsky, A.K.; Taneri, U.; Prykarpatsky, Y.A.

2009-01-01

Based on analysis of reduced geometric structures on fibered manifolds, invariant under action of a certain symmetry group, we construct the symplectic structures associated with connection forms on suitable principal fiber bundles. The application to the non-standard Hamiltonian analysis of the Maxwell and Yang-Mills type dynamical systems is presented. A symplectic reduction theory of the classical Maxwell electromagnetic field equations is formulated, the important Lorentz condition, ensuring the existence of electromagnetic waves, is naturally included into the Hamiltonian picture, thereby solving the well known Dirac, Fock and Podolsky problem. The symplectically reduced Poissonian structures and the related classical minimal interaction principle, concerning the Yang-Mills type equations, are considered. (author)

Deformations of coisotropic submanifolds in locally conformal symplectic manifolds

Czech Academy of Sciences Publication Activity Database

Le, Hong-Van; Oh, Y.-G.

2016-01-01

Roč. 20, č. 3 (2016), s. 553-596 ISSN 1093-6106 Institutional support: RVO:67985840 Keywords : locally conformal symplectic manifold * coisotropic submanifold * b-twisted differential * bulk deformation Subject RIV: BA - General Mathematics Impact factor: 0.895, year: 2016 http://intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0020/0003/a007/index.html

Exact symplectic structures and a classical model for the Dirac electron

International Nuclear Information System (INIS)

Rawnsley, J.

1992-01-01

We show how the classical model for the Dirac electron of Barut and coworkers can be obtained as a Hamiltonian theory by constructing an exact symplectic form on the total space of the spin bundle over spacetime. (orig.)

Multiparametric quantum symplectic phase space

International Nuclear Information System (INIS)

Parashar, P.; Soni, S.K.

1992-07-01

We formulate a consistent multiparametric differential calculus on the quadratic coordinate algebra of the quantum vector space and use this as a tool to obtain a deformation of the associated symplectic phase space involving n(n-1)/2+1 deformation parameters. A consistent calculus on the relation subspace is also constructed. This is achieved with the help of a restricted ansatz and solving the consistency conditions to directly arrive at the main commutation structures without any reference to the R-matrix. However, the non-standard R-matrices for GL r,qij (n) and Sp r,qij (2n) can be easily read off from the commutation relations involving coordinates and derivatives. (author). 9 refs

Periodic cluster mutations and related integrable maps

International Nuclear Information System (INIS)

Fordy, Allan P

2014-01-01

One of the remarkable properties of cluster algebras is that any cluster, obtained from a sequence of mutations from an initial cluster, can be written as a Laurent polynomial in the initial cluster (known as the ‘Laurent phenomenon’). There are many nonlinear recurrences which exhibit the Laurent phenomenon and thus unexpectedly generate integer sequences. The mutation of a typical quiver will not generate a recurrence, but rather an erratic sequence of exchange relations. How do we ‘design’ a quiver which gives rise to a given recurrence? A key role is played by the concept of ‘periodic cluster mutation’, introduced in 2009. Each recurrence corresponds to a finite dimensional map. In the context of cluster mutations, these are called ‘cluster maps’. What properties do cluster maps have? Are they integrable in some standard sense?In this review I describe how integrable maps arise in the context of cluster mutations. I first explain the concept of ‘periodic cluster mutation’, giving some classification results. I then give a review of what is meant by an integrable map and apply this to cluster maps. Two classes of integrable maps are related to interesting monodromy problems, which generate interesting Poisson algebras of functions, used to prove complete integrability and a linearization. A connection to the Hirota–Miwa equation is explained. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (review)

Hydrodynamic Covariant Symplectic Structure from Bilinear Hamiltonian Functions

Directory of Open Access Journals (Sweden)

Capozziello S.

2005-07-01

Full Text Available Starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields, it is possible to derive a general symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of motion directly related to a hydrodynamic picture. This feature is gauge free and it seems a deep link common to all interactions, electromagnetism and gravity included. This scheme could lead toward a full canonical quantization.

Principal and nonprincipal solutions of symplectic dynamic systems on time scales

Directory of Open Access Journals (Sweden)

Ondrej Dosly

2000-01-01

Full Text Available We establish the concept of the principal and nonprincipal solution for the so-called symplectic dynamic systems on time scales. We also present a brief survey of the history of these concept for differential and difference equations.

A period-doubling cascade precedes chaos for planar maps.

Science.gov (United States)

Sander, Evelyn; Yorke, James A

2013-09-01

A period-doubling cascade is often seen in numerical studies of those smooth (one-parameter families of) maps for which as the parameter is varied, the map transitions from one without chaos to one with chaos. Our emphasis in this paper is on establishing the existence of such a cascade for many maps with phase space dimension 2. We use continuation methods to show the following: under certain general assumptions, if at one parameter there are only finitely many periodic orbits, and at another parameter value there is chaos, then between those two parameter values there must be a cascade. We investigate only families that are generic in the sense that all periodic orbit bifurcations are generic. Our method of proof in showing there is one cascade is to show there must be infinitely many cascades. We discuss in detail two-dimensional families like those which arise as a time-2π maps for the Duffing equation and the forced damped pendulum equation.

Buffer Overflow Period in a MAP Queue

Directory of Open Access Journals (Sweden)

Andrzej Chydzinski

2007-01-01

Full Text Available The buffer overflow period in a queue with Markovian arrival process (MAP and general service time distribution is investigated. The results include distribution of the overflow period in transient and stationary regimes and the distribution of the number of cells lost during the overflow interval. All theorems are illustrated via numerical calculations.

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

International Nuclear Information System (INIS)

Xiao, Jianyuan; Liu, Jian; He, Yang; Zhang, Ruili; Qin, Hong; Sun, Yajuan

2015-01-01

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 http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five 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

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

Energy Technology Data Exchange (ETDEWEB)

Xiao, Jianyuan [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Qin, Hong [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA; Liu, Jian [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; He, Yang [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Zhang, Ruili [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Sun, Yajuan [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, China

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 five 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.

Symplectic integrators for large scale molecular dynamics simulations: A comparison of several explicit methods

International Nuclear Information System (INIS)

Gray, S.K.; Noid, D.W.; Sumpter, B.G.

1994-01-01

We test the suitability of a variety of explicit symplectic integrators for molecular dynamics calculations on Hamiltonian systems. These integrators are extremely simple algorithms with low memory requirements, and appear to be well suited for large scale simulations. We first apply all the methods to a simple test case using the ideas of Berendsen and van Gunsteren. We then use the integrators to generate long time trajectories of a 1000 unit polyethylene chain. Calculations are also performed with two popular but nonsymplectic integrators. The most efficient integrators of the set investigated are deduced. We also discuss certain variations on the basic symplectic integration technique

Supersymmetric symplectic quantum mechanics

Science.gov (United States)

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.

Higher-order force gradient symplectic algorithms

Science.gov (United States)

Chin, Siu A.; Kidwell, Donald W.

2000-12-01

We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10, and 12, the new algorithms are approximately a factor of 103, 104, 104, and 105 better.

Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties

OpenAIRE

Bellamy, Gwyn; Dodd, Christopher; McGerty, Kevin; Nevins, Thomas

2013-01-01

We prove a new symplectic analogue of Kashiwara’s equivalence from D–module\\ud theory. As a consequence, we establish a structure theory for module categories over\\ud deformation-quantizations that mirrors, at a higher categorical level, the BiałynickiBirula\\ud stratification of a variety with an action of the multiplicative group Gm . The\\ud resulting categorical cell decomposition provides an algebrogeometric parallel to the\\ud structure of Fukaya categories of Weinstein manifolds. From it,...

An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

KAUST Repository

Karlsson, Peer Jesper

2015-01-07

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading order term consisting of an error density that is computable from Symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations.

Free versus constrained evolution of the 2+1 equivariant wave map

International Nuclear Information System (INIS)

Peter, Ralf; Frauendiener, Jörg

2012-01-01

We compare the numerical solutions of the 2+1 equivariant wave map problem computed with the symplectic, constraint respecting Rattle algorithm and the well known fourth order Runge–Kutta method. We show the advantages of the Rattle algorithm for the constrained system compared to the free evolution with the Runge–Kutta method. We also present an expression, which represents the energy loss due to constraint violation. Taking this expression into account we can achieve energy conservation for the Runge–Kutta scheme, which is better than with the Rattle method. Using the symplectic scheme with constraint enforcement, we can reproduce previous calculations of the equivariant case without imposing the symmetry explicitly, thereby confirming that the critical behaviour is stable. (paper)

A Note on Symplectic, Multisymplectic Scheme in Finite Element Method

Institute of Scientific and Technical Information of China (English)

GUO Han-Ying; JI Xiao-Mei; LI Yu-Qi; WU Ke

2001-01-01

We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case respectively. These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice.``

Long-time correlations of periodic, area-preserving maps

International Nuclear Information System (INIS)

Meiss, J.D.; Cary, J.R.; Grebogi, C.; Crawford, J.D.; Kaufman, A.N.; Abarbanel, H.D.I.

1982-04-01

A simple analytical decay law for correlation functions of periodic, area-preserving maps is obtained. This law is compared with numerical experiments on the standard map. The agreement between experiment and theory is good when islands are absent, but poor when islands are present. When islands are present, the correlations have a long, slowly decaying tail

Asymptotic freedom and the symplectic and G2 groups

International Nuclear Information System (INIS)

Chaichian, M; Kolmakov, Yu. N.; Nelipa, N. F.

1978-01-01

It is shown that the symplectic Sp(4), Sp(6) and the exceptional G 2 gauge field theories with complete Spontaneous symmetry breaking through the Higgs mechanism are not asymptotically free. This, together with earlier results for other groups, hints at the existence of a general theorem according to which it would no longer be possible for asymptotic freedom to coexist with the absence of infrared divergences. (author)

An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

KAUST Repository

Karlsson, Peer Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

2015-01-01

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system

Classification of the linear canonical transformation and its associated real symplectic matrix

NARCIS (Netherlands)

Bastiaans, M.J.; Alieva, T.

2007-01-01

Based on the eigenvalues of the real symplectic ABCD-matrix that characterizes the linear canonical integral transformation, a classification of this transformation and the associated ABCD-system is proposed and some nuclei (i.e. elementary members) in each class are described. In the

Structure of period-2 step-1 accelerator island in area preserving maps

International Nuclear Information System (INIS)

Hirose, K.; Ichikawa, Y.H.; Saito, S.

1996-03-01

Since the multi-periodic accelerator modes manifest their contribution even in the region of small stochastic parameters, analysis of such regular motion appears to be critical to explore the stochastic properties of the Hamiltonian system. Here, structure of period-2 step-1 accelerator mode is analyzed for the systems described by the Harper map and by the standard map. The stability criterions have been analyzed in detail in comparison with numerical analyses. The period-3 squeezing around the period-2 step-1 islands is identified in the standard map. (author)

Stability Analysis of Periodic Systems by Truncated Point Mappings

Science.gov (United States)

Guttalu, R. S.; Flashner, H.

1996-01-01

An approach is presented deriving analytical stability and bifurcation conditions for systems with periodically varying coefficients. The method is based on a point mapping(period to period mapping) representation of the system's dynamics. An algorithm is employed to obtain an analytical expression for the point mapping and its dependence on the system's parameters. The algorithm is devised to derive the coefficients of a multinominal expansion of the point mapping up to an arbitrary order in terms of the state variables and of the parameters. Analytical stability and bifurcation condition are then formulated and expressed as functional relations between the parameters. To demonstrate the application of the method, the parametric stability of Mathieu's equation and of a two-degree of freedom system are investigated. The results obtained by the proposed approach are compared to those obtained by perturbation analysis and by direct integration which we considered to the "exact solution". It is shown that, unlike perturbation analysis, the proposed method provides very accurate solution even for large valuesof the parameters. If an expansion of the point mapping in terms of a small parameter is performed the method is equivalent to perturbation analysis. Moreover, it is demonstrated that the method can be easily applied to multiple-degree-of-freedom systems using the same framework. This feature is an important advantage since most of the existing analysis methods apply mainly to single-degree-of-freedom systems and their extension to higher dimensions is difficult and computationally cumbersome.

QCD gauge symmetries through Faddeev-Jackiw symplectic method

International Nuclear Information System (INIS)

Abreu, E.M.C.; Mendes, A.C.R.; Neves, C.; Oliveira, W.; Silva, R.C.N.

2013-01-01

Full text: The FJ method is an approach that is geometrically motivated. It is based on the symplectic structure of the phase space. The first-order characteristic allows to obtain the Hamiltonian equations of motion from a variational principle. Its geometric structure of the Hamiltonian phase-space will be carried out directly from the equations of motion via the inverse of the so-called symplectic two-form, if the inverse exists. Few years after its publication, the FJ formalism was extended and through the years it has been applied to different systems. Gauge invariance is one of the most well established concepts in theoretical physics and it is one of the main ingredients in Standard Model theory. However, we can ask if it could have an alternative origin connected to another theory or principle. With this motivation in mind we will show in this paper that gauge invariance could be considered an emergent concept having its origin in the algebraic formalism of a well known method that deals with constrained systems, namely, the Faddeev-Jackiw (FJ) technique. Of course the gauge invariance idea is older than FJ's, but the results obtained here will show that the connection between both will prove that SU(3) and SU(3) X SU(2) X U(1) gauge groups, which are fundamental to important theories like QCD and Standard Model, can be obtained through FJ formalism. (author)

Moment methods for nonlinear maps

International Nuclear Information System (INIS)

Pusch, G.D.; Atomic Energy of Canada Ltd., Chalk River, ON

1993-01-01

It is shown that Differential Algebra (DA) may be used to push moments of distributions through a map, at a computational cost per moment comparable to pushing a single particle. The algorithm is independent of order, and whether or not the map is symplectic. Starting from the known result that moment-vectors transform linearly - like a tensor - even under a nonlinear map, I suggest that the form of the moment transformation rule indicates that the moment-vectors are elements of the dual to DA-vector space. I propose several methods of manipulating moments and constructing invariants using DA. I close with speculations on how DA might be used to ''close the circle'' to solve the inverse moment problem, yielding an entirely DA-and-moment-based space-charge code. (Author)

Symplectic manifolds, coadjoint orbits, and Mean Field Theory

International Nuclear Information System (INIS)

Rosensteel, G.

1986-01-01

Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit

Symplectic invariants of some families of Lagrangian T3-fibrations

International Nuclear Information System (INIS)

Castano Bernard, R.

2003-12-01

We construct families of Lagrangian 3-torus fibrations resembling the topology of some of the singularities in Topological Mirror Symmetry. We perform a detailed analysis of the affine structure on the base of these fibrations near their discriminant loci. This permits us to classify the aforementioned families up to fibre preserving symplectomorphism. The kind of degenerations we investigate give rise to a large number of symplectic invariants. (author)

Fast symplectic map tracking for the CERN Large Hadron Collider

Directory of Open Access Journals (Sweden)

Dan T. Abell

2003-06-01

Full Text Available Tracking simulations remain the essential tool for evaluating how multipolar imperfections in ring magnets restrict the domain of stable phase-space motion. In the Large Hadron Collider (LHC at CERN, particles circulate at the injection energy, when multipole errors are most significant, for more than 10^{7} turns, but systematic tracking studies are limited to a small fraction of this total time—even on modern computers. A considerable speedup is expected by replacing element-by-element tracking with the use of a symplectified one-turn map. We have applied this method to the realistic LHC lattice, version 6, and report here our results for various map orders, with special emphasis on precision and speed.

Exact smooth classification of Hamiltonian vector fields on symplectic 2-manifolds

International Nuclear Information System (INIS)

Krouglikov, B.S.

1994-10-01

Complete exact classification of Hamiltonian systems with one degree of freedom and Morse Hamiltonian is carried out. As it is a main part of trajectory classification of integrable Hamiltonian systems with two degrees of freedom, the corresponding generalization is considered. The dual problem of classification of symplectic form together with Morse foliation is carried out as well. (author). 10 refs, 16 figs

The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies

NARCIS (Netherlands)

Kersten, P.H.M.; Krasil'shchik, I.; Verbovetsky, A.V.

2004-01-01

Using methods of geometry and cohomology developed recently, we study the Monge-Ampère equation, arising as the first nontrivial equation in the associativity equations, or WDVV equations. We describe Hamiltonian and symplectic structures as well as recursion operators for this equation in its

Differential and symplectic topology of knots and curves

CERN Document Server

Tabachnikov, S

1999-01-01

This book presents a collection of papers on two related topics: topology of knots and knot-like objects (such as curves on surfaces) and topology of Legendrian knots and links in 3-dimensional contact manifolds. Featured is the work of international experts in knot theory (""quantum"" knot invariants, knot invariants of finite type), in symplectic and contact topology, and in singularity theory. The interplay of diverse methods from these fields makes this volume unique in the study of Legendrian knots and knot-like objects such as wave fronts. A particularly enticing feature of the volume is

The endoscopic classification of representations orthogonal and symplectic groups

CERN Document Server

Arthur, James

2013-01-01

Within the Langlands program, endoscopy is a fundamental process for relating automorphic representations of one group with those of another. In this book, Arthur establishes an endoscopic classification of automorphic representations of orthogonal and symplectic groups G. The representations are shown to occur in families (known as global L-packets and A-packets), which are parametrized by certain self-dual automorphic representations of an associated general linear group GL(N). The central result is a simple and explicit formula for the multiplicity in the automorphic discrete spectrum of G

The combinatorics computation for Casimir operators of the symplectic Lie algebra and the application for determining the center of the enveloping algebra of a semidirect product

International Nuclear Information System (INIS)

Le Van Hop.

1989-12-01

The combinatorics computation is used to describe the Casimir operators of the symplectic Lie Algebra. This result is applied for determining the Center of the enveloping Algebra of the semidirect Product of the Heisenberg Lie Algebra and the symplectic Lie Algebra. (author). 10 refs

Bott–Kitaev periodic table and the diagonal map

International Nuclear Information System (INIS)

Kennedy, R; Zirnbauer, M R

2015-01-01

Building on the ten-way symmetry classification of disordered fermions, the authors have recently given a homotopy-theoretic proof of Kitaev's ‘periodic table’ for topological insulators and superconductors. The present paper offers an introduction to the physical setting and the mathematical model used. Basic to the proof is the so-called diagonal map, a natural transformation akin to the Bott map of algebraic topology, which increases by one unit both the momentum-space dimension and the symmetry index of translation-invariant ground states of gapped free-fermion systems. This mapping is illustrated here with a few examples of interest. (Based on a talk delivered by the senior author at the Nobel Symposium on ‘New Forms of Matter: Topological Insulators and Superconductors’; Stockholm, 13–15 June, 2014.) (topical article)

Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere

International Nuclear Information System (INIS)

Li Jinxing; Pu Zuyin; Xie Lun; Fu Suiyan; Qin Hong

2011-01-01

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 the 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.

Stability regions for synchronized τ-periodic orbits of coupled maps with coupling delay τ

Energy Technology Data Exchange (ETDEWEB)

Karabacak, Özkan, E-mail: ozkan2917@gmail.com [Department of Electronics and Communication Engineering, Istanbul Technical University, 34469 Istanbul (Turkey); Department of Electronic Systems, Aalborg University, 9220 Aalborg East (Denmark); Alikoç, Baran, E-mail: alikoc@itu.edu.tr [Department of Control and Automation Engineering, Istanbul Technical University, 34469 Istanbul (Turkey); Atay, Fatihcan M., E-mail: atay@member.ams.org [Department of Mathematics, Bilkent University, 06800 Ankara (Turkey)

2016-09-15

Motivated by the chaos suppression methods based on stabilizing an unstable periodic orbit, we study the stability of synchronized periodic orbits of coupled map systems when the period of the orbit is the same as the delay in the information transmission between coupled units. We show that the stability region of a synchronized periodic orbit is determined by the Floquet multiplier of the periodic orbit for the uncoupled map, the coupling constant, the smallest and the largest Laplacian eigenvalue of the adjacency matrix. We prove that the stabilization of an unstable τ-periodic orbit via coupling with delay τ is possible only when the Floquet multiplier of the orbit is negative and the connection structure is not bipartite. For a given coupling structure, it is possible to find the values of the coupling strength that stabilizes unstable periodic orbits. The most suitable connection topology for stabilization is found to be the all-to-all coupling. On the other hand, a negative coupling constant may lead to destabilization of τ-periodic orbits that are stable for the uncoupled map. We provide examples of coupled logistic maps demonstrating the stabilization and destabilization of synchronized τ-periodic orbits as well as chaos suppression via stabilization of a synchronized τ-periodic orbit.

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

Science.gov (United States)

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

Chern-Simons theories of symplectic super-diffeomorphisms

International Nuclear Information System (INIS)

Sezgin, E.; Sokatchev, E.

1989-04-01

We discuss the symplectic diffeomorphisms of a class of supermanifolds and the structure of the underlying infinite dimensional superalgebras. We construct a Chern-Simons (CS) gauge theory in 2+1 dimensions for these algebras. There exists a finite dimensional supersymmetric truncation which is the (2 n -1)-dimensional Hamiltonian superalgebra H-tilde(n). With a central charge added, it is a superalgebra, C(n), associated with a Clifford algebra. We find an embedding of d=3, N=2 anti-de Sitter superalgebra OSp(2|2)+OSp(2|2) in C(4), and construct a CS action for its infinite dimensional extension. We also discuss the construction of a CS action for the infinite dimensional extension of the d=3, N=2 superconformal algebra OSp(2,4). (author). 18 refs

Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps

International Nuclear Information System (INIS)

Avrutin, V; Granados, A; Schanz, M

2011-01-01

Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined discontinuous systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with one boundary in state space and become virtual, and, in the one-dimensional case, the map becomes continuous. Depending on the properties of the map near the codimension-two bifurcation point, there exist different scenarios regarding how the infinite number of periodic orbits are born, mainly the so-called period adding and period incrementing. In our work we prove that, in order to undergo a big bang bifurcation of the period incrementing type, it is sufficient for a piecewise-defined one-dimensional map that the colliding fixed points are attractive and with associated eigenvalues of different signs

Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps

Science.gov (United States)

Avrutin, V.; Granados, A.; Schanz, M.

2011-09-01

Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined discontinuous systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with one boundary in state space and become virtual, and, in the one-dimensional case, the map becomes continuous. Depending on the properties of the map near the codimension-two bifurcation point, there exist different scenarios regarding how the infinite number of periodic orbits are born, mainly the so-called period adding and period incrementing. In our work we prove that, in order to undergo a big bang bifurcation of the period incrementing type, it is sufficient for a piecewise-defined one-dimensional map that the colliding fixed points are attractive and with associated eigenvalues of different signs.

Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces

OpenAIRE

Khesin, Boris; Rosly, Alexei

2000-01-01

We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves of the latter are classified by restrictions of the bundles to certain divisors. This can be regarded as fixing a "complex analogue of the holonomy" of a connection along a "complex analogue of the boundary" in analogy with the real case.

Introduction to orthogonal, symplectic and unitary representations of finite groups

CERN Document Server

Riehm, Carl R

2011-01-01

Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of mathematics-linear representations of finite groups, and the theory of quadratic, skew symmetric and Hermitian forms-and thus inherit some of the characteristics of both. This book is written as an introduction to the subject and not as an encyclopaedic reference text. The principal goal is an exposition of the known results on the equivalence theory, and related matters such as the Witt and Witt-Grothendieck groups, over the "classical" fields-algebraically closed, rea

Increasing average period lengths by switching of robust chaos maps in finite precision

Science.gov (United States)

Nagaraj, N.; Shastry, M. C.; Vaidya, P. G.

2008-12-01

Grebogi, Ott and Yorke (Phys. Rev. A 38, 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits (T) of a dynamical system scales as a function of computer precision (ɛ) and the correlation dimension (d) of the chaotic attractor: T ˜ɛ-d/2. In this work, we are concerned with increasing the average period length which is desirable for chaotic cryptography applications. Our experiments reveal that random and chaotic switching of deterministic chaotic dynamical systems yield higher average length of periodic orbits as compared to simple sequential switching or absence of switching. To illustrate the application of switching, a novel generalization of the Logistic map that exhibits Robust Chaos (absence of attracting periodic orbits) is first introduced. We then propose a pseudo-random number generator based on chaotic switching between Robust Chaos maps which is found to successfully pass stringent statistical tests of randomness.

Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation

International Nuclear Information System (INIS)

Persohn, K.J.; Povinelli, R.J.

2012-01-01

Highlights: ► A chaotic pseudorandom number generator (C-PRNG) poorly explores the key space. ► A C-PRNG is finite and periodic when implemented on a finite precision computer. ► We present a method to determine the period lengths of a C-PRNG. - Abstract: Because of the mixing and aperiodic properties of chaotic maps, such maps have been used as the basis for pseudorandom number generators (PRNGs). However, when implemented on a finite precision computer, chaotic maps have finite and periodic orbits. This manuscript explores the consequences finite precision has on the periodicity of a PRNG based on the logistic map. A comparison is made with conventional methods of generating pseudorandom numbers. The approach used to determine the number, delay, and period of the orbits of the logistic map at varying degrees of precision (3 to 23 bits) is described in detail, including the use of the Condor high-throughput computing environment to parallelize independent tasks of analyzing a large initial seed space. Results demonstrate that in terms of pathological seeds and effective bit length, a PRNG based on the logistic map performs exponentially worse than conventional PRNGs.

Some New Constructions of Authentication Codes with Arbitration and Multi-Receiver from Singular Symplectic Geometry

Directory of Open Access Journals (Sweden)

You Gao

2011-01-01

Full Text Available A new construction of authentication codes with arbitration and multireceiver from singular symplectic geometry over finite fields is given. The parameters are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities of success for different types of deception are also computed.

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

Science.gov (United States)

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.

Denjoy minimal sets and Birkhoff periodic orbits for non-exact monotone twist maps

Science.gov (United States)

Qin, Wen-Xin; Wang, Ya-Nan

2018-06-01

A non-exact monotone twist map φbarF is a composition of an exact monotone twist map φ bar with a generating function H and a vertical translation VF with VF ((x , y)) = (x , y - F). We show in this paper that for each ω ∈ R, there exists a critical value Fd (ω) ≥ 0 depending on H and ω such that for 0 ≤ F ≤Fd (ω), the non-exact twist map φbarF has an invariant Denjoy minimal set with irrational rotation number ω lying on a Lipschitz graph, or Birkhoff (p , q)-periodic orbits for rational ω = p / q. Like the Aubry-Mather theory, we also construct heteroclinic orbits connecting Birkhoff periodic orbits, and show that quasi-periodic orbits in these Denjoy minimal sets can be approximated by periodic orbits. In particular, we demonstrate that at the critical value F =Fd (ω), the Denjoy minimal set is not uniformly hyperbolic and can be approximated by smooth curves.

Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov–Maxwell equations

Energy Technology Data Exchange (ETDEWEB)

Qin, Hong; Liu, Jian; Xiao, Jianyuan; Zhang, Ruili; He, Yang; Wang, Yulei; Sun, Yajuan; Burby, Joshua W.; Ellison, Leland; Zhou, Yao

2015-12-14

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 nonlinear 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.

Tongues of periodicity in a family of two-dimensional discontinuous maps of real Moebius type

International Nuclear Information System (INIS)

Sushko, Iryna; Gardini, Laura; Puu, Toenu

2004-01-01

In this paper we consider a two-dimensional piecewise-smooth discontinuous map representing the so-called 'relative dynamics' of an Hicksian business cycle model. The main features of the dynamics occur in the parameter region in which no fixed points at finite distance exist, but we may have attracting cycles of any periods. The bifurcations associated with the periodicity tongues of the map are studied making use of the first-return map on a suitable segment of the phase plane. The bifurcation curves bounding the periodicity tongues in the parameter plane are related with saddle-node and border-collision bifurcations of the first-return map. Moreover, the particular 'sausages structure' of the bifurcation tongues is also explained

Associated quantum vector bundles and symplectic structure on a quantum space

International Nuclear Information System (INIS)

Coquereaux, R.; Garcia, A.O.; Trinchero, R.

2000-01-01

We define a quantum generalization of the algebra of functions over an associated vector bundle of a principal bundle. Here the role of a quantum principal bundle is played by a Hopf-Galois extension. Smash products of an algebra times a Hopf algebra H are particular instances of these extensions, and in these cases we are able to define a differential calculus over their associated vector bundles without requiring the use of a (bicovariant) differential structure over H. Moreover, if H is coquasitriangular, it coacts naturally on the associated bundle, and the differential structure is covariant. We apply this construction to the case of the finite quotient of the SL q (2) function Hopf algebra at a root of unity (q 3 = 1) as the structure group, and a reduced 2-dimensional quantum plane as both the 'base manifold' and fibre, getting an algebra which generalizes the notion of classical phase space for this quantum space. We also build explicitly a differential complex for this phase space algebra, and find that levels 0 and 2 support a (co)representation of the quantum symplectic group. On this phase space we define vector fields, and with the help of the Sp q structure we introduce a symplectic form relating 1-forms to vector fields. This leads naturally to the introduction of Poisson brackets, a necessary step to do 'classical' mechanics on a quantum space, the quantum plane. (author)

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

Science.gov (United States)

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.

Transverse vibration of pipe conveying fluid made of functionally graded materials using a symplectic method

Energy Technology Data Exchange (ETDEWEB)

Wang, Zhong-Min, E-mail: wangzhongm@xaut.edu.cn; Liu, Yan-Zhuang

2016-03-15

Highlights: • We investigate the transverse vibration of FGM pipe conveying fluid. • The FGM pipe conveying fluid can be classified into two cases. • The variations between the frequency and the power law exponent are obtained. • “Case 1” is relatively more reasonable than “case 2”. - Abstract: Problems related to the transverse vibration of pipe conveying fluid made of functionally graded material (FGM) are addressed. Based on inside and outside surface material compositions of the pipe, FGM pipe conveying fluid can be classified into two cases. It is hypothesized that the physical parameters of the material along the direction of the pipe wall thickness change in the simple power law. A differential equation of motion expressed in non-dimensional quantities is derived by using Hamilton's principle for systems of changing mass. Using the assuming modal method, the pipe deflection function is expanded into a series, in which each term is expressed to admissible function multiplied by generalized coordinate. Then, the differential equation of motion is discretized into the two order differential equations expressed in the generalized coordinates. Based on symplectic elastic theory and the introduction of dual system and dual variable, Hamilton's dual equations are derived, and the original problem is reduced to eigenvalue and eigenvector problem in the symplectic space. Finally, a symplectic method is employed to analyze the vibration and stability of FGM pipe conveying fluid. For a clamped–clamped FGM pipe conveying fluid in “case 1” and “case 2”, the dimensionless critical flow velocity for first-mode divergence and the critical coupled-mode flutter flow velocity are obtained, and the variations between the real part and imaginary part of dimensionless complex frequency and fluid velocity, mass ratio and the power law exponent (or graded index, volume fraction) for FGM pipe conveying fluid are analyzed.

Transverse vibration of pipe conveying fluid made of functionally graded materials using a symplectic method

International Nuclear Information System (INIS)

Wang, Zhong-Min; Liu, Yan-Zhuang

2016-01-01

Highlights: • We investigate the transverse vibration of FGM pipe conveying fluid. • The FGM pipe conveying fluid can be classified into two cases. • The variations between the frequency and the power law exponent are obtained. • “Case 1” is relatively more reasonable than “case 2”. - Abstract: Problems related to the transverse vibration of pipe conveying fluid made of functionally graded material (FGM) are addressed. Based on inside and outside surface material compositions of the pipe, FGM pipe conveying fluid can be classified into two cases. It is hypothesized that the physical parameters of the material along the direction of the pipe wall thickness change in the simple power law. A differential equation of motion expressed in non-dimensional quantities is derived by using Hamilton's principle for systems of changing mass. Using the assuming modal method, the pipe deflection function is expanded into a series, in which each term is expressed to admissible function multiplied by generalized coordinate. Then, the differential equation of motion is discretized into the two order differential equations expressed in the generalized coordinates. Based on symplectic elastic theory and the introduction of dual system and dual variable, Hamilton's dual equations are derived, and the original problem is reduced to eigenvalue and eigenvector problem in the symplectic space. Finally, a symplectic method is employed to analyze the vibration and stability of FGM pipe conveying fluid. For a clamped–clamped FGM pipe conveying fluid in “case 1” and “case 2”, the dimensionless critical flow velocity for first-mode divergence and the critical coupled-mode flutter flow velocity are obtained, and the variations between the real part and imaginary part of dimensionless complex frequency and fluid velocity, mass ratio and the power law exponent (or graded index, volume fraction) for FGM pipe conveying fluid are analyzed.

Normalization of the parameterized Courant-Snyder matrix for symplectic factorization of a parameterized Taylor map

International Nuclear Information System (INIS)

Yan, Y.T.

1991-01-01

The transverse motion of charged particles in a circular accelerator can be well represented by a one-turn high-order Taylor map. For particles without energy deviation, the one-turn Taylor map is a 4-dimensional polynomials of four variables. The four variables are the transverse canonical coordinates and their conjugate momenta. To include the energy deviation (off-momentum) effects, the map has to be parameterized with a smallness factor representing the off-momentum and so the Taylor map becomes a 4-dimensional polynomials of five variables. It is for this type of parameterized Taylor map that a mehtod is presented for converting it into a parameterized Dragt-Finn factorization map. Parameterized nonlinear normal form and parameterized kick factorization can thus be obtained with suitable modification of the existing technique

The Koszul complex of a moment map

DEFF Research Database (Denmark)

Herbig, Hans-Christian; Schwarz, Gerald W.

2013-01-01

Let $K\\to\\U(V)$ be a unitary representation of the compact Lie group $K$. Then there is a canonical moment mapping $\\rho\\colon V\\to\\liek^*$. We have the Koszul complex ${\\mathcal K}(\\rho,\\mathcal C^\\infty(V))$ of the component functions $\\rho_1,\\dots,\\rho_k$ of $\\rho$. Let $G=K_\\C$, the complexif......Let $K\\to\\U(V)$ be a unitary representation of the compact Lie group $K$. Then there is a canonical moment mapping $\\rho\\colon V\\to\\liek^*$. We have the Koszul complex ${\\mathcal K}(\\rho,\\mathcal C^\\infty(V))$ of the component functions $\\rho_1,\\dots,\\rho_k$ of $\\rho$. Let $G......$ be a moment mapping and consider the Koszul complex given by the component functions of $\\rho$. We show that the Koszul complex is a resolution of the smooth functions on $Z=\\rho\\inv(0)$ if and only if the complexification of each symplectic slice representation at a point of $Z$ is $1$-large....

A symplectic map for trajectories of magnetic field lines in double-null divertor tokamaks

Science.gov (United States)

Crank, Willie; Ali, Halima; Punjabi, Alkesh

2009-11-01

The coordinates of the area-preserving map equations for integration of magnetic field line trajectories in tokamaks can be any coordinates for which a transformation to (ψ,θ,φ) coordinates exists [A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys. Lett. A 364, 140 (2007)]. ψ is toroidal magnetic flux, θ is poloidal angle, and φ is toroidal angle. This freedom is exploited to construct a map that represents the magnetic topology of double-null divertor tokamaks. For this purpose, the generating function of the simple map [A. Punjabi, A. Verma, and A. Boozer, Phys. Rev. Lett. 69, 3322 (1992)] is slightly modified. The resulting map equations for the double-null divertor tokamaks are: x1=x0-ky0(1-y0^2 ), y1=y0+kx1. k is the map parameter. It represents the generic topological effects of toroidal asymmetries. The O-point is at (0.0). The X-points are at (0,±1). The equilibrium magnetic surfaces are calculated. These surfaces are symmetric about the x- and y- axes. The widths of stochastic layer near the X-points in the principal plane, and the fractal dimensions of the magnetic footprints on the inboard and outboard side of upper and lower X-points are calculated from the map. This work is supported by US Department of Energy grants DE-FG02-07ER54937, DE-FG02-01ER54624 and DE-FG02-04ER54793.

Quantization of a symplectic manifold associated to a manifold with projective structure

International Nuclear Information System (INIS)

Biswas, Indranil

2009-01-01

Let X be a complex manifold equipped with a projective structure P. There is a holomorphic principal C*-bundle L P ' over X associated with P. We show that the holomorphic cotangent bundle of the total space of L P ' equipped with the Liouville symplectic form has a canonical deformation quantization. This generalizes the construction in the work of and Ben-Zvi and Biswas [''A quantization on Riemann surfaces with projective structure,'' Lett. Math. Phys. 54, 73 (2000)] done under the assumption that dim C X=1.

The symplectic algorithm for use in a model of laser field

International Nuclear Information System (INIS)

Liu Xiaoyan; Liu Xueshen; Ding Peizhu; Zhou Zhongyuan

2002-01-01

Using the asymptotic boundary condition the time-dependent Schroedinger equations with initial conditions in the infinite space can be transformed into the problem with initial and boundary conditions, and it can further be discrected into the inhomogeneous canonic equations. The symplectic algorithms to solve the inhomogeneous canonic equations have been developed and adopted to compute the high-order harmonics of one-dimensional Hydrogen in the laser field. We noticed that there is saturation intensity for generating high-order harmonics, which are agree with previous results, and there is a relationship between harmonics and bound state probabilities

Algebraic models of local period maps and Yukawa algebras

Science.gov (United States)

Bandiera, Ruggero; Manetti, Marco

2018-02-01

We describe some L_{∞} model for the local period map of a compact Kähler manifold. Applications include the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian of the de Rham cohomology. As a by-product, we obtain an interpretation in the framework of deformation theory of the Yukawa coupling.

From Stein to Weinstein and back symplectic geometry of affine complex manifolds

CERN Document Server

Cieliebak, Kai

2013-01-01

A beautiful and comprehensive introduction to this important field. -Dusa McDuff, Barnard College, Columbia University This excellent book gives a detailed, clear, and wonderfully written treatment of the interplay between the world of Stein manifolds and the more topological and flexible world of Weinstein manifolds. Devoted to this subject with a long history, the book serves as a superb introduction to this area and also contains the authors' new results. -Tomasz Mrowka, MIT This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine co

High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Skokos, Ch., E-mail: haris.skokos@uct.ac.za [Physics Department, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701 (South Africa); Gerlach, E. [Lohrmann Observatory, Technical University Dresden, D-01062 Dresden (Germany); Bodyfelt, J.D., E-mail: J.Bodyfelt@massey.ac.nz [Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University, Albany, Private Bag 102904, North Shore City, Auckland 0745 (New Zealand); Papamikos, G. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Eggl, S. [IMCCE, Observatoire de Paris, 77 Avenue Denfert-Rochereau, F-75014 Paris (France)

2014-05-01

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.

High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation

International Nuclear Information System (INIS)

Skokos, Ch.; Gerlach, E.; Bodyfelt, J.D.; Papamikos, G.; Eggl, S.

2014-01-01

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.

c-Map for Born–Infeld theories

Directory of Open Access Journals (Sweden)

L. Andrianopoli

2016-07-01

Full Text Available The c-map of four dimensional non-linear theories of electromagnetism is considered both in the rigid case and in its coupling to gravity. In this way theories with antisymmetric tensors and scalars are obtained, and the three non-linear representations of N = 2 supersymmetry partially broken to N = 1 related. The manifest Sp(2n and U(n covariance of these theories in their multifield extensions is also exhibited. This construction extends to H-invariant non-linear theories of Born–Infeld type with non-dynamical scalars spanning a symmetric coset manifold G/H and the vector field strengths and their duals in a symplectic representation of G as is the case for extended supergravity.

Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. II

International Nuclear Information System (INIS)

Arkad'ev, V.A.; Pogrebkov, A.K.; Polivanov, M.K.

1988-01-01

The concept of tangent vector is made more precise to meet the specific nature of the Sturm-Liouville problem, and on this basis a Poisson bracket that is modified compared with the Gardner form by special boundary terms is derived from the Zakharov-Faddeev symplectic form. This bracket is nondegenerate, and in it the variables of the discrete and continuous spectra are separated

Path integral quantization of the Symplectic Leaves of the SU(2)*Poisson-Lie Group

International Nuclear Information System (INIS)

Morariu, B.

1997-01-01

The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of Uq(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parameterizations and also compare the results with the path integral quantization of spin

Role of short periodic orbits in quantum maps with continuous openings

Science.gov (United States)

Prado, Carlos A.; Carlo, Gabriel G.; Benito, R. M.; Borondo, F.

2018-04-01

We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity functions. This is relevant in many situations that include optical microresonators and more complicated boundary conditions. In a perturbative regime, the shortest periodic orbits belonging to the classical repeller of the open map—a cantor set given by a region of exactly zero reflectivity—prove to be extremely robust in supporting a set of long-lived resonances of the continuously open quantum maps. Moreover, for steplike functions a significant reduction in the number needed is obtained, similarly to the completely open situation. This happens despite a strong change in the spectral properties when compared to the discontinuous reflectivity case. In order to give a more realistic interpretation of these results we compare with a Fresnel-type reflectivity function.

Existence and equivalence of twisted products on a symplectic manifold

International Nuclear Information System (INIS)

Lichnerowicz, A.

1979-01-01

The twisted products play an important role in Quantum Mechanics. A distinction is introduced between Vey *sub(γ) products and strong Vey *sub(γ) products and it is proved that each *sub(γ) product is equivalent to a Vey *sub(γ) product. If b 3 (W) = 0, the symplectic manifold (W,F) admits strong Vey *sub(Gn) products. If b 2 (W) = 0, all *sub(γ) products are equivalent as well as the Vey Lie algebras. In the general case the formal Lie algebras are characterized which are generated by a *sub(γ) product and it proved that the existance of a *sub(γ)-product is equivalent to the existance of a formal Lie algebra infinitesimally equivalent to a Vey Lie algebra at the first order. (Auth.)

Explicit higher order symplectic integrator for s-dependent magnetic field

International Nuclear Information System (INIS)

Wu, Y.; Forest, E.; Robin, D.S.

2001-01-01

We derive second and higher order explicit symplectic integrators for the charged particle motion in an s-dependent magnetic field with the paraxial approximation. The Hamiltonian of such a system takes the form of H (summation) k (p k - a k (rvec q), s) 2 + V((rvec q), s). This work solves a long-standing problem for modeling s-dependent magnetic elements. Important applications of this work include the studies of the charged particle dynamics in a storage ring with strong field wigglers, arbitrarily polarized insertion devices,and super-conducting magnets with strong fringe fields. Consequently, this work will have a significant impact on the optimal use of the above magnetic devices in the light source rings as well as in next generation linear collider damping rings

Notes on qubit phase space and discrete symplectic structures

International Nuclear Information System (INIS)

Livine, Etera R

2010-01-01

We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite-dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on these discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalize our analysis to Hilbert spaces of prime dimensions d and their associated d x d phase spaces.

Long-term numerical simulation of the interaction between a neutron field and a neutral meson field by a symplectic-preserving scheme

International Nuclear Information System (INIS)

Kong Linghua; Hong Jialin; Liu Ruxun

2008-01-01

In this paper, we propose a family of symplectic structure-preserving numerical methods for the coupled Klein-Gordon-Schroedinger (KGS) system. The Hamiltonian formulation is constructed for the KGS. We discretize the Hamiltonian system in space first with a family of canonical difference methods which convert an infinite-dimensional Hamiltonian system into a finite-dimensional one. Next, we discretize the finite-dimensional system in time by a midpoint rule which preserves the symplectic structure of the original system. The conservation laws of the schemes are analyzed in succession, including the charge conservation law and the residual of energy conservation law, etc. We analyze the truncation errors and global errors of the numerical solutions for the schemes to end the theoretical analysis. Extensive numerical tests show the accordance between the theoretical and numerical results

The role of extreme orbits in the global organization of periodic regions in parameter space for one dimensional maps

Energy Technology Data Exchange (ETDEWEB)

Costa, Diogo Ricardo da, E-mail: diogo_cost@hotmail.com [Departamento de Física, UNESP – Universidade Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP (Brazil); Hansen, Matheus [Departamento de Física, UNESP – Universidade Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP (Brazil); Instituto de Física, Univ. São Paulo, Rua do Matão, Cidade Universitária, 05314-970, São Paulo – SP (Brazil); Guarise, Gustavo [Departamento de Física, UNESP – Universidade Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP (Brazil); Medrano-T, Rene O. [Departamento de Ciências Exatas e da Terra, UNIFESP – Universidade Federal de São Paulo, Rua São Nicolau, 210, Centro, 09913-030, Diadema, SP (Brazil); Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Leonel, Edson D. [Departamento de Física, UNESP – Universidade Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP (Brazil); Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy)

2016-04-22

We show that extreme orbits, trajectories that connect local maximum and minimum values of one dimensional maps, play a major role in the parameter space of dissipative systems dictating the organization for the windows of periodicity, hence producing sets of shrimp-like structures. Here we solve three fundamental problems regarding the distribution of these sets and give: (i) their precise localization in the parameter space, even for sets of very high periods; (ii) their local and global distributions along cascades; and (iii) the association of these cascades to complicate sets of periodicity. The extreme orbits are proved to be a powerful indicator to investigate the organization of windows of periodicity in parameter planes. As applications of the theory, we obtain some results for the circle map and perturbed logistic map. The formalism presented here can be extended to many other different nonlinear and dissipative systems. - Highlights: • Extreme orbits and the organization of periodic regions in parameter space. • One-dimensional dissipative mappings. • The circle map and also a time perturbed logistic map were studied.

The role of extreme orbits in the global organization of periodic regions in parameter space for one dimensional maps

International Nuclear Information System (INIS)

Costa, Diogo Ricardo da; Hansen, Matheus; Guarise, Gustavo; Medrano-T, Rene O.; Leonel, Edson D.

2016-01-01

We show that extreme orbits, trajectories that connect local maximum and minimum values of one dimensional maps, play a major role in the parameter space of dissipative systems dictating the organization for the windows of periodicity, hence producing sets of shrimp-like structures. Here we solve three fundamental problems regarding the distribution of these sets and give: (i) their precise localization in the parameter space, even for sets of very high periods; (ii) their local and global distributions along cascades; and (iii) the association of these cascades to complicate sets of periodicity. The extreme orbits are proved to be a powerful indicator to investigate the organization of windows of periodicity in parameter planes. As applications of the theory, we obtain some results for the circle map and perturbed logistic map. The formalism presented here can be extended to many other different nonlinear and dissipative systems. - Highlights: • Extreme orbits and the organization of periodic regions in parameter space. • One-dimensional dissipative mappings. • The circle map and also a time perturbed logistic map were studied.

Long-time behaviour of discretizations of the simple pendulum equation

Energy Technology Data Exchange (ETDEWEB)

Cieslinski, Jan L [Uniwersytet w Bialymstoku, Wydzial Fizyki, ul. Lipowa 41, 15-424 Bialystok (Poland); Ratkiewicz, Boguslaw [Doctoral Studies, Wydzial Fizyki, Uniwersytet Adama Mickiewicza, Poznan (Poland)], E-mail: janek@alpha.uwb.edu.pl, E-mail: bograt@poczta.onet.pl

2009-03-13

We compare several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. The chosen numerical schemes are either symplectic maps or integrable (energy-preserving) maps, or both. Therefore, they preserve qualitative features of solutions (such as periodicity). We describe characteristic periodic time dependences of numerical estimates of the period and the amplitude, and explain them as systematic numerical by-effects produced by any method. Finally, we propose a new numerical scheme which is a modification of the discrete gradient method. This modified discrete gradient method preserves (almost exactly) the period of small oscillations for any time step.

Long-time behaviour of discretizations of the simple pendulum equation

International Nuclear Information System (INIS)

Cieslinski, Jan L; Ratkiewicz, Boguslaw

2009-01-01

We compare several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. The chosen numerical schemes are either symplectic maps or integrable (energy-preserving) maps, or both. Therefore, they preserve qualitative features of solutions (such as periodicity). We describe characteristic periodic time dependences of numerical estimates of the period and the amplitude, and explain them as systematic numerical by-effects produced by any method. Finally, we propose a new numerical scheme which is a modification of the discrete gradient method. This modified discrete gradient method preserves (almost exactly) the period of small oscillations for any time step

Symplectic Group Representation of the Two-Mode Squeezing Operator in the Coherent State Basis

Science.gov (United States)

Fan, Hong-Yi; Chen, Jun-Hua

2003-11-01

We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed. The project supported by National Natural Science Foundation of China under Grant No. 10575057

About periodic and quasi-periodic orbits of a new type for twist maps of the torus

Directory of Open Access Journals (Sweden)

SALVADOR ADDAS-ZANATA

2002-03-01

Full Text Available We prove that for a large and important class of C¹ twist maps of the torus periodic and quasi-periodic orbits of a new type exist, provided that there are no rotational invariant circles (R.I.C's. These orbits have a non-zero "vertical rotation number'' (V.R.N., in contrast to what happens to Birkhoff periodic orbits and Aubry-Mather sets. The V.R.N. is rational for a periodic orbit and irrational for a quasi-periodic. We also prove that the existence of an orbit with a V.R.N = a > 0, implies the existence of orbits with V.R.N = b, for all 0 Provamos que para uma relevante classe de aplicações C¹ no toro, que desviam a vertical para a direita, existem órbitas periódicas e quase-periódicas de um novo tipo, se e somente se, não existem círculos rotacionais invariantes. Essas órbitas têm um número de rotação vertical não nulo (N.R.V, em contraste com o que ocorre para órbitas periódicas do tipo Birkhoff e para os conjuntos de Aubry-Mather. O número de rotação vertical é racional para uma órbita periódica e irracional para uma quase-periódica. Também provamos que a existência de uma órbita com N.R.V = a implica a existência de órbitas com N.R.V = b, para todo 0 < b < a. Como consequência destes resultados, obtemos que uma aplicação do toro que desvia a vertical e não possui círculos rotacionais invariates, necessariamente tem entropia topológica positiva, que é um resultado clássico. No fim deste trabalho apresentamos aplicações e exemplos, como o Standard map, dos resultados obtidos.

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

Science.gov (United States)

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.

Effects of Colored Noise on Periodic Orbits in a One-Dimensional Map

Science.gov (United States)

Li, Feng-Guo; Ai, Bao-Quan

2011-06-01

Noise can induce inverse period-doubling transition and chaos. The effects of the colored noise on periodic orbits, of the different periodic sequences in the logistic map, are investigated. It is found that the dynamical behaviors of the orbits, induced by an exponentially correlated colored noise, are different in the mergence of transition, and the effects of the noise intensity on their dynamical behaviors are different from the effects of the correlation time of noise. Remarkably, the noise can induce new periodic orbits, namely, two new orbits emerge in the period-four sequence at the bifurcation parameter value μ = 3.5, four new orbits in the period-eight sequence at μ = 3.55, and three new orbits in the period-six sequence at μ = 3.846, respectively. Moreover, the dynamical behaviors of the new orbits clearly show the resonancelike response to the colored noise.

Effects of Colored Noise on Periodic Orbits in a One-Dimensional Map

International Nuclear Information System (INIS)

Li Fengguo; Ai Baoquan

2011-01-01

Noise can induce inverse period-doubling transition and chaos. The effects of the colored noise on periodic orbits, of the different periodic sequences in the logistic map, are investigated. It is found that the dynamical behaviors of the orbits, induced by an exponentially correlated colored noise, are different in the mergence of transition, and the effects of the noise intensity on their dynamical behaviors are different from the effects of the correlation time of noise. Remarkably, the noise can induce new periodic orbits, namely, two new orbits emerge in the period-four sequence at the bifurcation parameter value μ = 3.5, four new orbits in the period-eight sequence at μ = 3.55, and three new orbits in the period-six sequence at μ = 3.846, respectively. Moreover, the dynamical behaviors of the new orbits clearly show the resonancelike response to the colored noise. (general)

A symplectic integration method for elastic filaments

Science.gov (United States)

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.

Stochastic sensitivity analysis of periodic attractors in non-autonomous nonlinear dynamical systems based on stroboscopic map

Energy Technology Data Exchange (ETDEWEB)

Guo, Kong-Ming, E-mail: kmguo@xidian.edu.cn [School of Electromechanical Engineering, Xidian University, P.O. Box 187, Xi' an 710071 (China); Jiang, Jun, E-mail: jun.jiang@mail.xjtu.edu.cn [State Key Laboratory for Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China)

2014-07-04

To apply stochastic sensitivity function method, which can estimate the probabilistic distribution of stochastic attractors, to non-autonomous dynamical systems, a 1/N-period stroboscopic map for a periodic motion is constructed in order to discretize the continuous cycle into a discrete one. In this way, the sensitivity analysis of a cycle for discrete map can be utilized and a numerical algorithm for the stochastic sensitivity analysis of periodic solutions of non-autonomous nonlinear dynamical systems under stochastic disturbances is devised. An external excited Duffing oscillator and a parametric excited laser system are studied as examples to show the validity of the proposed method. - Highlights: • A method to analyze sensitivity of stochastic periodic attractors in non-autonomous dynamical systems is proposed. • Probabilistic distribution around periodic attractors in an external excited Φ{sup 6} Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined.

Development of potential map for landslides by comparing instability indices of various time periods

Science.gov (United States)

Chiang, Jie-Lun; Tian, Yu-Qing; Chen, Yie-Ruey; Tsai, Kuang-Jung

2017-04-01

In recent years, extreme rainfall events occur frequently and induced serious landslides and debris flow disasters in Taiwan. The instability indices will differ when using landslide maps of different time periods. We analyzed the landslide records during the period year, 2008 2012, the landslide area contributed 0.42% 2.94% of the total watershed area, the 2.94% was caused by the typhoon Morakot in August, 2009, which brought massive rainfall in which the cumulative maximum rainfall was up to 2900 mm. We analyzed the instability factors including elevation, slope, aspect, soil, and geology. And comparing the instability indices by using individual landslide map of 2008 2012, the landslide maps of the union of the five years, and interaction of the five years. The landslide area from union of the five years contributed 3.71%,the landslide area from interaction of the five years contributed 0.14%. In this study, Kriging was used to establish the susceptibility map in selected watershed. From interaction of the five years, we found the instability index above 4.3 can correspond to those landslide records. The potential landslide area of the selected watershed, where collapses occur more likely, belongs to high level and medium-high level; the area is 13.43% and 3.04% respectively.

Umov-Mandelshtam radiation conditions in elastic periodic waveguides

Energy Technology Data Exchange (ETDEWEB)

Nazarov, S. A., E-mail: srgnazarov@yahoo.co.uk [St. Petersburg State University, Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg (Russian Federation)

2014-07-31

We study settings of the problem of elasticity theory on wave propagation in an elastic periodic waveguide with radiation conditions at infinity. We present a mathematical theory for energy radiation conditions based on Mandelshtam's energy principle and the Umov-Poynting vector, as well as using the technique of weighted spaces with detached asymptotics and the energy transfer symplectic form. We establish that in a threshold situation, that is, when standing and polynomial elastic Floquet waves appear, the well-known limiting absorption principle, in contrast to the energy principle that is being applied, cannot identify the direction of the wave's motion. Bibliography: 37 titles. (paper)

Accumulation of unstable periodic orbits and the stickiness in the two-dimensional piecewise linear map.

Science.gov (United States)

Akaishi, A; Shudo, A

2009-12-01

We investigate the stickiness of the two-dimensional piecewise linear map with a family of marginal unstable periodic orbits (FMUPOs), and show that a series of unstable periodic orbits accumulating to FMUPOs plays a significant role to give rise to the power law correlation of trajectories. We can explicitly specify the sticky zone in which unstable periodic orbits whose stability increases algebraically exist, and find that there exists a hierarchy in accumulating periodic orbits. In particular, the periodic orbits with linearly increasing stability play the role of fundamental cycles as in the hyperbolic systems, which allows us to apply the method of cycle expansion. We also study the recurrence time distribution, especially discussing the position and size of the recurrence region. Following the definition adopted in one-dimensional maps, we show that the recurrence time distribution has an exponential part in the short time regime and an asymptotic power law part. The analysis on the crossover time T(c)(*) between these two regimes implies T(c)(*) approximately -log[micro(R)] where micro(R) denotes the area of the recurrence region.

Highly accurate symplectic element based on two variational principles

Science.gov (United States)

Qing, Guanghui; Tian, Jia

2018-02-01

For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element (NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses.

Studies of phase return map and symbolic dynamics in a periodically driven Hodgkin—Huxley neuron

International Nuclear Information System (INIS)

Ding Jiong; Zhang Hong; Tong Qin-Ye; Chen Zhuo

2014-01-01

How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin—Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional (1D) map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm — symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented. (general)

Theoretical model simulations for the global Thermospheric Mapping Study (TMS) periods

Science.gov (United States)

Rees, D.; Fuller-Rowell, T. J.

Theoretical and semiempirical models of the solar UV/EUV and of the geomagnetic driving forces affecting the terrestrial mesosphere and thermosphere have been used to generate a series of representative numerical time-dependent and global models of the thermosphere, for the range of solar and geoamgnetic activity levels which occurred during the three Thermospheric Mapping Study periods. The simulations obtained from these numerical models are compared with observations, and with the results of semiempirical models of the thermosphere. The theoretical models provide a record of the magnitude of the major driving forces which affected the thermosphere during the study periods, and a baseline against which the actual observed structure and dynamics can be compared.

Physical mapping of the Period gene on meiotic chromosomes of South American grasshoppers (Acridomorpha, Orthoptera).

Science.gov (United States)

Souza, T E; Oliveira, D L; Santos, J F; Rieger, T T

2014-12-19

The single-copy gene Period was located in five grasshopper species belonging to the Acridomorpha group through permanent in situ hybridization (PISH). The mapping revealed one copy of this gene in the L1 chromosome pair in Ommexecha virens, Xyleus discoideus angulatus, Tropidacris collaris, Schistocerca pallens, and Stiphra robusta. A possible second copy was mapped on the L2 chromosome pair in S. robusta, which should be confirmed by further studies. Except for the latter case, the chromosomal position of the Period gene was highly conserved among the four families studied. The S. robusta karyotype also differs from the others both in chromosome number and morphology. The position conservation of the single-copy gene Period contrasts with the location diversification of multigene families in these species. The localization of single-copy genes by PISH can provide new insights about the genomic content and chromosomal evolution of grasshoppers and others insects.

The symplectic fermion ribbon quasi-Hopf algebra and the SL(2,Z)-action on its centre

Energy Technology Data Exchange (ETDEWEB)

Farsad, Vanda

2017-06-14

This thesis is concerned with ''N pairs of symplectic fermions'' which are examples of logarithmic conformal field theories in two dimensions. The mathematical language of two-dimensional conformal field theories (on Riemannian surfaces of genus zero) are vertex operator algebras. The representation category of the even part of the symplectic fermion vertex operator super-algebra Rep V{sub ev} is conjecturally a factorisable finite ribbon tensor category. This determines an isomorphism of projective representations between two SL(2,Z)-actions associated to V{sub ev}. The first action is obtained by modular transformations on the space of so-called pseudo-trace functions of a vertex operator algebra. For V{sub ev} this was developed by A.M.Gaberdiel and I. Runkel. For the action one uses that Rep V{sub ev} is conjecturally a factorisable finite ribbon tensor category and thus carries a projective SL(2,Z)-action on a certain Hom-space [Ly1,Ly2,KL]. To do so we calculate the SL(2,Z)-action on the representation category of a general factorisable quasi-Hopf algebras. Then we show that Rep V{sub ev} is conjecturally ribbon equivalent to Rep Q, for Q a factorisable quasi-Hopf algebra, and calculate the SL(2,Z)-action explicitly on Rep Q. The result is that the two SL(2,Z)-action indeed agree. This poses the first example of such comparison for logarithmic conformal field theories.

The role of extreme orbits in the global organization of periodic regions in parameter space for one dimensional maps

Science.gov (United States)

da Costa, Diogo Ricardo; Hansen, Matheus; Guarise, Gustavo; Medrano-T, Rene O.; Leonel, Edson D.

2016-04-01

We show that extreme orbits, trajectories that connect local maximum and minimum values of one dimensional maps, play a major role in the parameter space of dissipative systems dictating the organization for the windows of periodicity, hence producing sets of shrimp-like structures. Here we solve three fundamental problems regarding the distribution of these sets and give: (i) their precise localization in the parameter space, even for sets of very high periods; (ii) their local and global distributions along cascades; and (iii) the association of these cascades to complicate sets of periodicity. The extreme orbits are proved to be a powerful indicator to investigate the organization of windows of periodicity in parameter planes. As applications of the theory, we obtain some results for the circle map and perturbed logistic map. The formalism presented here can be extended to many other different nonlinear and dissipative systems.

Submaximal Riemann-Roch expected curves and symplectic packing.

Directory of Open Access Journals (Sweden)

Wioletta Syzdek

2007-06-01

Full Text Available We study Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ in the context of the Nagata-Biran conjecture. This conjecture predicts that for sufficiently large number of points multiple points Seshadri constants of an ample line bundle on algebraic surface are maximal. Biran gives an effective lower bound $N_0$. We construct examples verifying to the effect that the assertions of the Nagata-Biran conjecture can not hold for small number of points. We discuss cases where our construction fails. We observe also that there exists a strong relation between Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ and the symplectic packing problem. Biran relates the packing problem to the existence of solutions of certain Diophantine equations. We construct such solutions for any ample line bundle on $mathbb{P}^1 imes mathbb{P}^1$ and a relatively smallnumber of points. The solutions geometrically correspond to Riemann-Roch expected curves. Finally we discuss in how far the Biran number $N_0$ is optimal in the case of mathbb{P}^1 imes mathbb{P}^1. In fact we conjecture that it can be replaced by a lower number and we provide evidence justifying this conjecture.

Fusion Approaches for Land Cover Map Production Using High Resolution Image Time Series without Reference Data of the Corresponding Period

Directory of Open Access Journals (Sweden)

Benjamin Tardy

2017-11-01

Full Text Available Optical sensor time series images allow one to produce land cover maps at a large scale. The supervised classification algorithms have been shown to be the best to produce maps automatically with good accuracy. The main drawback of these methods is the need for reference data, the collection of which can introduce important production delays. Therefore, the maps are often available too late for some applications. Domain adaptation methods seem to be efficient for using past data for land cover map production. According to this idea, the main goal of this study is to propose several simple past data fusion schemes to override the current land cover map production delays. A single classifier approach and three voting rules are considered to produce maps without reference data of the corresponding period. These four approaches reach an overall accuracy of around 80% with a 17-class nomenclature using Formosat-2 image time series. A study of the impact of the number of past periods used is also done. It shows that the overall accuracy increases with the number of periods used. The proposed methods require at least two or three previous years to be used.

Stability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map

Energy Technology Data Exchange (ETDEWEB)

Mejri, Youssef, E-mail: josef-bizert@hotmail.fr [Aix Marseille Universite, Toulon Universite, CNRS, CPT, Marseille (France); Dép. des Mathématiques, Faculté des Sciences de Bizerte, 7021 Jarzouna (Tunisia); Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT BP 37, Le Belvedere, 1002 Tunis (Tunisia)

2016-06-15

In this article, we study the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic Schrödinger equation in a periodic quantum cylindrical waveguide, by knowledge of the Dirichlet-to-Neumann map. We prove a Hölder stability estimate with respect to the Dirichlet-to-Neumann map, by means of the geometrical optics solutions of the magnetic Schrödinger equation.

The Differential-Algebraic Analysis of Symplectic and Lax Structures Related with New Riemann-Type Hydrodynamic Systems

Science.gov (United States)

Prykarpatsky, Yarema A.; Artemovych, Orest D.; Pavlov, Maxim V.; Prykarpatski, Anatolij K.

2013-06-01

A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic hierarchy, proposed recently by O. D. Artemovych, M. V. Pavlov, Z. Popowicz and A. K. Prykarpatski, is developed. In addition to the Lax-type representation, found before by Z. Popowicz, a closely related representation is constructed in exact form by means of a new differential-functional technique. The bi-Hamiltonian integrability and compatible Poisson structures of the generalized Riemann type hierarchy are analyzed by means of the symplectic and gradient-holonomic methods. An application of the devised differential-algebraic approach to other Riemann and Vakhnenko type hydrodynamic systems is presented.

Symplectic finite element scheme: application to a driven problem with a regular singularity

Energy Technology Data Exchange (ETDEWEB)

Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)

1996-02-01

A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear `tent` elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs.

Symplectic finite element scheme: application to a driven problem with a regular singularity

International Nuclear Information System (INIS)

Pletzer, A.

1996-02-01

A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear 'tent' elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs

Invariant metric for nonlinear symplectic maps

Indian Academy of Sciences (India)

One popular method of treating Hamiltonian systems perturbatively is the Lie ... to be a symmetric, positive definite, bilinear form that is invariant under the action of ... we apply the above procedure to a FODO lattice (a common component of a.

Interactive remote data processing using Pixelize Wavelet Filtration (PWF-method) and PeriodMap analysis

Science.gov (United States)

Sych, Robert; Nakariakov, Valery; Anfinogentov, Sergey

Wavelet analysis is suitable for investigating waves and oscillating in solar atmosphere, which are limited in both time and frequency. We have developed an algorithms to detect this waves by use the Pixelize Wavelet Filtration (PWF-method). This method allows to obtain information about the presence of propagating and non-propagating waves in the data observation (cube images), and localize them precisely in time as well in space. We tested the algorithm and found that the results of coronal waves detection are consistent with those obtained by visual inspection. For fast exploration of the data cube, in addition, we applied early-developed Period- Map analysis. This method based on the Fast Fourier Transform and allows on initial stage quickly to look for "hot" regions with the peak harmonic oscillations and determine spatial distribution at the significant harmonics. We propose the detection procedure of coronal waves separate on two parts: at the first part, we apply the PeriodMap analysis (fast preparation) and than, at the second part, use information about spatial distribution of oscillation sources to apply the PWF-method (slow preparation). There are two possible algorithms working with the data: in automatic and hands-on operation mode. Firstly we use multiply PWF analysis as a preparation narrowband maps at frequency subbands multiply two and/or harmonic PWF analysis for separate harmonics in a spectrum. Secondly we manually select necessary spectral subband and temporal interval and than construct narrowband maps. For practical implementation of the proposed methods, we have developed the remote data processing system at Institute of Solar-Terrestrial Physics, Irkutsk. The system based on the data processing server - http://pwf.iszf.irk.ru. The main aim of this resource is calculation in remote access through the local and/or global network (Internet) narrowband maps of wave's sources both in whole spectral band and at significant harmonics. In addition

Noise destroys the coexistence of periodic orbits of a piecewise linear map

International Nuclear Information System (INIS)

Wang Can-Jun; Yang Ke-Li; Qu Shi-Xian

2013-01-01

The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5 (P-5) and period-6 (P-6) in their coexisting domain of a piecewise linear map are investigated numerically. The probability densities of some orbits are calculated. When the noise intensity is D = 0.0001, only the orbits of P-5 exist, and the coexisting phenomenon is destroyed. On the other hand, the self-correlation time τ of the colored noise also affects the coexisting phenomenon. When τ c c , only the orbits of P-5 appear, and the stability of the orbits of P-5 is enhanced. However, when τ > τ' c (τ c and τ c ' are critical values), only the orbits of P-6 exist, and the stability of the P-6 orbits is enhanced greatly. When τ c , the orbits of P-5 and P-6 coexist, but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing

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

Energy Technology Data Exchange (ETDEWEB)

Luo, Yun [Brookhaven National Laboratory (BNL), Upton, NY (United States)

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, physics models, and some selected examples of its applications to RHIC and a future electron-ion collider design eRHIC.

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

Energy Technology Data Exchange (ETDEWEB)

Luo, Yun

2015-11-21

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 paper, I will present the code architecture, physics models, and some selected examples of its applications to RHIC and a future electron-ion collider design eRHIC.

Fast periodic stimulation (FPS): a highly effective approach in fMRI brain mapping.

Science.gov (United States)

Gao, Xiaoqing; Gentile, Francesco; Rossion, Bruno

2018-03-03

Defining the neural basis of perceptual categorization in a rapidly changing natural environment with low-temporal resolution methods such as functional magnetic resonance imaging (fMRI) is challenging. Here, we present a novel fast periodic stimulation (FPS)-fMRI approach to define face-selective brain regions with natural images. Human observers are presented with a dynamic stream of widely variable natural object images alternating at a fast rate (6 images/s). Every 9 s, a short burst of variable face images contrasting with object images in pairs induces an objective face-selective neural response at 0.111 Hz. A model-free Fourier analysis achieves a twofold increase in signal-to-noise ratio compared to a conventional block-design approach with identical stimuli and scanning duration, allowing to derive a comprehensive map of face-selective areas in the ventral occipito-temporal cortex, including the anterior temporal lobe (ATL), in all individual brains. Critically, periodicity of the desired category contrast and random variability among widely diverse images effectively eliminates the contribution of low-level visual cues, and lead to the highest values (80-90%) of test-retest reliability in the spatial activation map yet reported in imaging higher level visual functions. FPS-fMRI opens a new avenue for understanding brain function with low-temporal resolution methods.

Quasi-periodic motions in families of dynamical systems order amidst chaos

CERN Document Server

Broer, Hendrik W; Sevryuk, Mikhail B

1996-01-01

This book is on Kolmogorov-Arnol'd-Moser theory for quasi-periodic tori in dynamical systems. It gives an up-to-date report on the role parameters play for persis- tence of such tori, typically occuring on Cantor sets of positive Hausdorff measure inside phase and parameter space. The cases with preservation of symplectic or volume forms or time-reversal symmetries are included. The concepts of Whitney-smoothness and Diophantine approximation of Cantor sets on submanifolds of Euclidean space are treated, as well as Bruno's theory on analytic continuation of tori. Partly this material is new to Western mathematicians. The reader should be familiar with dynamical systems theory, differen- tial equations and some analysis. The book is directed to researchers, but its entrance level is introductory.

Geometry of the local equivalence of states

Energy Technology Data Exchange (ETDEWEB)

Sawicki, A; Kus, M, E-mail: assawi@cft.edu.pl, E-mail: marek.kus@cft.edu.pl [Center for Theoretical Physics, Polish Academy of Sciences, Al Lotnikow 32/46, 02-668 Warszawa (Poland)

2011-12-09

We present a description of locally equivalent states in terms of symplectic geometry. Using the moment map between local orbits in the space of states and coadjoint orbits of the local unitary group, we reduce the problem of local unitary equivalence to an easy part consisting of identifying the proper coadjoint orbit and a harder problem of the geometry of fibers of the moment map. We give a detailed analysis of the properties of orbits of 'equally entangled states'. In particular, we show connections between certain symplectic properties of orbits such as their isotropy and coisotropy with effective criteria of local unitary equivalence. (paper)

Bargmann Symmetry Constraint for a Family of Liouville Integrable Differential-Difference Equations

International Nuclear Information System (INIS)

Xu Xixiang

2012-01-01

A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system. (general)

On complex periodic motions and bifurcations in a periodically forced, damped, hardening Duffing oscillator

International Nuclear Information System (INIS)

Guo, Yu; Luo, Albert C.J.

2015-01-01

In this paper, analytically predicted are complex periodic motions in the periodically forced, damped, hardening Duffing oscillator through discrete implicit maps of the corresponding differential equations. Bifurcation trees of periodic motions to chaos in such a hardening Duffing oscillator are obtained. The stability and bifurcation analysis of periodic motion in the bifurcation trees is carried out by eigenvalue analysis. The solutions of all discrete nodes of periodic motions are computed by the mapping structures of discrete implicit mapping. The frequency-amplitude characteristics of periodic motions are computed that are based on the discrete Fourier series. Thus, the bifurcation trees of periodic motions are also presented through frequency-amplitude curves. Finally, based on the analytical predictions, the initial conditions of periodic motions are selected, and numerical simulations of periodic motions are carried out for comparison of numerical and analytical predictions. The harmonic amplitude spectrums are also given for the approximate analytical expressions of periodic motions, which can also be used for comparison with experimental measurement. This study will give a better understanding of complex periodic motions in the hardening Duffing oscillator.

A projection-based model reduction strategy for the wave and vibration analysis of rotating periodic structures

Science.gov (United States)

Beli, D.; Mencik, J.-M.; Silva, P. B.; Arruda, J. R. F.

2018-05-01

The wave finite element method has proved to be an efficient and accurate numerical tool to perform the free and forced vibration analysis of linear reciprocal periodic structures, i.e. those conforming to symmetrical wave fields. In this paper, its use is extended to the analysis of rotating periodic structures, which, due to the gyroscopic effect, exhibit asymmetric wave propagation. A projection-based strategy which uses reduced symplectic wave basis is employed, which provides a well-conditioned eigenproblem for computing waves in rotating periodic structures. The proposed formulation is applied to the free and forced response analysis of homogeneous, multi-layered and phononic ring structures. In all test cases, the following features are highlighted: well-conditioned dispersion diagrams, good accuracy, and low computational time. The proposed strategy is particularly convenient in the simulation of rotating structures when parametric analysis for several rotational speeds is usually required, e.g. for calculating Campbell diagrams. This provides an efficient and flexible framework for the analysis of rotordynamic problems.

Complex motion of elevators in piecewise map model combined with circle map

Science.gov (United States)

Nagatani, Takashi

2013-11-01

We study the dynamic behavior in the elevator traffic controlled by capacity when the inflow rate of passengers into elevators varies periodically with time. The dynamics of elevators is described by the piecewise map model combined with the circle map. The motion of the elevators depends on the inflow rate, its period, and the number of elevators. The motion in the piecewise map model combined with the circle map shows a complex behavior different from the motion in the piecewise map model.

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

Science.gov (United States)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Topological Poisson Sigma models on Poisson-Lie groups

International Nuclear Information System (INIS)

Calvo, Ivan; Falceto, Fernando; Garcia-Alvarez, David

2003-01-01

We solve the topological Poisson Sigma model for a Poisson-Lie group G and its dual G*. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of both models in the open geometry reveals that there exists a map from the reduced phase of each model (P and P*) to the main symplectic leaf of the Heisenberg double (D 0 ) such that the symplectic forms on P, P* are obtained as the pull-back by those maps of the symplectic structure on D 0 . This uncovers a duality between P and P* under the exchange of bulk degrees of freedom of one model with boundary degrees of freedom of the other one. We finally solve the Poisson Sigma model for the Poisson structure on G given by a pair of r-matrices that generalizes the Poisson-Lie case. The Hamiltonian analysis of the theory requires the introduction of a deformation of the Heisenberg double. (author)

Hitchin's connection, Toeplitz operators, and symmetry invariant deformation quantization

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard

2012-01-01

We introduce the notion of a rigid family of Kähler structures on a symplectic manifold. We then prove that a Hitchin connection exists for any rigid holomorphic family of Kähler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints...... a mapping class group invariant formal quantization of the smooth symplectic leaves of the moduli space of flat SU(n)-connections on any compact surface....... quantization. Finally, these results are applied to the moduli space situation in which Hitchin originally constructed his connection. First we get a proof that the Hitchin connection in this case is the same as the connection constructed by Axelrod, Della Pietra, and Witten. Second we obtain in this way...

Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds

Energy Technology Data Exchange (ETDEWEB)

Heller, Marc Andre [Particle Theory and Cosmology Group, Department of Physics,Graduate School of Science, Tohoku University,Aoba-ku, Sendai 980-8578 (Japan); Ikeda, Noriaki [Department of Mathematical Sciences, Ritsumeikan University,Kusatsu, Shiga 525-8577 (Japan); Watamura, Satoshi [Particle Theory and Cosmology Group, Department of Physics,Graduate School of Science, Tohoku University,Aoba-ku, Sendai 980-8578 (Japan)

2017-02-15

We give a systematic derivation of the local expressions of the NS H-flux, geometric F- as well as non-geometric Q- and R-fluxes in terms of bivector β- and two-form B-potentials including vielbeins. They are obtained using a supergeometric method on QP-manifolds by twist of the standard Courant algebroid on the generalized tangent space without flux. Bianchi identities of the fluxes are easily deduced. We extend the discussion to the case of the double space and present a formulation of T-duality in terms of canonical transformations between graded symplectic manifolds. Thus, we find a unified description of geometric as well as non-geometric fluxes and T-duality transformations in double field theory. Finally, the construction is compared to the formerly introduced Poisson Courant algebroid, a Courant algebroid on a Poisson manifold, as a model for R-flux.

Hill's formula

Energy Technology Data Exchange (ETDEWEB)

Bolotin, Sergey V [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation); Treschev, Dmitrii V [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

2010-07-27

In his study of periodic orbits of the three-body problem, Hill obtained a formula connecting the characteristic polynomial of the monodromy matrix of a periodic orbit with the infinite determinant of the Hessian of the action functional. A mathematically rigorous definition of the Hill determinant and a proof of Hill's formula were obtained later by Poincare. Here two multidimensional generalizations of Hill's formula are given: for discrete Lagrangian systems (symplectic twist maps) and for continuous Lagrangian systems. Additional aspects appearing in the presence of symmetries or reversibility are discussed. Also studied is the change of the Morse index of a periodic trajectory upon reduction of order in a system with symmetries. Applications are given to the problem of stability of periodic orbits. Bibliography: 34 titles.

On palaeogeographic map

Directory of Open Access Journals (Sweden)

Zeng-Zhao Feng

2016-01-01

Full Text Available The palaeogeographic map is a graphic representation of physical geographical characteristics in geological history periods and human history periods. It is the most important result of palaeogeographic study. The author, as the Editor-in-Chief of Journal of Palaeogeography, Chinese Edition and English Edition, aimed at the problems of the articles submitted to and published in the Journal of Palaeogeography in recent years and the relevant papers and books of others, and integrated with his practice of palaeogeographic study and mapping, wrote this paper. The content mainly includes the data of palaeogeographic mapping, the problems of palaeogeographic mapping method, the “Single factor analysis and multifactor comprehensive mapping method —— Methodology of quantitative lithofacies palaeogeography”, i.e., the “4 steps mapping method”, the nomenclature of each palaeogeographic unit in palaeogeographic map, the explanation of each palaeogeographic unit in palaeogeographic map, the explanation of significance of palaeogeographic map and palaeogeographic article, the evaluative standards of palaeogeographic map and palaeogeographic article, and the self-evaluation. Criticisms and corrections are welcome.

Importance sampling with imperfect cloning for the computation of generalized Lyapunov exponents

Science.gov (United States)

Anteneodo, Celia; Camargo, Sabrina; Vallejos, Raúl O.

2017-12-01

We revisit the numerical calculation of generalized Lyapunov exponents, L (q ) , in deterministic dynamical systems. The standard method consists of adding noise to the dynamics in order to use importance sampling algorithms. Then L (q ) is obtained by taking the limit noise-amplitude → 0 after the calculation. We focus on a particular method that involves periodic cloning and pruning of a set of trajectories. However, instead of considering a noisy dynamics, we implement an imperfect (noisy) cloning. This alternative method is compared with the standard one and, when possible, with analytical results. As a workbench we use the asymmetric tent map, the standard map, and a system of coupled symplectic maps. The general conclusion of this study is that the imperfect-cloning method performs as well as the standard one, with the advantage of preserving the deterministic dynamics.

Journal of Astrophysics and Astronomy | Indian Academy of Sciences

Indian Academy of Sciences (India)

2016-01-27

Jan 27, 2016 ... Comparing Maps to Symplectic Integrators in a Galactic Type Hamiltonian ... a two dimensional, resonant, galactic type Hamiltonian using conventional numerical integration, ... Journal of Astrophysics and Astronomy | News ...

LIDAR AND INS FUSION IN PERIODS OF GPS OUTAGES FOR MOBILE LASER SCANNING MAPPING SYSTEMS

Directory of Open Access Journals (Sweden)

I. Klein

2012-09-01

Full Text Available Mobile laser scanning systems are becoming an increasingly popular means to obtain 3D coverage on a large scale. To perform the mapping, the exact position of the vehicle must be known throughout the trajectory. Exact position is achieved via integration of Global Positioning Systems (GPS and Inertial Navigation Systems (INS. Yet, in urban environments, cases of complete or even partial GPS outages may occur leaving the navigation solution to rely only on the INS. The INS navigation solution degrades with time as the Inertial Measurement Unit (IMU measurements contains noise, which permeates into the navigation equations. Degradation of the position determination leads to loss of data in such segments. To circumvent such drift and its effects, we propose fusing INS with lidar data by using building edges. This detection of edges is then translated into position data, which is used as an aiding to the INS. It thereby enables the determination of the vehicle position with a satisfactory level accuracy, sufficient to perform the laser-scanning based mapping in those outage periods.

Algebraic methods in random matrices and enumerative geometry

CERN Document Server

Eynard, Bertrand

2008-01-01

We review the method of symplectic invariants recently introduced to solve matrix models loop equations, and further extended beyond the context of matrix models. For any given spectral curve, one defined a sequence of differential forms, and a sequence of complex numbers Fg . We recall the definition of the invariants Fg, and we explain their main properties, in particular symplectic invariance, integrability, modularity,... Then, we give several example of applications, in particular matrix models, enumeration of discrete surfaces (maps), algebraic geometry and topological strings, non-intersecting brownian motions,...

Chaos to periodicity and periodicity to chaos by periodic perturbations in the Belousov-Zhabotinsky reaction

International Nuclear Information System (INIS)

Li Qianshu; Zhu Rui

2004-01-01

A three-variable model of the Belousov-Zhabotinsky reaction system subject to external sinusoidal perturbations is investigated by means of frequency spectrum analysis. In the period-1 window of the model, the transitions from periodicity to chaos are observed; in the chaotic window, the transitions from chaos to periodicity are found. The former might be understood by the circle map of two coupled oscillators, and the latter is partly explained by the resonance between the main frequency of the chaos and the frequency of the external periodic perturbations

Numerical methods for finding periodic points in discrete maps. High order islands chains and noble barriers in a toroidal magnetic configuration

Energy Technology Data Exchange (ETDEWEB)

Steinbrecher, G. [Association Euratom-Nasti Romania, Dept. of Theoretical Physics, Physics Faculty, University of Craiova (Romania); Reuss, J.D.; Misguich, J.H. [Association Euratom-CEA Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee

2001-11-01

We first remind usual physical and mathematical concepts involved in the dynamics of Hamiltonian systems, and namely in chaotic systems described by discrete 2D maps (representing the intersection points of toroidal magnetic lines in a poloidal plane in situations of incomplete magnetic chaos in Tokamaks). Finding the periodic points characterizing chains of magnetic islands is an essential step not only to determine the skeleton of the phase space picture, but also to determine the flux of magnetic lines across semi-permeable barriers like Cantori. We discuss here several computational methods used to determine periodic points in N dimensions, which amounts to solve a set of N nonlinear coupled equations: Newton method, minimization techniques, Laplace or steepest descend method, conjugated direction method and Fletcher-Reeves method. We have succeeded to improve this last method in an important way, without modifying its useful double-exponential convergence. This improved method has been tested and applied to finding periodic points of high order m in the 2D 'Tokamap' mapping, for values of m along rational chains of winding number n/m converging towards a noble value where a Cantorus exists. Such precise positions of periodic points have been used in the calculation of the flux across this Cantorus. (authors)

Genome-Wide Association Mapping of Flowering and Ripening Periods in Apple

Directory of Open Access Journals (Sweden)

Jorge Urrestarazu

2017-11-01

Full Text Available Deciphering the genetic control of flowering and ripening periods in apple is essential for breeding cultivars adapted to their growing environments. We implemented a large Genome-Wide Association Study (GWAS at the European level using an association panel of 1,168 different apple genotypes distributed over six locations and phenotyped for these phenological traits. The panel was genotyped at a high-density of SNPs using the Axiom®Apple 480 K SNP array. We ran GWAS with a multi-locus mixed model (MLMM, which handles the putatively confounding effect of significant SNPs elsewhere on the genome. Genomic regions were further investigated to reveal candidate genes responsible for the phenotypic variation. At the whole population level, GWAS retained two SNPs as cofactors on chromosome 9 for flowering period, and six for ripening period (four on chromosome 3, one on chromosome 10 and one on chromosome 16 which, together accounted for 8.9 and 17.2% of the phenotypic variance, respectively. For both traits, SNPs in weak linkage disequilibrium were detected nearby, thus suggesting the existence of allelic heterogeneity. The geographic origins and relationships of apple cultivars accounted for large parts of the phenotypic variation. Variation in genotypic frequency of the SNPs associated with the two traits was connected to the geographic origin of the genotypes (grouped as North+East, West and South Europe, and indicated differential selection in different growing environments. Genes encoding transcription factors containing either NAC or MADS domains were identified as major candidates within the small confidence intervals computed for the associated genomic regions. A strong microsynteny between apple and peach was revealed in all the four confidence interval regions. This study shows how association genetics can unravel the genetic control of important horticultural traits in apple, as well as reduce the confidence intervals of the associated

Rigorous bounds on survival times in circular accelerators and efficient computation of fringe-field transfer maps

International Nuclear Information System (INIS)

Hoffstaetter, G.H.

1994-12-01

Analyzing stability of particle motion in storage rings contributes to the general field of stability analysis in weakly nonlinear motion. A method which we call pseudo invariant estimation (PIE) is used to compute lower bounds on the survival time in circular accelerators. The pseudeo invariants needed for this approach are computed via nonlinear perturbative normal form theory and the required global maxima of the highly complicated multivariate functions could only be rigorously bound with an extension of interval arithmetic. The bounds on the survival times are large enough to the relevant; the same is true for the lower bounds on dynamical aperatures, which can be computed. The PIE method can lead to novel design criteria with the objective of maximizing the survival time. A major effort in the direction of rigourous predictions only makes sense if accurate models of accelerators are available. Fringe fields often have a significant influence on optical properties, but the computation of fringe-field maps by DA based integration is slower by several orders of magnitude than DA evaluation of the propagator for main-field maps. A novel computation of fringe-field effects called symplectic scaling (SYSCA) is introduced. It exploits the advantages of Lie transformations, generating functions, and scaling properties and is extremely accurate. The computation of fringe-field maps is typically made nearly two orders of magnitude faster. (orig.)

The differential-geometric aspects of integrable dynamical systems

International Nuclear Information System (INIS)

Prykarpatsky, Y.A.; Samoilenko, A.M.; Prykarpatsky, A.K.; Bogolubov, N.N. Jr.; Blackmore, D.L.

2007-05-01

The canonical reduction method on canonically symplectic manifolds is analyzed in detail, and the relationships with the geometric properties of associated principal fiber bundles endowed with connection structures are described. Some results devoted to studying geometrical properties of nonabelian Yang-Mills type gauge field equations are presented. A symplectic theory approach is developed for partially solving the problem of algebraic-analytical construction of integral submanifold embeddings for integrable (via the abelian and nonabelian Liouville-Arnold theorems) Hamiltonian systems on canonically symplectic phase spaces. The fundamental role of the so-called Picard-Fuchs type equations is revealed, and their differential-geometric and algebraic properties are studied in detail. Some interesting examples of integrable Hamiltonian systems are are studied in detail in order to demonstrate the ease of implementation and effectiveness of the procedure for investigating the integral submanifold embedding mapping. (author)

(Non)local Hamiltonian and symplectic structures, recursions and hierarchies: a new approach and applications to the N = 1 supersymmetric KdV equation

International Nuclear Information System (INIS)

Kersten, P; Krasil'shchik, I; Verbovetsky, A

2004-01-01

Using methods of Kersten et al (2004 J. Geom. Phys. 50 273-302) and Krasil'shchik and Kersten (2000 Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations (Dordrecht: Kluwer)), we accomplish an extensive study of the N = 1 supersymmetric Korteweg-de Vries (KdV) equation. The results include a description of local and nonlocal Hamiltonian and symplectic structures, five hierarchies of symmetries, the corresponding hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. We stress that the main point of the paper is not just the results on super-KdV equation itself, but merely exposition of the efficiency of the geometrical approach and of the computational algorithms based on it

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

Science.gov (United States)

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".

Pre-holography

International Nuclear Information System (INIS)

Kay, Bernard S.; Larkin, Peter

2008-01-01

We construct a symplectic isomorphism h from classical Klein Gordon solutions of mass m on (d+1)-dimensional Lorentzian anti-de Sitter space (equipped with the usual symplectic form) to a certain symplectic space of functions on its conformal boundary (only) for all integer and half-integer Δ (=(d/2)+(1/2)(d 2 +4m 2 ) 1/2 ). h induces a large family of new examples of Rehren's algebraic holography in which the net of local quantum Klein Gordon algebras in AdS is seen to map to a suitably defined net of local algebras for the (generalized free) scalar conformal field with anomalous dimension Δ on d-dimensional Minkowski space (the AdS boundary). Relatedly, we show for these models that Bertola et al.'s boundary-limit holography becomes a quantum duality (only) if the test functions for boundary Wightman distributions are restricted in a particular way

Group representations via geometric quantization of the momentum map

International Nuclear Information System (INIS)

Mladenov, I.M.; Tsanov, V.V.

1992-09-01

In this paper, we treat a general method of quantization of Hamiltonian systems whose flow is a subgroup (not necessarily closed) of a torus acting freely and symplectically on the phase space. The quantization of some classes of completely integrable systems as well as the Borel-Weil-Bott version of representation theory are special cases. (author). 14 refs

Integrable mappings via rational elliptic surfaces

International Nuclear Information System (INIS)

Tsuda, Teruhisa

2004-01-01

We present a geometric description of the QRT map (which is an integrable mapping introduced by Quispel, Roberts and Thompson) in terms of the addition formula of a rational elliptic surface. By this formulation, we classify all the cases when the QRT map is periodic; and show that its period is 2, 3, 4, 5 or 6. A generalization of the QRT map which acts birationally on a pencil of K3 surfaces, or Calabi-Yau manifolds, is also presented

12000 rotation periods of Kepler stars (Nielsen+, 2013)

DEFF Research Database (Denmark)

Nielsen, M. B.; Gizon, L.; Schunker, H.

2013-01-01

Rotation periods of 12253 stars in the Kepler field. The periods are determined by the brightness variations, from star spots or active regions, in the light curves of the white light photometry obtained by the Kepler spacecraft. The median absolute deviation from the median (MAD) of the periods...... shows the scatter of periods for each star, over 6 or more (out of 8 analyzed) Kepler quarters. The g-r color index, E(B-V), radius, surface gravity, and effective temperature are from the Kepler Input Catalog (KIC). Column 9 (TF) indicates whether or not the msMAP data for a given star satisfies...... the selection criteria described in section 2. Of these, there are 86 stars with periods from the msMAP data that differ from the period derived from the PDCMAP data by more than one frequency resolution element (1/90d-1). For these stars the msMAP periods are therefore given in column 10 as a none-zero value...

Quasi-period oscillations of relay feedback systems

International Nuclear Information System (INIS)

Wen Guilin; Wang Qingguo; Lee, T.H.

2007-01-01

This paper presents an analytical method for investigation of the existence and stability of quasi-period oscillations (torus solutions) for a class of relay feedback systems. The idea is to analyze Poincare map from one switching surface to the next based on the Hopf bifurcation theory of maps. It is shown that there exist quasi-period oscillations in certain relay feedback systems

Dynamics of unidirectionally coupled bistable Henon maps

International Nuclear Information System (INIS)

Sausedo-Solorio, J.M.; Pisarchik, A.N.

2011-01-01

We study dynamics of two bistable Henon maps coupled in a master-slave configuration. In the case of coexistence of two periodic orbits, the slave map evolves into the master map state after transients, which duration determines synchronization time and obeys a -1/2 power law with respect to the coupling strength. This scaling law is almost independent of the map parameter. In the case of coexistence of chaotic and periodic attractors, very complex dynamics is observed, including the emergence of new attractors as the coupling strength is increased. The attractor of the master map always exists in the slave map independently of the coupling strength. For a high coupling strength, complete synchronization can be achieved only for the attractor similar to that of the master map. -- Highlights: → We study dynamics of two bistable Henon maps coupled in a master-slave configuration. → Synchronization time for periodic orbits obeys a -1/2 power law with respect to coupling. → For a high coupling strength, the slave map remains bistable. → Complete synchronization can be achieved only when both maps stay at the same attractor.

Toward a periodic table of personality: Mapping personality scales between the five-factor model and the circumplex model.

Science.gov (United States)

Woods, Stephen A; Anderson, Neil R

2016-04-01

In this study, we examine the structures of 10 personality inventories (PIs) widely used for personnel assessment by mapping the scales of PIs to the lexical Big Five circumplex model resulting in a Periodic Table of Personality. Correlations between 273 scales from 10 internationally popular PIs with independent markers of the lexical Big Five are reported, based on data from samples in 2 countries (United Kingdom, N = 286; United States, N = 1,046), permitting us to map these scales onto the Abridged Big Five Dimensional Circumplex model (Hofstee, de Raad, & Goldberg, 1992). Emerging from our findings we propose a common facet framework derived from the scales of the PIs in our study. These results provide important insights into the literature on criterion-related validity of personality traits, and enable researchers and practitioners to understand how different PI scales converge and diverge and how compound PI scales may be constructed or replicated. Implications for research and practice are considered. (c) 2016 APA, all rights reserved).

Seismic activity maps for the Armenian Highlands

Energy Technology Data Exchange (ETDEWEB)

Karapetyan, N.K.; Manukyan, Zh.O.

1976-01-01

Seismic activity maps for the periods 1952 to 1967 and 1952 to 1968 were compiled for the Armenian Highlands in order to study the spatial distribution of earthquake recurrence and to construct maps in isolines of seismic activity. Diagrams are presented illustrating such seismic activity maps for the indicated periods. 4 references, 3 figures, 1 table.

On parabolic external maps

DEFF Research Database (Denmark)

Lomonaco, Luna; Petersen, Carsten Lunde; Shen, Weixiao

2017-01-01

We prove that any C1+BV degree d ≥ 2 circle covering h having all periodic orbits weakly expanding, is conjugate by a C1+BV diffeomorphism to a metrically expanding map. We use this to connect the space of parabolic external maps (coming from the theory of parabolic-like maps) to metrically expan...

Properties making a chaotic system a good Pseudo Random Number Generator

OpenAIRE

Falcioni, Massimo; Palatella, Luigi; Pigolotti, Simone; Vulpiani, Angelo

2005-01-01

We discuss two properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy and high-dimensionality. We propose the multi dimensional Anosov symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic features of this map are useful for generating Pseudo Random Numbers and investigate numerically which of them survive in the discrete version of the map. Testing and comparisons with other generat...

The structure of mode-locking regions of piecewise-linear continuous maps: II. Skew sawtooth maps

Science.gov (United States)

Simpson, D. J. W.

2018-05-01

In two-parameter bifurcation diagrams of piecewise-linear continuous maps on , mode-locking regions typically have points of zero width known as shrinking points. Near any shrinking point, but outside the associated mode-locking region, a significant proportion of parameter space can be usefully partitioned into a two-dimensional array of annular sectors. The purpose of this paper is to show that in these sectors the dynamics is well-approximated by a three-parameter family of skew sawtooth circle maps, where the relationship between the skew sawtooth maps and the N-dimensional map is fixed within each sector. The skew sawtooth maps are continuous, degree-one, and piecewise-linear, with two different slopes. They approximate the stable dynamics of the N-dimensional map with an error that goes to zero with the distance from the shrinking point. The results explain the complicated radial pattern of periodic, quasi-periodic, and chaotic dynamics that occurs near shrinking points.

Spatiotemporal chaos in coupled logistic maps

International Nuclear Information System (INIS)

Varella Guedes, Andre; Amorim Savi, Marcelo

2010-01-01

The objective of this work is to investigate the spatiotemporal dynamics of coupled logistic maps. These maps are prototypes of high-dimensional dynamical systems and have been used to describe the evolution and pattern formation in different systems. Here, the logistic map lattice is coupled by a power law and, therefore, each map is influenced by other maps in its neighborhood. The Kolmogorov-Sinai entropy density is employed to quantify the complexity of system behavior, permitting a general qualitative understanding of different aspects of system dynamics. Three kinds of boundary conditions are treated and the influence of initial conditions is also of concern. Non-homogeneous maps are investigated, showing interesting aspects of spatiotemporal dynamics. The idea is to analyze the spatial interaction between two qualitative different types of behavior from a grid that is split into two parts. Numerical simulations show what types of conditions present a greater tendency to develop chaotic, periodic and synchronized responses. It should be highlighted that non-homogeneous grids have situations where a chaotic pattern can emerge from two periodic responses and also situations where a periodic pattern can emerge from chaos.

Measuring transient chaos in nonlinear one- and two-dimensional maps

International Nuclear Information System (INIS)

Buszko, Katarzyna; Stefanski, Krzysztof

2006-01-01

In this paper, we present results of numerical experiments on chaotic transients in families of the logistic and Henon maps. The duration of chaotic transients (the rambling time) for logistic maps estimated according to a rigorous criterion shows monotonic regularities with respect to both the period and the number of periodic window in a series of a given period. Due to inapplicability of this criterion to multidimensional maps, a more universal, though approximate, criterion is systematically studied on the family of logistic maps to optimize a choice of the free parameter value. The same approximate criterion is used to estimate rambling time for a number of periodic windows for the family of Henon maps. The dependence of the rambling time on the width of periodic windows is tested

The canonical Lagrangian approach to three-space general relativity

Science.gov (United States)

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.

The Europa Global Geologic Map

Science.gov (United States)

Leonard, E. J.; Patthoff, D. A.; Senske, D. A.; Collins, G. C.

2018-06-01

The Europa Global Geologic Map reveals three periods in Europa's surface history as well as an interesting distribution of microchaos. We will discuss the mapping and the interesting implications of our analysis of Europa's surface.

Application of the Frequency Map Analysis to the Study of the Beam Dynamics of Light Sources

International Nuclear Information System (INIS)

Nadolski, Laurent

2001-01-01

The topic of this thesis is the study of beam dynamics in storage rings with a restriction to single particle transverse dynamics. In a first part, tools (Frequency Map Analysis, Hamiltonian, Integrator) are presented for studying and exploring the dynamics. Numerical simulations of four synchrotron radiation sources (the ALS, the ESRF, SOLEIL and Super-ACO) are performed. We construct a tracking code based on a new class of symplectic integrators (Laskar and Robutel, 2000). These integrators with only positive steps are more precise by an order of magnitude than the standard Forest and Ruth's scheme. Comparisons with the BETA, DESPOT and MAD codes are carried out. Frequency Map Analysis (Laskar, 1990) is our main analysis tool. This is a numerical method for analysing a conservative dynamical system. Based on a refined Fourier technique, it enables us to compute frequency maps which are real footprints of the beam dynamics of an accelerator. We stress the high sensitivity of the dynamics to magnetics errors and sextipolar strengths. The second part of this work is dedicated to the analysis of experimental results from two light sources. Together with the ALS accelerator team (Berkeley), we succeeded in obtaining the first experimental frequency map of an accelerator. The agreement with the machine model is very impressive. At the Super-ACO ring, the study of the tune shift with amplitude enabled us to highlight a strong octupolar-like component related to the quadrupole fringe field. The aftermaths for the beam dynamics are important and give us a better understanding the measured ring performance. All these results are based on turn by turn measurements. Many closely related phenomena are treated such as response matrix analysis or beam decoherence. (author) [fr

Wiggling throat of extremal black holes

International Nuclear Information System (INIS)

Compère, G.; Hajian, K.; Seraj, A.; Sheikh-Jabbari, M.M.

2015-01-01

We construct the classical phase space of geometries in the near-horizon region of vacuum extremal black holes as announced in [arXiv:1503.07861]. Motivated by the uniqueness theorems for such solutions and for perturbations around them, we build a family of metrics depending upon a single periodic function defined on the torus spanned by the U(1) isometry directions. We show that this set of metrics is equipped with a consistent symplectic structure and hence defines a phase space. The phase space forms a representation of an infinite dimensional algebra of so-called symplectic symmetries. The symmetry algebra is an extension of the Virasoro algebra whose central extension is the black hole entropy. We motivate the choice of diffeomorphisms leading to the phase space and explicitly derive the symplectic structure, the algebra of symplectic symmetries and the corresponding conserved charges. We also discuss a formulation of these charges with a Liouville type stress-tensor on the torus defined by the U(1) isometries and outline possible future directions.

MAPS OF ROMAN DACIA. I. THE MAP OF PETRUS KAERIUS (1571-1646

Directory of Open Access Journals (Sweden)

Florin Fodorean

2014-04-01

Full Text Available In the following, we would like to present and describe a very interesting map, engraved in the XVIIth or at the end of the XVIth century by a famous Dutch cartographer, engraver, and publisher: Pieter van der Keere (Petrus Kaerius. Born in Ghent in 1571, Van der Keere (1571-1646 developed his business in Amsterdam at the end of the XVIth century. The map described in our article is entitled Vetus Descriptio Daciarum nec non Moesiarum. The document is important for the history of cartography because it enable us to identify and comment upon the level of knowledge of Van der Keere about a region not so familiar to him. In fact, the map reflects a medieval version of the map of Ptolemy. This period is connected to the rediscovery of Ptolemy. Besides data from the famous work of the geographer born in Alexandria, Van der Keere included some interesting notations and details which reflect the middle Ages conceptions or geographical features invented in this period.

Detecting unstable periodic orbits of nonlinear mappings by a novel quantum-behaved particle swarm optimization non-Lyapunov way

International Nuclear Information System (INIS)

Gao Fei; Gao Hongrui; Li Zhuoqiu; Tong Hengqing; Lee, Ju-Jang

2009-01-01

It is well known that set of unstable periodic orbits (UPOs) can be thought of as the skeleton for the dynamics. However, detecting UPOs of nonlinear map is one of the most challenging problems of nonlinear science in both numerical computations and experimental measures. In this paper, a new method is proposed to detect the UPOs in a non-Lyapunov way. Firstly three special techniques are added to quantum-behaved particle swarm optimization (QPSO), a novel mbest particle, contracting the searching space self-adaptively and boundaries restriction (NCB), then the new method NCB-QPSO is proposed. It can maintain an effective search mechanism with fine equilibrium between exploitation and exploration. Secondly, the problems of detecting the UPOs are converted into a non-negative functions' minimization through a proper translation in a non-Lyapunov way. Thirdly the simulations to 6 benchmark optimization problems and different high order UPOs of 5 classic nonlinear maps are done by the proposed method. And the results show that NCB-QPSO is a successful method in detecting the UPOs, and it has the advantages of fast convergence, high precision and robustness.

MAP3S Precipitation Chemistry Network: second periodic summary report, July 1977--June 1978

Energy Technology Data Exchange (ETDEWEB)

1979-01-01

The MAP3S Precipitation Chemistry Network consists of eight sites located in the northeastern United States. Precipitation event samples are collected by cooperating site operators, using specially developed sampling equipment. The concentration data collected over the period July 1, 1977 to July 1, 1978, are listed as a summary of the data reported monthly throughout the year. Samples were chemically analyzed at a central laboratory for 13 pollutant species - pH, conductivity, SO/sub 2/, SO/sub 4//sup =/, NH/sub 4//sup +/, NO/sub 2//sup -/, NO/sub 3//sup -/, Cl/sup -/, PO/sub 4//sup 3 -/, Na/sup +/, K/sup +/, Ca/sup + +/, and Mg/sup + +/ - using ion chromatography, automated wet chemistry, atomic absorption spectrophotometry, and electrode techniques. Second-year developments included: the installation of refrigeration equipment in all Battelle collectors; the initiation of an externally administered quality control program; and use of ion chromatography for cation as well as anion species. Supplementary research efforts included a special collector comparison study at the Pennsylvania State site and further analysis of sulfite versus sulfate deposition.

Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts

International Nuclear Information System (INIS)

Luo, Albert C.J.; Chen Lidi

2005-01-01

In this paper, an idealized, piecewise linear system is presented to model the vibration of gear transmission systems. Periodic motions in a generalized, piecewise linear oscillator with perfectly plastic impacts are predicted analytically. The analytical predictions of periodic motion are based on the mapping structures, and the generic mappings based on the discontinuous boundaries are developed. This method for the analytical prediction of the periodic motions in non-smooth dynamic systems can give all possible periodic motions based on the adequate mapping structures. The stability and bifurcation conditions for specified periodic motions are obtained. The periodic motions and grazing motion are demonstrated. This model is applicable to prediction of periodic motion in nonlinear dynamics of gear transmission systems

Nonlinear dynamics of the relativistic standard map

International Nuclear Information System (INIS)

Nomura, Y.; Ichikawa, Y.H.; Horton, W.

1991-04-01

Heating and acceleration of charged particles by RF fields have been extensively investigated by the standard map. The question arises as to how the relativistic effects change the nonlinear dynamical behavior described by the classical standard map. The relativistic standard map is a two parameter (K, Β = ω/kc) family of dynamical systems reducing to the standard map when Β → 0. For Β ≠ 0 the relativistic mass increase suppresses the onset of stochasticity. It shown that the speed of light limits the rate of advance of the phase in the relativistic standard map and introduces KAM surfaces persisting in the high momentum region. An intricate structure of mixing in the higher order periodic orbits and chaotic orbits is analyzed using the symmetry properties of the relativistic standard map. The interchange of the stability of the periodic orbits in the relativistic standard map is also observed and is explained by the local linear stability of the orbits. 12 refs., 16 figs

Canonical integration and analysis of periodic maps using non-standard analysis and life methods

Energy Technology Data Exchange (ETDEWEB)

Forest, E.; Berz, M.

1988-06-01

We describe a method and a way of thinking which is ideally suited for the study of systems represented by canonical integrators. Starting with the continuous description provided by the Hamiltonians, we replace it by a succession of preferably canonical maps. The power series representation of these maps can be extracted with a computer implementation of the tools of Non-Standard Analysis and analyzed by the same tools. For a nearly integrable system, we can define a Floquet ring in a way consistent with our needs. Using the finite time maps, the Floquet ring is defined only at the locations s/sub i/ where one perturbs or observes the phase space. At most the total number of locations is equal to the total number of steps of our integrator. We can also produce pseudo-Hamiltonians which describe the motion induced by these maps. 15 refs., 1 fig.

Exact boson mappings for nuclear neutron (proton) shell-model algebras having SU(3) subalgebras

International Nuclear Information System (INIS)

Bonatsos, D.; Klein, A.

1986-01-01

In this paper the commutation relations of the fermion pair operators of identical nucleons coupled to spin zero are given for the general nuclear major shell in LST coupling. The associated Lie algebras are the unitary symplectic algebras Sp(2M). The corresponding multipole subalgebras are the unitary algebras U(M), which possess SU(3) subalgebras. Number conserving exact boson mappings of both the Dyson and hermitian form are given for the nuclear neutron (proton) s--d, p--f, s--d--g, and p--f--h shells, and their group theoretical structure is emphasized. The results are directly applicable in the case of the s--d shell, while in higher shells the experimentally plausible pseudo-SU(3) symmetry makes them applicable. The final purpose of this work is to provide a link between the shell model and the Interacting Boson Model (IBM) in the deformed limit. As already implied in the work of Draayer and Hecht, it is difficult to associate the boson model developed here with the conventional IBM model. The differences between the two approaches (due mainly to the effects of the Pauli principle) as well as their physical implications are extensively discussed

A guide of patent map

International Nuclear Information System (INIS)

1999-12-01

This book introduces application and characteristic of patent information, types of patent information data and research of patent information, arrangement of patent information and patent map, analysis of patent information, necessity, writing period arrangement way of patent map, cases of patent map on selection of task of research and development, system of research and development and application, examples of PM such as MAP by year, application, technique, Inventor, and claim point map and computerization like data arrangement of PM patent, collection of analysis range and item analysis of patent, cases and written reports on patent analysis.

AN ANNOTATED BIBLIOGRAPHY OF CLIMATIC MAPS OF ANGOLA,

Science.gov (United States)

Contents: Map of political divisions of Africa; Map of Angola; Sources with abstracts listed alphabetically by author; Alphabetical author index ; Subject heading index with period of record; Subject heading index with map scales.

Dynamic Analysis of the Carotid-Kundalini Map

Science.gov (United States)

Wang, Xingyuan; Liang, Qingyong; Meng, Juan

The nature of the fixed points of the Carotid-Kundalini (C-K) map was studied and the boundary equation of the first bifurcation of the C-K map in the parameter plane is presented. Using the quantitative criterion and rule of chaotic system, the paper reveals the general features of the C-K Map transforming from regularity to chaos. The following conclusions are obtained: (i) chaotic patterns of the C-K map may emerge out of double-periodic bifurcation; (ii) the chaotic crisis phenomena are found. At the same time, the authors analyzed the orbit of critical point of the complex C-K Map and put forward the definition of Mandelbrot-Julia set of the complex C-K Map. The authors generalized the Welstead and Cromer's periodic scanning technique and using this technology constructed a series of the Mandelbrot-Julia sets of the complex C-K Map. Based on the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing, we investigated the symmetry of the Mandelbrot-Julia set and studied the topological inflexibility of distribution of the periodic region in the Mandelbrot set, and found that the Mandelbrot set contains abundant information of the structure of Julia sets by finding the whole portray of Julia sets based on Mandelbrot set qualitatively.

Approach of simultaneous localization and mapping based on local maps for robot

Institute of Scientific and Technical Information of China (English)

CHEN Bai-fan; CAI Zi-xing; HU De-wen

2006-01-01

An extended Kalman filter approach of simultaneous localization and mapping(SLAM) was proposed based on local maps.A local frame of reference was established periodically at the position of the robot, and then the observations of the robot and landmarks were fused into the global frame of reference. Because of the independence of the local map, the approach does not cumulate the estimate and calculation errors which are produced by SLAM using Kalman filter directly. At the same time, it reduces the computational complexity. This method is proven correct and feasible in simulation experiments.

Quadratic rational rotations of the torus and dual lattice maps

CERN Document Server

Kouptsov, K L; Vivaldi, F

2002-01-01

We develop a general formalism for computed-assisted proofs concerning the orbit structure of certain non ergodic piecewise affine maps of the torus, whose eigenvalues are roots of unity. For a specific class of maps, we prove that if the trace is a quadratic irrational (the simplest nontrivial case, comprising 8 maps), then the periodic orbits are organized into finitely many renormalizable families, with exponentially increasing period, plus a finite number of exceptional families. The proof is based on exact computations with algebraic numbers, where units play the role of scaling parameters. Exploiting a duality existing between these maps and lattice maps representing rounded-off planar rotations, we establish the global periodicity of the latter systems, for a set of orbits of full density.

The geological map of Uruguay

International Nuclear Information System (INIS)

Bossi, J.; Ferrando, L.; Fernandez, A.; Elizalde, G.; Morales, H.; Ledesma, J.; Carballo, E.; Medina, E.; Ford, I.; Montana, J.

1975-01-01

The geological map of Uruguay is about the morphological characteristics of the soil such as rocks, sediments and granites belong to different periods. These periods are the proterozoic, paleozoic, permian, mesozoic, jurassic, cretaceous, cenozoic and holocene.

Discrete Routh reduction

International Nuclear Information System (INIS)

Jalnapurkar, Sameer M; Leok, Melvin; Marsden, Jerrold E; West, Matthew

2006-01-01

This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double spherical pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a non-trivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure

Attractors for discrete periodic dynamical systems

Science.gov (United States)

John E. Franke; James F. Selgrade

2003-01-01

A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the unin of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an...

Reverse bifurcation and fractal of the compound logistic map

Science.gov (United States)

Wang, Xingyuan; Liang, Qingyong

2008-07-01

The nature of the fixed points of the compound logistic map is researched and the boundary equation of the first bifurcation of the map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, the paper reveal the general features of the compound logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the map may emerge out of double-periodic bifurcation and (2) the chaotic crisis phenomena and the reverse bifurcation are found. At the same time, we analyze the orbit of critical point of the compound logistic map and put forward the definition of Mandelbrot-Julia set of compound logistic map. We generalize the Welstead and Cromer's periodic scanning technology and using this technology construct a series of Mandelbrot-Julia sets of compound logistic map. We investigate the symmetry of Mandelbrot-Julia set and study the topological inflexibility of distributing of period region in the Mandelbrot set, and finds that Mandelbrot set contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot set qualitatively.

The symmetric quartic map for trajectories of magnetic field lines in elongated divertor tokamak plasmas

Science.gov (United States)

Jones, Morgin; Wadi, Hasina; Ali, Halima; Punjabi, Alkesh

2009-04-01

The coordinates of the area-preserving map equations for integration of magnetic field line trajectories in divertor tokamaks can be any coordinates for which a transformation to (ψt,θ,φ) coordinates exists [A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys. Lett. A 364, 140 (2007)]. ψt is toroidal magnetic flux, θ is poloidal angle, and φ is toroidal angle. This freedom is exploited to construct the symmetric quartic map such that the only parameter that determines magnetic geometry is the elongation of the separatrix surface. The poloidal flux inside the separatrix, the safety factor as a function of normalized minor radius, and the magnetic perturbation from the symplectic discretization are all held constant, and only the elongation is κ varied. The width of stochastic layer, the area, and the fractal dimension of the magnetic footprint and the average radial diffusion coefficient of magnetic field lines from the stochastic layer; and how these quantities scale with κ is calculated. The symmetric quartic map gives the correct scalings which are consistent with the scalings of coordinates with κ. The effects of m =1, n =±1 internal perturbation with the amplitude that is expected to occur in tokamaks are calculated by adding a term [H. Ali, A. Punjabi, A. H. Boozer, and T. Evans, Phys. Plasmas 11, 1908 (2004)] to the symmetric quartic map. In this case, the width of stochastic layer scales as 0.35 power of κ. The area of the footprint is roughly constant. The average radial diffusion coefficient of field lines near the X-point scales linearly with κ. The low mn perturbation changes the quasisymmetric structure of the footprint, and reorganizes it into a single, large scale, asymmetric structure. The symmetric quartic map is combined with the dipole map [A. Punjabi, H. Ali, and A. H. Boozer, Phys. Plasmas 10, 3992 (2003)] to calculate the effects of magnetic perturbation from a current carrying coil. The coil position and coil current coil are

The symmetric quartic map for trajectories of magnetic field lines in elongated divertor tokamak plasmas

International Nuclear Information System (INIS)

Jones, Morgin; Wadi, Hasina; Ali, Halima; Punjabi, Alkesh

2009-01-01

The coordinates of the area-preserving map equations for integration of magnetic field line trajectories in divertor tokamaks can be any coordinates for which a transformation to (ψ t ,θ,φ) coordinates exists [A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys. Lett. A 364, 140 (2007)]. ψ t is toroidal magnetic flux, θ is poloidal angle, and φ is toroidal angle. This freedom is exploited to construct the symmetric quartic map such that the only parameter that determines magnetic geometry is the elongation of the separatrix surface. The poloidal flux inside the separatrix, the safety factor as a function of normalized minor radius, and the magnetic perturbation from the symplectic discretization are all held constant, and only the elongation is κ varied. The width of stochastic layer, the area, and the fractal dimension of the magnetic footprint and the average radial diffusion coefficient of magnetic field lines from the stochastic layer; and how these quantities scale with κ is calculated. The symmetric quartic map gives the correct scalings which are consistent with the scalings of coordinates with κ. The effects of m=1, n=±1 internal perturbation with the amplitude that is expected to occur in tokamaks are calculated by adding a term [H. Ali, A. Punjabi, A. H. Boozer, and T. Evans, Phys. Plasmas 11, 1908 (2004)] to the symmetric quartic map. In this case, the width of stochastic layer scales as 0.35 power of κ. The area of the footprint is roughly constant. The average radial diffusion coefficient of field lines near the X-point scales linearly with κ. The low mn perturbation changes the quasisymmetric structure of the footprint, and reorganizes it into a single, large scale, asymmetric structure. The symmetric quartic map is combined with the dipole map [A. Punjabi, H. Ali, and A. H. Boozer, Phys. Plasmas 10, 3992 (2003)] to calculate the effects of magnetic perturbation from a current carrying coil. The coil position and coil current coil are

Generalized Miura transformations, two-bosons KP hierarchies and their reduction to KdV hierarchies

International Nuclear Information System (INIS)

Aratyn, H.; Ferreira, L.A.; Gomes, J.F.; Medeiros, R.T.; Zimerman, A.H.

1993-02-01

Bracket preserving gauge equivalence is established between several two-boson generated KP type of hierarchies. These KP hierarchies reduce under symplectic reduction (via Dirac constraints) to KdV and Schwarzian KdV hierarchies. Under this reduction the gauge equivalence is taking form of the conventional Miura maps between the above KdV type of hierarchies. (author). 16 refs

Generalized Miura transformations, two-bosons KP hierarchies and their reduction to KdV hierarchies

Energy Technology Data Exchange (ETDEWEB)

Aratyn, H. [Illinois Univ., Chicago, IL (United States). Dept. of Physics; Ferreira, L.A.; Gomes, J.F.; Medeiros, R.T.; Zimerman, A.H.

1993-02-01

Bracket preserving gauge equivalence is established between several two-boson generated KP type of hierarchies. These KP hierarchies reduce under symplectic reduction (via Dirac constraints) to KdV and Schwarzian KdV hierarchies. Under this reduction the gauge equivalence is taking form of the conventional Miura maps between the above KdV type of hierarchies. (author). 16 refs.

2D discontinuous piecewise linear map: Emergence of fashion cycles.

Science.gov (United States)

Gardini, L; Sushko, I; Matsuyama, K

2018-05-01

We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity, regions associated with attracting cycles of different periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are obtained analytically in explicit form. We show the existence of several partially overlapping period incrementing structures, that is, a novelty for the considered class of maps. Moreover, we show that if the time-delay in the discrete time formulation of the model shrinks to zero, the number of period incrementing structures tends to infinity and the dynamics of the discrete time fashion cycle model converges to those of continuous-time fashion cycle model.

Land survey map of air pollutants

International Nuclear Information System (INIS)

Hadzi-Mishev, Dimitar

1996-01-01

The first step toward finding a solution to the problems with air pollution is the realization of a land survey map of polluters and a constant acquisition of data from periodical controls of emission of harmful materials, which will be carried out with a determined dynamic. Such a land survey map is not a project which should be finished within a strict time limit, but is intended to create all conditions for a periodical monitoring of emission of harmful materials from registered polluters in order to make a periodical, exact picture of the quantity of harmful materials, which are conveyed by polluters in certain city, a part of the state or the whole country. (author). 4 ills

MAP3S precipitation chemistry network: fourth periodic summary report (1980)

Energy Technology Data Exchange (ETDEWEB)

1981-12-01

This, the fourth in a series of summary reports, contains complete field and chemical data from the MAP3S/RAINE (Multistate Atmospheric Power Production Pollution Studies) Precipitation Chemistry Network for the year 1980. The 1980 data were added to the previous data base, and an update of the previous statistical summary completed. Included are basic statistics, time trend analyses, and monthly averages.

Chaoticity of interval self-maps with positive entropy

International Nuclear Information System (INIS)

Xiong Jincheng.

1988-12-01

Li and Yorke originally introduced the notion of chaos for continuous self-map of the interval I = (0,1). In the present paper we show that an interval self-map with positive topological entropy has a chaoticity more complicated than the chaoticity in the sense of Li and Yorke. The main result is that if f:I → I is continuous and has a periodic point with odd period > 1 then there exists a closed subset K of I invariant with respect to f such that the periodic points are dense in K, the periods of periodic points in K form an infinite set and f|K is topologically mixing. (author). 9 refs

Bifurcation and Fractal of the Coupled Logistic Map

Science.gov (United States)

Wang, Xingyuan; Luo, Chao

The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.

Chaos and Fractals in C-K Map

Science.gov (United States)

Wang, Xing-Yuan; Liang, Qing-Yong; Meng, Juan

The characteristic of the fixed points of the Carotid-Kundalini (C-K) map is investigated and the boundary equation of the first bifurcation of the C-K map in the parameter plane is given. Based on the studies of the phase graph, the power spectrum, the correlation dimension and the Lyapunov exponents, the paper reveals the general features of the C-K map transforming from regularity. Meanwhile, using the periodic scanning technology proposed by Welstead and Cromer, a series of Mandelbrot-Julia (M-J) sets of the complex C-K map are constructed. The symmetry of M-J set and the topological inflexibility of distributing of periodic region in the Mandelbrot set are investigated. By founding the whole portray of Julia sets based on Mandelbrot set qualitatively, we find out that Mandelbrot sets contain abundant information of structure of Julia sets.

Effect of robust torus on the dynamical transport

International Nuclear Information System (INIS)

Martins, C G L; Carvalho, R Egydio de; Caldas, I L; Roberto, M

2010-01-01

In the present work, we quantify the fraction of trajectories that reach a specific region of the phase space when we vary a control parameter using two symplectic maps: one non-twist and another one twist. The two maps were studied with and without a robust torus. We compare the obtained patterns and we identify the effect of the robust torus on the dynamical transport. We show that the effect of meandering-like barriers loses importance in blocking the radial transport when the robust torus is present.

Further results on periods and period doubling for iterates of the trapezoic function

International Nuclear Information System (INIS)

Beyer, W.A.; Stein, P.R.

1982-01-01

The trapezoidal function lambda f/sub e/(x), is defined for fixed e element of (0,1] and for lambda element of [1,2] by lambda f/sub e/ (x) = lambda for /x-1/< 1-e and lambda f/sub e/(x) = lambda(1-/x-1/)/(1-e) for 1 greater than or equal to /x-1/greater than or equal to 1-e. For a fixed e, this is a one parameter family of endomorphisms of the interval [0,2]. The structure of the periods (or cycles) of these mappings is studied. In addition, the metric properties of the corresponding bifurcation diagrams are considered; in particular, the rate of convergence of a sequence of bifurcation points in the (x,lambda) plane is studied. It is shown to be different from that found by Feigenbaum and others for mappings which are not flat at the top. The limiting case e = 1 is of special interest. For cycles and containing a point x element of[e,2-e], the period quadruplicates instead of doubling as it does in the usual case

Exploring the Middle Ages with the Medieval Map.

Science.gov (United States)

Parry, Joseph D.

1998-01-01

Illustrates how medieval maps provide a means for studying the Middle Ages by allowing students to explore the ideology and representations of the medieval world conveyed by the maps. Explains that students also can compare the maps with literature from the same time period to further analyze the representations of the culture. (CMK)

Global Ionosphere Mapping and Differential Code Bias Estimation during Low and High Solar Activity Periods with GIMAS Software

Directory of Open Access Journals (Sweden)

Qiang Zhang

2018-05-01

Full Text Available Ionosphere research using the Global Navigation Satellite Systems (GNSS techniques is a hot topic, with their unprecedented high temporal and spatial sampling rate. We introduced a new GNSS Ionosphere Monitoring and Analysis Software (GIMAS in order to model the global ionosphere vertical total electron content (VTEC maps and to estimate the GPS and GLObalnaya NAvigatsionnaya Sputnikovaya Sistema (GLONASS satellite and receiver differential code biases (DCBs. The GIMAS-based Global Ionosphere Map (GIM products during low (day of year from 202 to 231, in 2008 and high (day of year from 050 to 079, in 2014 solar activity periods were investigated and assessed. The results showed that the biases of the GIMAS-based VTEC maps relative to the International GNSS Service (IGS Ionosphere Associate Analysis Centers (IAACs VTEC maps ranged from −3.0 to 1.0 TECU (TEC unit (1 TECU = 1 × 1016 electrons/m2. The standard deviations (STDs ranged from 0.7 to 1.9 TECU in 2008, and from 2.0 to 8.0 TECU in 2014. The STDs at a low latitude were significantly larger than those at middle and high latitudes, as a result of the ionospheric latitudinal gradients. When compared with the Jason-2 VTEC measurements, the GIMAS-based VTEC maps showed a negative systematic bias of about −1.8 TECU in 2008, and a positive systematic bias of about +2.2 TECU in 2014. The STDs were about 2.0 TECU in 2008, and ranged from 2.2 to 8.5 TECU in 2014. Furthermore, the aforementioned characteristics were strongly related to the conditions of the ionosphere variation and the geographic latitude. The GPS and GLONASS satellite and receiver P1-P2 DCBs were compared with the IAACs DCBs. The root mean squares (RMSs were 0.16–0.20 ns in 2008 and 0.13–0.25 ns in 2014 for the GPS satellites and 0.26–0.31 ns in 2014 for the GLONASS satellites. The RMSs of receiver DCBs were 0.21–0.42 ns in 2008 and 0.33–1.47 ns in 2014 for GPS and 0.67–0.96 ns in 2014 for GLONASS. The monthly

Chaotic and stable perturbed maps: 2-cycles and spatial models

Science.gov (United States)

Braverman, E.; Haroutunian, J.

2010-06-01

As the growth rate parameter increases in the Ricker, logistic and some other maps, the models exhibit an irreversible period doubling route to chaos. If a constant positive perturbation is introduced, then the Ricker model (but not the classical logistic map) experiences period doubling reversals; the break of chaos finally gives birth to a stable two-cycle. We outline the maps which demonstrate a similar behavior and also study relevant discrete spatial models where the value in each cell at the next step is defined only by the values at the cell and its nearest neighbors. The stable 2-cycle in a scalar map does not necessarily imply 2-cyclic-type behavior in each cell for the spatial generalization of the map.

Mapping the HISS Dipole

International Nuclear Information System (INIS)

McParland, C.; Bieser, F.

1984-01-01

The principal component of the Bevalac HISS facility is a large super-conducting 3 Tesla dipole. The facility's need for a large magnetic volume spectrometer resulted in a large gap geometry - a 2 meter pole tip diameter and a 1 meter pole gap. Obviously, the field required detailed mapping for effective use as a spectrometer. The mapping device was designed with several major features in mind. The device would measure field values on a grid which described a closed rectangular solid. The grid would be a regular with the exact measurement intervals adjustable by software. The device would function unattended over the long period of time required to complete a field map. During this time, the progress of the map could be monitored by anyone with access to the HISS VAX computer. Details of the mechanical, electrical, and control design follow

Natural differential operations on manifolds: an algebraic approach

International Nuclear Information System (INIS)

Katsylo, P I; Timashev, D A

2008-01-01

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 V,W→M all the natural differential operations D:Γ(V)→Γ(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.

Geometrical interpretation of the topological recursion, and integrable string theories

CERN Document Server

Eynard, Bertrand

2009-01-01

Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative geometry like maps, partitions, Hurwitz numbers, intersection numbers, Gromov-Witten invariants... The problem is thus to understand what they count, or in other words, given a spectral curve, construct an enumerative geometry problem. This is what we do in a semi-heuristic approach in this article. Starting from a spectral curve, i.e. an integrable system, we use its flat connection and flat coordinates, to define a family of worldsheets, whose enumeration is indeed solved by the topological recursion and symplectic invariants. In other words, for any spectral curve, we construct a corresponding string theory, whose target space is a submanifold of the Jacobian.

Dynamics of exponential maps

OpenAIRE

Rempe, Lasse

2003-01-01

This thesis contains several new results about the dynamics of exponential maps $z\\mapsto \\exp(z)+\\kappa$. In particular, we prove that periodic external rays of exponential maps with nonescaping singular value always land. This is an analog of a theorem of Douady and Hubbard for polynomials. We also answer a question of Herman, Baker and Rippon by showing that the boundary of an unbounded exponential Siegel disk always contains the singular value. In addition to the presentation of new resul...

Mimicking Nonequilibrium Steady States with Time-Periodic Driving

Science.gov (United States)

2016-08-29

construction does not require the solution of any differential equations , only linear algebraic equations . By contrast, a mapping in the opposite...set of algebraic linear equations . The mapping between NESS and SP presented above was not intended as a set of operational instructions for... differential equations with time-periodic parameters. Typically, this can only be done numerically. In some applications, transition rates are constrained by

Theory and praxis pf map analsys in CHEF part 1: Linear normal form

Energy Technology Data Exchange (ETDEWEB)

Michelotti, Leo; /Fermilab

2008-10-01

This memo begins a series which, put together, could comprise the 'CHEF Documentation Project' if there were such a thing. The first--and perhaps only--three will telegraphically describe theory, algorithms, implementation and usage of the normal form map analysis procedures encoded in CHEF's collection of libraries. [1] This one will begin the sequence by explaining the linear manipulations that connect the Jacobian matrix of a symplectic mapping to its normal form. It is a 'Reader's Digest' version of material I wrote in Intermediate Classical Dynamics (ICD) [2] and randomly scattered across technical memos, seminar viewgraphs, and lecture notes for the past quarter century. Much of its content is old, well known, and in some places borders on the trivial.1 Nevertheless, completeness requires their inclusion. The primary objective is the 'fundamental theorem' on normalization written on page 8. I plan to describe the nonlinear procedures in a subsequent memo and devote a third to laying out algorithms and lines of code, connecting them with equations written in the first two. Originally this was to be done in one short paper, but I jettisoned that approach after its first section exceeded a dozen pages. The organization of this document is as follows. A brief description of notation is followed by a section containing a general treatment of the linear problem. After the 'fundamental theorem' is proved, two further subsections discuss the generation of equilibrium distributions and issue of 'phase'. The final major section reviews parameterizations--that is, lattice functions--in two and four dimensions with a passing glance at the six-dimensional version. Appearances to the contrary, for the most part I have tried to restrict consideration to matters needed to understand the code in CHEF's libraries.

Explore Stochastic Instabilities of Periodic Points by Transition Path Theory

Science.gov (United States)

Cao, Yu; Lin, Ling; Zhou, Xiang

2016-06-01

We consider the noise-induced transitions from a linearly stable periodic orbit consisting of T periodic points in randomly perturbed discrete logistic map. Traditional large deviation theory and asymptotic analysis at small noise limit cannot distinguish the quantitative difference in noise-induced stochastic instabilities among the T periodic points. To attack this problem, we generalize the transition path theory to the discrete-time continuous-space stochastic process. In our first criterion to quantify the relative instability among T periodic points, we use the distribution of the last passage location related to the transitions from the whole periodic orbit to a prescribed disjoint set. This distribution is related to individual contributions to the transition rate from each periodic points. The second criterion is based on the competency of the transition paths associated with each periodic point. Both criteria utilize the reactive probability current in the transition path theory. Our numerical results for the logistic map reveal the transition mechanism of escaping from the stable periodic orbit and identify which periodic point is more prone to lose stability so as to make successful transitions under random perturbations.

A simple electronic circuit realization of the tent map

Energy Technology Data Exchange (ETDEWEB)

Campos-Canton, I. [Fac. de Ciencias, Universidad Autonoma de San Luis Potosi, Alvaro Obregon 64, 78000 San Luis Potosi, SLP (Mexico)], E-mail: icampos@galia.fc.uaslp.mx; Campos-Canton, E. [Departamento de Fisico Matematicas, Universidad Autonoma de San Luis Potosi, Alvaro Obregon 64, 78000 San Luis Potosi, SLP (Mexico)], E-mail: ecamp@uaslp.mx; Murguia, J.S. [Departamento de Fisico Matematicas, Universidad Autonoma de San Luis Potosi, Alvaro Obregon 64, 78000 San Luis Potosi, SLP (Mexico)], E-mail: ondeleto@uaslp.mx; Rosu, H.C. [Division de Materiales Avanzados, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San Jose 2055, 78216 San Luis Potosi, SLP (Mexico)], E-mail: hcr@ipicyt.edu.mx

2009-10-15

We present a very simple electronic implementation of the tent map, one of the best-known discrete dynamical systems. This is achieved by using integrated circuits and passive elements only. The experimental behavior of the tent map electronic circuit is compared with its numerical simulation counterpart. We find that the electronic circuit presents fixed points, periodicity, period doubling, chaos and intermittency that match with high accuracy the corresponding theoretical values.

Spreading Sequences Generated Using Asymmetrical Integer-Number Maps

Directory of Open Access Journals (Sweden)

V. Sebesta

2007-09-01

Full Text Available Chaotic sequences produced by piecewise linear maps can be transformed to binary sequences. The binary sequences are optimal for the asynchronous DS/CDMA systems in case of certain shapes of the maps. This paper is devoted to the one-to-one integer-number maps derived from the suitable asymmetrical piecewise linear maps. Such maps give periodic integer-number sequences, which can be transformed to the binary sequences. The binary sequences produced via proposed modified integer-number maps are perfectly balanced and embody good autocorrelation and crosscorrelation properties. The number of different binary sequences is sizable. The sequences are suitable as spreading sequences in DS/CDMA systems.

Lunar Geologic Mapping: A Preliminary Map of a Portion of the LQ-10 ("Marius") Quadrangle

Science.gov (United States)

Gregg, T. K. P.; Yingst, R. A.

2009-01-01

Since the first lunar mapping program ended in the 1970s, new topographical, multispectral, elemental and albedo imaging datasets have become available (e.g., Clementine, Lunar Prospector, Galileo). Lunar science has also advanced within the intervening time period. A new systematic lunar geologic mapping effort endeavors to build on the success of earlier mapping programs by fully integrating the many disparate datasets using GIS software and bringing to bear the most current understanding of lunar geologic history. As part of this program, we report on a 1:2,500,000-scale preliminary map of a subset of Lunar Quadrangle 10 ("LQ-10" or the "Marius Quadrangle," see Figures 1 and 2), and discuss the first-order science results. By generating a geologic map of this region, we can constrain the stratigraphic and geologic relationships between features, revealing information about the Moon s chemical and thermal evolution.

Schedule and complex motion of shuttle bus induced by periodic inflow of passengers

International Nuclear Information System (INIS)

Nagatani, Takashi; Naito, Yuichi

2011-01-01

We have studied the dynamic behavior of a bus in the shuttle bus transportation with a periodic inflow. A bus schedule is closely related to the dynamics. We present the modified circle map model for the dynamics of the shuttle bus. The motion of the shuttle bus depends on the loading parameter and the inflow period. The shuttle bus displays the periodic, quasi-periodic, and chaotic motions with varying both loading parameter and inflow rate. -- Highlights: → We studied the dynamic behavior of a bus in the shuttle bus transportation. → We presented the modified circle map model for the bus schedule. → We clarified the dependence of the tour time on both loading parameter and inflow period.

Transient chaos in the Lorenz-type map with periodic forcing.

Science.gov (United States)

Maslennikov, Oleg V; Nekorkin, Vladimir I; Kurths, Jürgen

2018-03-01

We consider a case study of perturbing a system with a boundary crisis of a chaotic attractor by periodic forcing. In the static case, the system exhibits persistent chaos below the critical value of the control parameter but transient chaos above the critical value. We discuss what happens to the system and particularly to the transient chaotic dynamics if the control parameter periodically oscillates. We find a non-exponential decaying behavior of the survival probability function, study the impact of the forcing frequency and amplitude on the escape rate, analyze the phase-space image of the observed dynamics, and investigate the influence of initial conditions.

Exact treatment of mode locking for a piecewise linear map

International Nuclear Information System (INIS)

Ding, E.J.; Hemmer, P.C.

1987-01-01

A piecewise linear map with one discontinuity is studied by analytic means in the two-dimensional parameter space. When the slope of the map is less than unity, periodic orbits are present, and they give the precise symbolic dynamic classification of these. The localization of the periodic domains in parameter space is given by closed expressions. The winding number forms a devil's terrace, a two-dimensional function whose cross sections are complete devil's staircases. In such a cross section the complementary set to the periodic intervals is a Cantor set with dimension D = 0

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.

Science.gov (United States)

Levnajić, Zoran; Mezić, Igor

2015-05-01

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.

A simplectic formulation of relativistic particle dynamics

International Nuclear Information System (INIS)

Tulczyjew, W.M.

1976-12-01

Particle mechanics is formulated in terms of symplectic relations and infinitesimal symplectic relations. Generating functions of symplectic relations are shown to be classical counterparts of Green's functions of wave mechanics. (orig.) [de

External Periodic Force Control of a Single-Degree-of-Freedom Vibroimpact System

Directory of Open Access Journals (Sweden)

Jingyue Wang

2013-01-01

Full Text Available A single-degree-of-freedom mechanical model of vibro-impact system is established. Bifurcation and chaos in the system are revealed with the time history diagram, phase trajectory map, and Poincaré map. According to the bifurcation and chaos of the actual vibro-impact system, the paper puts forward external periodic force control strategy. The method of controlling chaos by external periodic force feedback controller is developed to guide chaotic motions towards regular motions. The stability of the control system is also analyzed especially by theory. By selecting appropriate feedback coefficients, the unstable periodic orbits of the original chaotic orbit can be stabilized to the stable periodic orbits. The effectiveness of this control method is verified by numerical simulation.

A time-delayed method for controlling chaotic maps

International Nuclear Information System (INIS)

Chen Maoyin; Zhou Donghua; Shang Yun

2005-01-01

Combining the repetitive learning strategy and the optimality principle, this Letter proposes a time-delayed method to control chaotic maps. This method can effectively stabilize unstable periodic orbits within chaotic attractors in the sense of least mean square. Numerical simulations of some chaotic maps verify the effectiveness of this method

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

International Nuclear Information System (INIS)

Cai Yunhai; Irwin, John; Nosochkov, Yuri; Yan, Yiton

1997-01-01

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

Intensity Based Seismic Hazard Map of Republic of Macedonia

Science.gov (United States)

Dojcinovski, Dragi; Dimiskovska, Biserka; Stojmanovska, Marta

2016-04-01

The territory of the Republic of Macedonia and the border terrains are among the most seismically active parts of the Balkan Peninsula belonging to the Mediterranean-Trans-Asian seismic belt. The seismological data on the R. Macedonia from the past 16 centuries point to occurrence of very strong catastrophic earthquakes. The hypocenters of the occurred earthquakes are located above the Mohorovicic discontinuity, most frequently, at a depth of 10-20 km. Accurate short -term prognosis of earthquake occurrence, i.e., simultaneous prognosis of time, place and intensity of their occurrence is still not possible. The present methods of seismic zoning have advanced to such an extent that it is with a great probability that they enable efficient protection against earthquake effects. The seismic hazard maps of the Republic of Macedonia are the result of analysis and synthesis of data from seismological, seismotectonic and other corresponding investigations necessary for definition of the expected level of seismic hazard for certain time periods. These should be amended, from time to time, with new data and scientific knowledge. The elaboration of this map does not completely solve all issues related to earthquakes, but it provides basic empirical data necessary for updating the existing regulations for construction of engineering structures in seismically active areas regulated by legal regulations and technical norms whose constituent part is the seismic hazard map. The map has been elaborated based on complex seismological and geophysical investigations of the considered area and synthesis of the results from these investigations. There were two phases of elaboration of the map. In the first phase, the map of focal zones characterized by maximum magnitudes of possible earthquakes has been elaborated. In the second phase, the intensities of expected earthquakes have been computed according to the MCS scale. The map is prognostic, i.e., it provides assessment of the

Seasonality and the logistic map

International Nuclear Information System (INIS)

Silva, Emily; Peacock-Lopez, Enrique

2017-01-01

Nonlinear difference equations, such as the logistic map, have been used to study chaos and also to model population dynamics. Here we propose a model that extends the “lose + lose = win” behavior found in Parrondo’s Paradox, where switching between chaotic parameters in the logistic map yields periodic behavior (“chaos + chaos = order”). The model uses twelve parameters each reflecting the conditions of one of the twelve months. In this paper we study the effects of smooth-transitioning parameters and the robust system that emerges.

Perturbation methods and closure approximations in nonlinear systems

International Nuclear Information System (INIS)

Dubin, D.H.E.

1984-01-01

In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed

Controlling chaos in dynamical systems described by maps

International Nuclear Information System (INIS)

Crispin, Y.; Marduel, C.

1994-01-01

The problem of suppressing chaotic behavior in dynamical systems is treated using a feedback control method with limited control effort. The proposed method is validated on archetypal systems described by maps, i.e. discrete-time difference equations. The method is also applicable to dynamical systems described by flows, i.e. by systems of ordinary differential equations. Results are presented for the one-dimensional logistic map and for a two-dimensional Lotka-Volterra map describing predator-prey population dynamics. It is shown that chaos can be suppressed and the system stabilized about a period-1 fixed point of the maps

Late emergence of the vibrissa direction selectivity map in the rat barrel cortex.

Science.gov (United States)

Kremer, Yves; Léger, Jean-François; Goodman, Dan; Brette, Romain; Bourdieu, Laurent

2011-07-20

In the neocortex, neuronal selectivities for multiple sensorimotor modalities are often distributed in topographical maps thought to emerge during a restricted period in early postnatal development. Rodent barrel cortex contains a somatotopic map for vibrissa identity, but the existence of maps representing other tactile features has not been clearly demonstrated. We addressed the issue of the existence in the rat cortex of an intrabarrel map for vibrissa movement direction using in vivo two-photon imaging. We discovered that the emergence of a direction map in rat barrel cortex occurs long after all known critical periods in the somatosensory system. This map is remarkably specific, taking a pinwheel-like form centered near the barrel center and aligned to the barrel cortex somatotopy. We suggest that this map may arise from intracortical mechanisms and demonstrate by simulation that the combination of spike-timing-dependent plasticity at synapses between layer 4 and layer 2/3 and realistic pad stimulation is sufficient to produce such a map. Its late emergence long after other classical maps suggests that experience-dependent map formation and refinement continue throughout adult life.

The global thermospheric mapping study

International Nuclear Information System (INIS)

Oliver, W.L.; Salah, J.E.

1988-01-01

The Global Thermospheric Mapping Study (GTMS) is a multitechnique experimental pilot study of the Earth's thermosphere designed to map simultaneously its spatial and temporal morphology. This paper provides the background for the study and presents the analysis techniques employed at Millstone Hill and results to date on thermospheric structure and dynamics. The first latitudinal-temporal maps of exospheric temperature obtained from the incoherent scatter radar chain at 70W meridian are presented for the two solstice periods, revealing substantial seasonal differences between them. The observed structure shows a relatively depressed temperature at high latitude in summer in contrast to the mass spectrometer/incoherent scatter 1983 [MSIS-83] empirical model, which shows a maximum temperature at polar latitudes. The MSIS-83 model predictions are in good agreement with the observed latitudinal-temporal structure in winter. Comparison with the numerical predictions made for the June 26-28, 1984 period with the National Center for Atmospheric Research thermospheric general circulation model shows reasonable agreement in the latitudinal gradient but the observations indicate a cooler thermosphere by several hundred degrees. Neutral winds at mid-latitudes are presented showing the expected strong southward winds at night, which are found to be consistent with the temperature gradients observed in the latitudinal maps. There is good agreement in the June winds between the available numerical model calculations and the observations. Work performed elsewhere on the GTMS data base is summarized for completeness

Circle maps and the Devil's staircase in a periodically perturbed Oregonator

DEFF Research Database (Denmark)

Brøns, Morten; Gross, Peter; Bar-Eli, Kedma

1997-01-01

Markman and Bar-Eli has studied a periodically forced Oregonator numerically and found a parameter range with the following properties: (1) Only periodic solutions are found in frequency-locked steps, each with a certain pattern of large and small oscillations (2) Between any two steps there is a....... Using invariant manifold theory we argue that an invariant circle must indeed exist when, as in the present case, the unforced system is close to a saddle-loop bifurcation. Generalisations of the results are briefly discussed....

Data Management Plan: HarassMap

Directory of Open Access Journals (Sweden)

Reem Wael

2017-07-01

Full Text Available HarassMap is an Egyptian organisation that works to create an environment where sexual harassment is not tolerated, and where individuals and institutions take action against it. For the purpose of this project, the project team cleaned up, organised, and made openly available for the public to access and use through a web portal, three main types of data: Crowdsourced reports of sexual harassment incidents (reports on HarassMap’s online reporting and mapping system - CSV and XLS Field data from HarassMap’s research on sexual harassment using traditional qualitative and quantitative research methods - DOCX, PDF, SAV, MP3 Social media conversations (comment threads and messages related to sexual harassment on harassMap’s Facebook page - XLS The social media data was collected retrospectively from our Facebook page during the project period and covers the period 2010-2016. The crowdsourced data and the research data was cleaned and organised to make sure it is usable for the public but still kept in its raw format. During the collection and organisation period, we also made sure to clear out all personal identifiers from the data to ensure anonymity and confidentiality, and prepared descriptions of each dataset that will help the public understand how the data was collected and how it can and cannot be used. The data is stored online on a web portal that we built together with a web developer during the project period. On the web portal, the data is available for the public to view, search and download for research or other purposes. The data is also backed up on a hard drive and the cloud. The web portal and HarassMap open data will be advertised on our website, and the direct link shared with our contacts and others who approach us with interest in our data.

Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate

Science.gov (United States)

Ren, Jingli; Yuan, Qigang

2017-08-01

A three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincaré map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincaré map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last.

Mimicking Nonequilibrium Steady States with Time-Periodic Driving (Open Source)

Science.gov (United States)

2016-05-18

construction does not require the solution of any differential equations , only linear algebraic equations . By contrast, a mapping in the opposite...set of algebraic linear equations . The mapping between NESS and SP presented above was not intended as a set of operational instructions for... differential equations with time-periodic parameters. Typically, this can only be done numerically. In some applications, transition rates are constrained by

Hydrometeorological aspects of the Real-Time Ultrafinescale Forecast Support during the Special Observing Period of the MAP*

Directory of Open Access Journals (Sweden)

R. Benoit

2003-01-01

Full Text Available During the Special Observation Period (SOP, 7 September–15 November, 1999 of the Mesoscale Alpine Programme (MAP, the Canadian Mesoscale Compressible Community Model (MC2 was run in real time at a horizontal resolution of 3 km on a computational domain of 350☓300☓50 grid points, covering the whole of the Alpine region. The WATFLOOD model was passively coupled to the MC2; the former is an integrated set of computer programs to forecast flood flows, using all available data, for catchments with response times ranging from one hour to several weeks. The unique aspect of this contribution is the operational application of numerical weather prediction data to forecast flows over a very large, multinational domain. An overview of the system performance from the hydrometeorological aspect is presented, mostly for the real-time results, but also from subsequent analyses. A streamflow validation of the precipitation is included for large basins covering upper parts of the Rhine and the Rhone, and parts of the Po and of the Danube. In general, the MC2/WATFLOOD model underestimated the total runoff because of the under-prediction of precipitation by MC2 during the MAP SOP. After the field experiment, a coding error in the cloud microphysics scheme of MC2 explains this underestimation to a large extent. A sensitivity study revealed that the simulated flows reproduce the major features of the observed flow record for most of the flow stations. The experiment was considered successful because two out of three possible flood events in the Swiss-Italian border region were predicted correctly by data from the numerical weather models linked to the hydrological model and no flow events were missed. This study has demonstrated that a flow forecast from a coupled atmospheric-hydrological model can serve as a useful first alert and quantitative forecast. Keywords: mesoscale atmospheric model, hydrological model, flood forecasting, Alps

Research in accelerator physics (theory)

International Nuclear Information System (INIS)

Ohnuma, Shoroku.

1993-01-01

The authors discuss the present status, expected effort during the remainder of the project, and some of the results of their activities since the beginning of the project. Some of the areas covered are: (1) effects of helical insertial devices on beam dynamics; (2) coupling impedance of apertures in accelerator beam pipes; (3) new calculation of diffusion rate; (4) integrable polynomial factorization for symplectic map tracking; and (5) physics of magnet sorting in superconducting rings

Seismic hazard map of the western hemisphere

Science.gov (United States)

Shedlock, K.M.; Tanner, J.G.

1999-01-01

Vulnerability to natural disasters increases with urbanization and development of associated support systems (reservoirs, power plants, etc.). Catastrophic earthquakes account for 60% of worldwide casualties associated with natural disasters. Economic damage from earthquakes is increasing, even in technologically advanced countries with some level of seismic zonation, as shown by the 1989 Loma Prieta, CA ($6 billion), 1994 Northridge, CA ($ 25 billion), and 1995 Kobe, Japan (> $ 100 billion) earthquakes. The growth of megacities in seismically active regions around the world often includes the construction of seismically unsafe buildings and infrastructures, due to an insufficient knowledge of existing seismic hazard. Minimization of the loss of life, property damage, and social and economic disruption due to earthquakes depends on reliable estimates of seismic hazard. National, state, and local governments, decision makers, engineers, planners, emergency response organizations, builders, universities, and the general public require seismic hazard estimates for land use planning, improved building design and construction (including adoption of building construction codes), emergency response preparedness plans, economic forecasts, housing and employment decisions, and many more types of risk mitigation. The seismic hazard map of the Americas is the concatenation of various national and regional maps, involving a suite of approaches. The combined maps and documentation provide a useful global seismic hazard framework and serve as a resource for any national or regional agency for further detailed studies applicable to their needs. This seismic hazard map depicts Peak Ground Acceleration (PGA) with a 10% chance of exceedance in 50 years for the western hemisphere. PGA, a short-period ground motion parameter that is proportional to force, is the most commonly mapped ground motion parameter because current building codes that include seismic provisions specify the

Seismic hazard map of the western hemisphere

Directory of Open Access Journals (Sweden)

J. G. Tanner

1999-06-01

Full Text Available Vulnerability to natural disasters increases with urbanization and development of associated support systems (reservoirs, power plants, etc.. Catastrophic earthquakes account for 60% of worldwide casualties associated with natural disasters. Economic damage from earthquakes is increasing, even in technologically advanced countries with some level of seismic zonation, as shown by the 1989 Loma Prieta, CA ($ 6 billion, 1994 Northridge, CA ($ 25 billion, and 1995 Kobe, Japan (> $ 100 billion earthquakes. The growth of megacities in seismically active regions around the world often includes the construction of seismically unsafe buildings and infrastructures, due to an insufficient knowledge of existing seismic hazard. Minimization of the loss of life, property damage, and social and economic disruption due to earthquakes depends on reliable estimates of seismic hazard. National, state, and local governments, decision makers, engineers, planners, emergency response organizations, builders, universities, and the general public require seismic hazard estimates for land use planning, improved building design and construction (including adoption of building construction codes, emergency response preparedness plans, economic forecasts, housing and employment decisions, and many more types of risk mitigation. The seismic hazard map of the Americas is the concatenation of various national and regional maps, involving a suite of approaches. The combined maps and documentation provide a useful global seismic hazard framework and serve as a resource for any national or regional agency for further detailed studies applicable to their needs. This seismic hazard map depicts Peak Ground Acceleration (PGA with a 10% chance of exceedance in 50 years for the western hemisphere. PGA, a short-period ground motion parameter that is proportional to force, is the most commonly mapped ground motion parameter because current building codes that include seismic provisions

Seismic hazard map of North and Central America and the Caribbean

Directory of Open Access Journals (Sweden)

K. M. Shedlock

1999-06-01

Full Text Available Minimization of the loss of life, property damage, and social and economic disruption due to earthquakes depends on reliable estimates of seismic hazard. National, state, and local governments, decision makers, engineers, planners, emergency response organizations, builders, universities, and the general public require seismic hazard estimates for land use planning, improved building design and construction (including adoption of building construction codes, emergency response preparedness plans, economic forecasts, housing and employment decisions, and many more types of risk mitigation. The seismic hazard map of North and Central America and the Caribbean is the concatenation of various national and regional maps, involving a suite of approaches. The combined maps and documentation provide a useful regional seismic hazard framework and serve as a resource for any national or regional agency for further detailed studies applicable to their needs. This seismic hazard map depicts Peak Ground Acceleration (PGA with a 10% chance of exceedance in 50 years. PGA, a short-period ground motion parameter that is proportional to force, is the most commonly mapped ground motion parameter because current building codes that include seismic provisions specify the horizontal force a building should be able to withstand during an earthquake. This seismic hazard map of North and Central America and the Caribbean depicts the likely level of short-period ground motion from earthquakes in a fifty-year window. Short-period ground motions effect short-period structures (e.g., one-to-two story buildings. The highest seismic hazard values in the region generally occur in areas that have been, or are likely to be, the sites of the largest plate boundary earthquakes.

Web mapping application of Roman Catholic Church administration in the Czech lands in the early modern period

Directory of Open Access Journals (Sweden)

Pavel Seemann

2017-03-01

Full Text Available Reconstruction of historical spatial relationships is still a topical issue in historical geography. In this respect, the Church history has not been well explored. The parish administration in the Czech lands is evolving since the advent of Christianity in 863, and a number of reforms have passed over the centuries. Significant changes in the administration also underwent during recatholisation of the Czech lands in the 17th and 18thcentury. From this Baroque era, there are written sources which have been preserved, so they can be utilized to reconstruct historical Church administration in the form of web mapping application. The paper briefly introduces methods which were used to build a spatial database filled with historical data. However, the main outcome of this paper is to describe the creation of the web mapping application that provides visualisation of this data. Discussed are topics like cartographic project, choice of map symbols, data generalization for different levels of detail and placement of annotations. Display of cartographic data were performed using the ArcGIS platform, through a combination of map tiles and feature services that are bundled into the application template created in Web AppBuilder.

Nonlinear dynamics of the relativistic standard map

International Nuclear Information System (INIS)

Nomura, Y.; Ichikawa, Y.H.; Horton, W.

1991-01-01

Heating and acceleration of charged particles by RF fields have been extensively investigated by the standard map (ST). Thus, it is natural to pose the question asking how the relativistic effects change the nonlinear dynamical behavior described by the classical ST map. The authors show that the speed of light limits the rate of advance of the phase in the relativistic standard map (RST) and introduces KAM surfaces persisting in the high momentum region. The RST map is a two parameter (k, β = ω/kc) family of dynamics reducing to the ST map when β → 0. For β ≠ 0 the relativity suppresses the onset of stochasticity. Chernikov et al. has also reported this effect. They have carried out extensive studies of nonlinear dynamics of the RST map and found very intricate structure of mixing of the higher order periodic orbits and chaotic orbits. They have shown that no matter how its gets chaotic the symmetry properties of the RST map determines its nonlinear dynamical behavior. 1 ref

Mapping online journalism in transition

DEFF Research Database (Denmark)

Hartley, Jannie Møller; Houman Ellersgaard, Christoph

2013-01-01

By operationalising Pierre Bourdieu’s concepts of field, capital and positions of autonomy and heteronomy, and applying a Principal Component Analysis (PCA) to data gathered from a large content analysis, the article explores the relations between online newspapers and their corresponding print...... or broadcast versions within a constructed Danish “field of news” by graphically presenting the data as maps of the changes in these relations. First, mapping transformations graphically shows that the online newspapers have gained autonomy from their “parent platforms”, but we see that in the same period...... they have increased their dependence on news agency stories. Furthermore, the mapping demonstrates how the online newspapers differ in terms of news productions strategies and in their relation to their parent platforms, meaning they take up different...

Pig-MAP and haptoglobin concentration reference values in swine from commercial farms.

Science.gov (United States)

Piñeiro, Carlos; Piñeiro, Matilde; Morales, Joaquín; Andrés, Marta; Lorenzo, Elia; Pozo, Mateo Del; Alava, María A; Lampreave, Fermín

2009-01-01

Pig-MAP (Major Acute-phase Protein) and haptoglobin concentrations were determined in pigs from commercial farms, and reference intervals obtained for different productive stages. Pig-MAP serum concentrations were lower in sows than in adult boars (mean values 0.81 vs. 1.23 mg/mL) and the opposite was observed for haptoglobin (1.47 vs. 0.94 mg/mL). No differences were found between parities, except for a minor decrease in haptoglobin concentration in the 4th parity. A linear correlation between pig-MAP and haptoglobin concentration was observed. In the period 4-12 weeks of life, pig-MAP mean concentrations were around 1mg/mL, being lower in the finishing period (0.7-0.8 mg/mL). Haptoglobin concentrations increased with time, from around 0.6 mg/mL at 4 weeks of age to 1.4 mg/mL at 12 weeks. Mean values of around 0.9 mg/mL were observed in the finishing period. A wider distribution of values was observed for haptoglobin than for pig-MAP concentrations. Differences between herds were observed, with the highest values obtained in a herd with signs of respiratory disease.

Maps of space in human frontoparietal cortex.

Science.gov (United States)

Jerde, Trenton A; Curtis, Clayton E

2013-12-01

Prefrontal cortex (PFC) and posterior parietal cortex (PPC) are neural substrates for spatial cognition. We here review studies in which we tested the hypothesis that human frontoparietal cortex may function as a priority map. According to priority map theory, objects or locations in the visual world are represented by neural activity that is proportional to their attentional priority. Using functional magnetic resonance imaging (fMRI), we first identified topographic maps in PFC and PPC as candidate priority maps of space. We then measured fMRI activity in candidate priority maps during the delay periods of a covert attention task, a spatial working memory task, and a motor planning task to test whether the activity depended on the particular spatial cognition. Our hypothesis was that some, but not all, candidate priority maps in PFC and PPC would be agnostic with regard to what was being prioritized, in that their activity would reflect the location in space across tasks rather than a particular kind of spatial cognition (e.g., covert attention). To test whether patterns of delay period activity were interchangeable during the spatial cognitive tasks, we used multivariate classifiers. We found that decoders trained to predict the locations on one task (e.g., working memory) cross-predicted the locations on the other tasks (e.g., covert attention and motor planning) in superior precentral sulcus (sPCS) and in a region of intraparietal sulcus (IPS2), suggesting that these patterns of maintenance activity may be interchangeable across the tasks. Such properties make sPCS in frontal cortex and IPS2 in parietal cortex viable priority map candidates, and suggest that these areas may be the human homologs of the monkey frontal eye field (FEF) and lateral intraparietal area (LIP). Copyright © 2013 Elsevier Ltd. All rights reserved.

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

Science.gov (United States)

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.

Noncommutative configuration space. Classical and quantum mechanical aspects

OpenAIRE

Vanhecke, F. J.; Sigaud, C.; da Silva, A. R.

2005-01-01

In this work we examine noncommutativity of position coordinates in classical symplectic mechanics and its quantisation. In coordinates $\\{q^i,p_k\\}$ the canonical symplectic two-form is $\\omega_0=dq^i\\wedge dp_i$. It is well known in symplectic mechanics {\\bf\\cite{Souriau,Abraham,Guillemin}} that the interaction of a charged particle with a magnetic field can be described in a Hamiltonian formalism without a choice of a potential. This is done by means of a modified symplectic two-form $\\ome...

Seidel-Smith cohomology for tangles

DEFF Research Database (Denmark)

Rezazadegan, Reza

2009-01-01

We generalize the “symplectic Khovanov cohomology” of Seidel and Smith (Duke Math J 134(3):453–514, 2006) to tangles using the notion of symplectic valued topological field theory introduced by Wehrheim and Woodward (arXiv:0905.1368).......We generalize the “symplectic Khovanov cohomology” of Seidel and Smith (Duke Math J 134(3):453–514, 2006) to tangles using the notion of symplectic valued topological field theory introduced by Wehrheim and Woodward (arXiv:0905.1368)....

Mapping out Map Libraries

Directory of Open Access Journals (Sweden)

Ferjan Ormeling

2008-09-01

Full Text Available Discussing the requirements for map data quality, map users and their library/archives environment, the paper focuses on the metadata the user would need for a correct and efficient interpretation of the map data. For such a correct interpretation, knowledge of the rules and guidelines according to which the topographers/cartographers work (such as the kind of data categories to be collected, and the degree to which these rules and guidelines were indeed followed are essential. This is not only valid for the old maps stored in our libraries and archives, but perhaps even more so for the new digital files as the format in which we now have to access our geospatial data. As this would be too much to ask from map librarians/curators, some sort of web 2.0 environment is sought where comments about data quality, completeness and up-to-dateness from knowledgeable map users regarding the specific maps or map series studied can be collected and tagged to scanned versions of these maps on the web. In order not to be subject to the same disadvantages as Wikipedia, where the ‘communis opinio’ rather than scholarship, seems to be decisive, some checking by map curators of this tagged map use information would still be needed. Cooperation between map curators and the International Cartographic Association ( ICA map and spatial data use commission to this end is suggested.

Automated first-principles mapping for phase-change materials.

Science.gov (United States)

Esser, Marc; Maintz, Stefan; Dronskowski, Richard

2017-04-05

Plotting materials on bi-coordinate maps according to physically meaningful descriptors has a successful tradition in computational solid-state science spanning more than four decades. Equipped with new ab initio techniques introduced in this work, we generate an improved version of the treasure map for phase-change materials (PCMs) as introduced previously by Lencer et al. which, other than before, charts all industrially used PCMs correctly. Furthermore, we suggest seven new PCM candidates, namely SiSb 4 Te 7 , Si 2 Sb 2 Te 5 , SiAs 2 Te 4 , PbAs 2 Te 4 , SiSb 2 Te 4 , Sn 2 As 2 Te 5 , and PbAs 4 Te 7 , to be used as synthetic targets. To realize aforementioned maps based on orbital mixing (or "hybridization") and ionicity coordinates, structural information was first included into an ab initio numerical descriptor for sp 3 orbital mixing and then generalized beyond high-symmetry structures. In addition, a simple, yet powerful quantum-mechanical ionization measure also including structural information was introduced. Taken together, these tools allow for (automatically) generating materials maps solely relying on first-principles calculations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

A NUMERICAL STUDY OF UNIVERSALITY AND SELF-SIMILARITY IN SOME FAMILIES OF FORCED LOGISTIC MAPS

NARCIS (Netherlands)

Rabassa, Pau; Jorba, Angel; Carles Tatjer, Joan

We explore different two-parametric families of quasi-periodically Forced Logistic Maps looking for universality and self-similarity properties. In the bifurcation diagram of the one-dimensional Logistic Map, it is well known that there exist parameter values s(n) where the 2(n)-periodic orbit is

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

International Nuclear Information System (INIS)

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

1997-01-01

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 1997 American Institute of Physics

Self-similarities of periodic structures for a discrete model of a two-gene system

International Nuclear Information System (INIS)

Souza, S.L.T. de; Lima, A.A.; Caldas, I.L.; Medrano-T, R.O.; Guimarães-Filho, Z.O.

2012-01-01

We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps. -- Highlights: ► The existence of noticeable periodic windows has been reported recently for several nonlinear systems. ► The periodic window distributions appear highly organized in two-parameter space. ► We characterize self-similar properties of Arnold tongues and shrimps for a two-gene model. ► We determine the period of the Arnold tongues recognizing a Fibonacci-type sequence. ► We explore self-similar features of the shrimps identifying multiple period-three structures.

Self-similarities of periodic structures for a discrete model of a two-gene system

Energy Technology Data Exchange (ETDEWEB)

Souza, S.L.T. de, E-mail: thomaz@ufsj.edu.br [Departamento de Física e Matemática, Universidade Federal de São João del-Rei, Ouro Branco, MG (Brazil); Lima, A.A. [Escola de Farmácia, Universidade Federal de Ouro Preto, Ouro Preto, MG (Brazil); Caldas, I.L. [Instituto de Física, Universidade de São Paulo, São Paulo, SP (Brazil); Medrano-T, R.O. [Departamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo, Diadema, SP (Brazil); Guimarães-Filho, Z.O. [Aix-Marseille Univ., CNRS PIIM UMR6633, International Institute for Fusion Science, Marseille (France)

2012-03-12

We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps. -- Highlights: ► The existence of noticeable periodic windows has been reported recently for several nonlinear systems. ► The periodic window distributions appear highly organized in two-parameter space. ► We characterize self-similar properties of Arnold tongues and shrimps for a two-gene model. ► We determine the period of the Arnold tongues recognizing a Fibonacci-type sequence. ► We explore self-similar features of the shrimps identifying multiple period-three structures.

A class of conservative Hamiltonians with exactly integrable discrete two-dimensional parametric maps

International Nuclear Information System (INIS)

Dikande, Alain M; Njumbe, E Epie

2010-01-01

A class of discrete conservative Hamiltonians with completely integrable two-dimensional (2D) mappings is constructed whose generic models are three families of non-integrable discrete Hamiltonians with on-site potentials whose double-well shapes vary. Unlike the discrete 2D mappings associated with the generic models, which all display pitchfork bifurcations towards randomly pinned states with chaotic features, for the derived models the pitchfork bifurcation leads to fixed points always surrounded by periodic trajectories. A nonlinear stability analysis reveals a finite crossover on the bifurcation line at which the pitchfork transition takes the maps from regular real periodic trajectories towards a regime dominated by a cluster of periodic point trajectories representing the allowed real solutions. The rich variety of structures displayed by the new class of discrete maps, combined with their complete integrability, offer rich perspectives for theoretical modelling of a wide class of systems undergoing structural instabilities without noticeable chaotic precursors.

Using periodic orbits to compute chaotic transport rates between resonance zones

Science.gov (United States)

Sattari, Sulimon; Mitchell, Kevin A.

2017-11-01

Transport properties of chaotic systems are computable from data extracted from periodic orbits. Given a sufficient number of periodic orbits, the escape rate can be computed using the spectral determinant, a function that incorporates the eigenvalues and periods of periodic orbits. The escape rate computed from periodic orbits converges to the true value as more and more periodic orbits are included. Escape from a given region of phase space can be computed by considering only periodic orbits that lie within the region. An accurate symbolic dynamics along with a corresponding partitioning of phase space is useful for systematically obtaining all periodic orbits up to a given period, to ensure that no important periodic orbits are missing in the computation. Homotopic lobe dynamics (HLD) is an automated technique for computing accurate partitions and symbolic dynamics for maps using the topological forcing of intersections of stable and unstable manifolds of a few periodic anchor orbits. In this study, we apply the HLD technique to compute symbolic dynamics and periodic orbits, which are then used to find escape rates from different regions of phase space for the Hénon map. We focus on computing escape rates in parameter ranges spanning hyperbolic plateaus, which are parameter intervals where the dynamics is hyperbolic and the symbolic dynamics does not change. After the periodic orbits are computed for a single parameter value within a hyperbolic plateau, periodic orbit continuation is used to compute periodic orbits over an interval that spans the hyperbolic plateau. The escape rates computed from a few thousand periodic orbits agree with escape rates computed from Monte Carlo simulations requiring hundreds of billions of orbits.

Probabilistic Flood Maps to support decision-making: Mapping the Value of Information

Science.gov (United States)

Alfonso, L.; Mukolwe, M. M.; Di Baldassarre, G.

2016-02-01

Floods are one of the most frequent and disruptive natural hazards that affect man. Annually, significant flood damage is documented worldwide. Flood mapping is a common preimpact flood hazard mitigation measure, for which advanced methods and tools (such as flood inundation models) are used to estimate potential flood extent maps that are used in spatial planning. However, these tools are affected, largely to an unknown degree, by both epistemic and aleatory uncertainty. Over the past few years, advances in uncertainty analysis with respect to flood inundation modeling show that it is appropriate to adopt Probabilistic Flood Maps (PFM) to account for uncertainty. However, the following question arises; how can probabilistic flood hazard information be incorporated into spatial planning? Thus, a consistent framework to incorporate PFMs into the decision-making is required. In this paper, a novel methodology based on Decision-Making under Uncertainty theories, in particular Value of Information (VOI) is proposed. Specifically, the methodology entails the use of a PFM to generate a VOI map, which highlights floodplain locations where additional information is valuable with respect to available floodplain management actions and their potential consequences. The methodology is illustrated with a simplified example and also applied to a real case study in the South of France, where a VOI map is analyzed on the basis of historical land use change decisions over a period of 26 years. Results show that uncertain flood hazard information encapsulated in PFMs can aid decision-making in floodplain planning.

Geologic mapping procedure: Final draft

International Nuclear Information System (INIS)

1987-09-01

Geologic mapping will provide a baseline record of the subsurface geology in the shafts and drifts of the Exploratory Shaft Facility (ESF). This information will be essential in confirming the specific repository horizon, selecting representative locations for the in situ tests, providing information for construction and decommissioning seal designs, documenting the excavation effects, and in providing information for performance assessment, which relates to the ultimate suitability of the site as a nuclear waste repository. Geologic mapping will be undertaken on the walls and roof, and locally on the floor within the completed At-Depth Facility (ADF) and on the walls of the two access shafts. Periodic mapping of the exposed face may be conducted during construction of the ADF. The mapping will be oriented toward the collection and presentation of geologic information in an engineering format and the portrayal of detailed stratigraphic information which may be useful in confirmation of drillhole data collected as part of the surface-based testing program. Geologic mapping can be considered as a predictive tool as well as a means of checking design assumptions. This document provides a description of the required procedures for geologic mapping for the ESF. Included in this procedure is information that qualified technical personnel can use to collect the required types of geologic descriptions, at the appropriate level of detail. 5 refs., 3 figs., 1 tab

Fuel loads and fuel type mapping

Science.gov (United States)

Chuvieco, Emilio; Riaño, David; Van Wagtendonk, Jan W.; Morsdof, Felix; Chuvieco, Emilio

2003-01-01

Correct description of fuel properties is critical to improve fire danger assessment and fire behaviour modeling, since they guide both fire ignition and fire propagation. This chapter deals with properties of fuel that can be considered static in short periods of time: biomass loads, plant geometry, compactness, etc. Mapping these properties require a detail knowledge of vegetation vertical and horizontal structure. Several systems to classify the great diversity of vegetation characteristics in few fuel types are described, as well as methods for mapping them with special emphasis on those based on remote sensing images.

Mapping Nursing language terms of Parkinson's disease

Directory of Open Access Journals (Sweden)

Michelle Hyczy de Siqueira Tosin

2015-06-01

Full Text Available OBJECTIVE Implementing cross-mapping of Nursing language terms with the terminology of NANDA International, contained in records of patients with Parkinson's disease in rehabilitation. METHOD Descriptive study of cross mapping, carried out in three steps. A simple random sample of 67 files of patients who participated in the rehabilitation in the period between March 2009 and April 2013. RESULTS We identified 454 terms of Nursing language that resulted in 54 diagnoses after cross-mapping, present in 11 of the 13 taxonomy domains. The most mapped diagnosis was "Impaired urinary elimination" (59.7%, followed by "Urgent urinary incontinence" (55.2%, "Willingness to self-control improved health" (50.7%, "Constipation" (47.8% and "Compromised physical mobility" (29.9%. Seven described terms were not mapped due to a corresponding defining characteristic being absent. CONCLUSION It was possible to determine the profile of patients, as well as the complexity of nursing care in the rehabilitation of patients with Parkinson's disease.

Mapping Deviant Democracy

DEFF Research Database (Denmark)

Seeberg, Michael

2014-01-01

A number of countries have emerged as stable (though minimalist) democracies despite low levels of modernization, lack of democratic neighbouring countries and other factors consistently related to democratic stability in the literature. The study of these deviant democracies is a promising new...... research field but it is afflicted by a notable problem, viz. the lack of a consensus as to which countries are actually instances of deviant democracy. The present article attempts to solve this problem by carrying out a comprehensive mapping of deviant democracies. First, I review the existing literature...... to provide an overview of the cases most often identified as deviant democracies. Second, I use a large-N analysis to systematically map deviant democracies. The analysis includes 159 countries covering the time period 1993–2008. The analysis points to 12 cases that merits further attention, viz...

Using periodic modulation to control coexisting attractors induced by delayed feedback

International Nuclear Information System (INIS)

Martinez-Zerega, B.E.; Pisarchik, A.N.; Tsimring, L.S.

2003-01-01

A delay in feedback can stabilize simultaneously several unstable periodic orbits embedded in a chaotic attractor. We show that by modulating the feedback variable it is possible to lock one of these states and eliminate other coexisting periodic attractors. The method is demonstrated with both a logistic map and a CO 2 laser model

K-decompositions and 3d gauge theories

Science.gov (United States)

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.

The Hopf algebra structure of the character rings of classical groups

International Nuclear Information System (INIS)

Fauser, Bertfried; Jarvis, Peter D; King, Ronald C

2013-01-01

The character ring Char-GL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra Symm-Λ of symmetric functions. Here we study the character rings Char-O and Char-Sp of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions. We show that Char-O and Char-Sp also admit natural Hopf algebra structures that are isomorphic to that of Char-GL, and hence to Symm-Λ. The isomorphisms are determined explicitly, along with the specification of standard bases for Char-O and Char-Sp analogous to those used for Symm-Λ. A major structural change arising from the adoption of these bases is the introduction of new orthogonal and symplectic Schur–Hall scalar products. Significantly, the adjoint with respect to multiplication no longer coincides, as it does in the Char-GL case, with a Foulkes derivative or skew operation. The adjoint and Foulkes derivative now require separate definitions, and their properties are explored here in the orthogonal and symplectic cases. Moreover, the Hopf algebras Char-O and Char-Sp are not self-dual. The dual Hopf algebras Char-O * and Char-Sp are identified. Finally, the Hopf algebra of the universal rational character ring Char-GLrat of mixed irreducible tensor representations of the general linear group is introduced and its structure maps identified. (paper)

Fermat varieties and the periods of some hypersurfaces

NARCIS (Netherlands)

Looijenga, Eduard

2010-01-01

The variety of all smooth hypersurfaces of given degree and dimension has the Fermat hypersurface as a natural base point. In order to study the period map for such varieties, we first determine the integral polarized Hodge structure of the primitive cohomology of a Fermat hypersurface (as a module

Mapping and Naming the Moon

Science.gov (United States)

Whitaker, Ewen A.

2003-12-01

Preface; Introduction; Part I. First Era: From Prehistoric Images to Archetype Map: 1. Pre-telescopic lunar observations; 2. Early telescopic observations of the Moon; 3. Van Langren (Langrenus) and the birth of selenography; 4. Six more years of sporadic activity; Part II. Second Era: From Archetype to Maturity: 5. 140 years of sporadic activity; 6. A globe, tree rings, and a city; 7. Lunar cartography comes of age; Part III. Third Era: From proliferation to standardisation: 8. Lunar mapping in the Victorian period; 9. Nomenclature gets international attention; Part IV. The Space Age Demands Changes: 10. Setting up guidelines; 11. Planets and satellites set the rules. Appendices 1 - 22.

Ethnic Maps: Between Reality and Propaganda

Directory of Open Access Journals (Sweden)

Mladen Klemenčić

2006-12-01

Full Text Available Ethnic maps provide insight into the ethnically complex populations of certain areas. They are a cartographic way of portraying a part of geographic reality. Southeastern Europe appears as an ideal area for ethnic maps drawers: there is a variety of different ethnic groups living in a relatively small area. Moreover, political boundaries often do not correspond with so-called ethnic borders, i.e. divisions between majority areas of different nations and/or ethnic groups. The history of South-Eastern Europe offers a number of examples of ethnic maps drawing and their use in political context. The paper focused on ethnic maps drawn and published in the context of the break-up of Yugoslav federation during the first half of the 1990’s. The maps were produced mainly by scientific institutions or under the supervision of such institutions or experts, but always with the specific goal to back and justify political standpoints of their respective country's governments during a turbulent period of geopolitical change and transition. Generally, figures and statistics were presented professionally and correctly. Map authors and compilers did not try to falsify figures. The degree of intent in mapmaking is registered primarily through the choice of cartographic technique, including certain elements of the map design (choice of colours. In that regard, one can identify a technique favoured by Croatian sources (pie charts and another one often used by Serbian mapmakers (choropleth maps. Maps were understood to be powerful media tools and influential visual images that could be used to create a particular perception.

A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps

International Nuclear Information System (INIS)

Behnia, S.; Akhshani, A.; Ahadpour, S.; Mahmodi, H.; Akhavan, A.

2007-01-01

In recent years, a growing number of discrete chaotic cryptographic algorithms have been proposed. However, most of them encounter some problems such as the lack of robustness and security. In this Letter, we introduce a new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps. The system is a measurable dynamical system with an interesting property of being either ergodic or having stable period-one fixed point. They bifurcate from a stable single periodic state to chaotic one and vice versa without having usual period-doubling or period-n-tippling scenario. Also, we present the KS-entropy of this maps with respect to control parameter. This algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security

Introduction to "Mapping Vietnameseness"

Directory of Open Access Journals (Sweden)

Hue-Tam Ho Tai

2016-09-01

Full Text Available Vietnam and China are currently engaged in a map war, with each country using ancient maps to buttress its claims to territorial sovereignty over some uninhabited islands in the South China Sea (in Chinese terminology, also known as the Eastern Sea (in Vietnamese. But what do maps in fact represent? What is meant by “territory”? How are territorial limits conceived? These questions were raised in a May 2015 workshop inspired by Thongchai Winichakul’s Siam Mapped: A History of the Geo-Body of a Nation (1994, a groundbreaking book that traces the transformation of Thai geographical consciousness as a result of Siam’s encounter with Western powers in the nineteenth century. While many of Thongchai’s insights apply to the Vietnamese case, as the first of the three articles included in this special issue of Cross-Currents shows, some of the 2015 workshop participants’ conclusions departed from his, especially regarding the formation of a Vietnamese geographical consciousness before the colonial period.[i] This is true of the other two papers, which focus specifically on the construction of borders and the associated production of maps in the nineteenth century before French colonial conquest... Notes 1 Thanks are due to the Max Planck Institute for the Study of Religious and Ethnic Change in Gottingen, Germany, for its gracious hosting and generous funding of the conference, together with the Asia Center of Harvard University.

Pulsation properties of Mira long period variables

International Nuclear Information System (INIS)

Cahn, J.H.

1980-01-01

A matter of great interest to variable star students concerns the mode of pulsation of Mira long period variables. In this report we first give observational evidence for the pulsation constant Q. We then compare the observations with calculations. Next, we review two interesting groups of papers dealing with hydrodynamic properties of long period variables. In the first, a fully dynamic nonlinear calculation maps out the Mira instability domain. In the second, special attention is paid to shock propagation beyond the photosphere which in large measure accounts for the complex spectra from this region. (orig./WL)

Duality and self-duality (energy reflection symmetry) of quasi-exactly solvable periodic potentials

International Nuclear Information System (INIS)

Dunne, Gerald V.; Shifman, M.

2002-01-01

A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential. The self-dual point of this transformation corresponds to the energy-reflection symmetry found previously for certain QES systems. The duality transformation interchanges bands at the bottom (top) of the spectrum of one potential with gaps at the top (bottom) of the spectrum of the other, dual, potential. Thus, the duality transformation provides an exact mapping between the weak coupling (perturbative) and semiclassical (nonperturbative) sectors

Pseudo random number generator based on quantum chaotic map

Science.gov (United States)

Akhshani, A.; Akhavan, A.; Mobaraki, A.; Lim, S.-C.; Hassan, Z.

2014-01-01

For many years dissipative quantum maps were widely used as informative models of quantum chaos. In this paper, a new scheme for generating good pseudo-random numbers (PRNG), based on quantum logistic map is proposed. Note that the PRNG merely relies on the equations used in the quantum chaotic map. The algorithm is not complex, which does not impose high requirement on computer hardware and thus computation speed is fast. In order to face the challenge of using the proposed PRNG in quantum cryptography and other practical applications, the proposed PRNG is subjected to statistical tests using well-known test suites such as NIST, DIEHARD, ENT and TestU01. The results of the statistical tests were promising, as the proposed PRNG successfully passed all these tests. Moreover, the degree of non-periodicity of the chaotic sequences of the quantum map is investigated through the Scale index technique. The obtained result shows that, the sequence is more non-periodic. From these results it can be concluded that, the new scheme can generate a high percentage of usable pseudo-random numbers for simulation and other applications in scientific computing.

Picard-Fuchs uniformization and modularity of the mirror map

International Nuclear Information System (INIS)

Doran, C.F.

2000-01-01

Arithmetic properties of mirror symmetry (type IIA-IIB string duality) are studied. We give criteria for the mirror map q-series of certain families of Calabi-Yau manifolds to be automorphic functions. For families of elliptic curves and lattice polarized K3 surfaces with surjective period mappings, global Torelli theorems allow one to present these criteria in terms of the ramification behavior of natural algebraic invariants - the functional and generalized functional invariants respectively. In particular, when applied to one parameter families of rank 19 lattice polarized K3 surfaces, our criterion demystifies the mirror-Moonshine phenomenon of Lian and Yau and highlights its non-monstrous nature. The lack of global Torelli theorems and presence of instanton corrections makes Calabi-Yau threefold families more complicated. Via the constraints of special geometry, the Picard-Fuchs equations for one parameter families of Calabi-Yau threefolds imply a differential equation criterion for automorphicity of the mirror map in terms of the Yukawa coupling. In the absence of instanton corrections, the projective periods map to a twisted cubic space curve. A hierarchy of ''algebraic'' instanton corrections correlated with the differential Galois group of the Picard-Fuchs equation is proposed. (orig.)

Stochastic Urban Pluvial Flood Hazard Maps Based upon a Spatial-Temporal Rainfall Generator

Directory of Open Access Journals (Sweden)

Nuno Eduardo Simões

2015-06-01

Full Text Available It is a common practice to assign the return period of a given storm event to the urban pluvial flood event that such storm generates. However, this approach may be inappropriate as rainfall events with the same return period can produce different urban pluvial flooding events, i.e., with different associated flood extent, water levels and return periods. This depends on the characteristics of the rainfall events, such as spatial variability, and on other characteristics of the sewer system and the catchment. To address this, the paper presents an innovative contribution to produce stochastic urban pluvial flood hazard maps. A stochastic rainfall generator for urban-scale applications was employed to generate an ensemble of spatially—and temporally—variable design storms with similar return period. These were used as input to the urban drainage model of a pilot urban catchment (~9 km2 located in London, UK. Stochastic flood hazard maps were generated through a frequency analysis of the flooding generated by the various storm events. The stochastic flood hazard maps obtained show that rainfall spatial-temporal variability is an important factor in the estimation of flood likelihood in urban areas. Moreover, as compared to the flood hazard maps obtained by using a single spatially-uniform storm event, the stochastic maps generated in this study provide a more comprehensive assessment of flood hazard which enables better informed flood risk management decisions.

Areas activated during naturalistic reading comprehension overlap topological visual, auditory, and somatotomotor maps.

Science.gov (United States)

Sood, Mariam R; Sereno, Martin I

2016-08-01

Cortical mapping techniques using fMRI have been instrumental in identifying the boundaries of topological (neighbor-preserving) maps in early sensory areas. The presence of topological maps beyond early sensory areas raises the possibility that they might play a significant role in other cognitive systems, and that topological mapping might help to delineate areas involved in higher cognitive processes. In this study, we combine surface-based visual, auditory, and somatomotor mapping methods with a naturalistic reading comprehension task in the same group of subjects to provide a qualitative and quantitative assessment of the cortical overlap between sensory-motor maps in all major sensory modalities, and reading processing regions. Our results suggest that cortical activation during naturalistic reading comprehension overlaps more extensively with topological sensory-motor maps than has been heretofore appreciated. Reading activation in regions adjacent to occipital lobe and inferior parietal lobe almost completely overlaps visual maps, whereas a significant portion of frontal activation for reading in dorsolateral and ventral prefrontal cortex overlaps both visual and auditory maps. Even classical language regions in superior temporal cortex are partially overlapped by topological visual and auditory maps. By contrast, the main overlap with somatomotor maps is restricted to a small region on the anterior bank of the central sulcus near the border between the face and hand representations of M-I. Hum Brain Mapp 37:2784-2810, 2016. © 2016 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc. © 2016 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

ETLMR: A Highly Scalable Dimensional ETL Framework based on MapReduce

DEFF Research Database (Denmark)

Xiufeng, Liu; Thomsen, Christian; Pedersen, Torben Bach

2011-01-01

Extract-Transform-Load (ETL) flows periodically populate data warehouses (DWs) with data from different source systems. An increasing challenge for ETL fl ows is processing huge volumes of data quickly. MapReduce is establishing itself as the de-facto standard for large-scale data-intensive process......Extract-Transform-Load (ETL) flows periodically populate data warehouses (DWs) with data from different source systems. An increasing challenge for ETL fl ows is processing huge volumes of data quickly. MapReduce is establishing itself as the de-facto standard for large-scale data...

Multilayered tori in a system of two coupled logistic maps

DEFF Research Database (Denmark)

Zhusubaliyev, Zhanybai; Mosekilde, Erik

2009-01-01

of two coupled logistic maps through period-doubling or pitchfork bifurcations of the saddle cycle on an ordinary resonance torus. We hereafter present two different scenarios by which a multilayered torus can be destructed. One scenario involves a cascade of period-doubling bifurcations of both...

The Periodic Table. Physical Science in Action[TM]. Schlessinger Science Library. [Videotape].

Science.gov (United States)

2000

Kids know that when they are lost, they look at a map to find their way. It's no different in the world of science, as they'll learn in The Periodic Table--a fun and engaging look at the road map of the elements. Young students will learn about key information included on the table, including atomic number, atomic mass and chemical symbol. They'll…

Conductance maps of quantum rings due to a local potential perturbation.

Science.gov (United States)

Petrović, M D; Peeters, F M; Chaves, A; Farias, G A

2013-12-11

We performed a numerical simulation of the dynamics of a Gaussian shaped wavepacket inside a small sized quantum ring, smoothly connected to two leads and exposed to a perturbing potential of a biased atomic force microscope tip. Using the Landauer formalism, we calculated conductance maps of this system in the case of single and two subband transport. We explain the main features in the conductance maps as due to the AFM tip influence on the wavepacket phase and amplitude. In the presence of an external magnetic field, the tip modifies the ϕ0 periodic Aharonov-Bohm oscillation pattern into a ϕ0/2 periodic Al'tshuler-Aronov-Spivak oscillation pattern. Our results in the case of multiband transport suggest tip selectivity to higher subbands, making them more observable in the total conductance map.

Periodic solutions of Volterra integral equations

Directory of Open Access Journals (Sweden)

M. N. Islam

1988-01-01

Full Text Available Consider the system of equationsx(t=f(t+∫−∞tk(t,sx(sds,           (1andx(t=f(t+∫−∞tk(t,sg(s,x(sds.       (2Existence of continuous periodic solutions of (1 is shown using the resolvent function of the kernel k. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1 it is necessary that the resolvent of k is integrable in some sense. For a scalar convolution kernel k some explicit conditions are derived to determine whether or not the resolvent of k is integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1 and (2 are btained using the contraction mapping principle as the basic tool.

International Map Year: Results and Implications

Science.gov (United States)

Rystedt, Bengt; Ormeling, Ferjan; Buckley, Aileen; Coetzee, Serena; Voženilek, Vit; Fairbairn, David; Kagawa, Ayako

2018-05-01

IMY was a worldwide celebration of maps and their unique role in our world. Supported by the United Nations, IMY provides opportunities to demonstrate, follow, and get involved in the art, science, and technology of making and using maps and geographic information. International Map Year (IMY) started in Paris 2011 when the General Assembly of the International Cartographic Association (ICA) asked the ICA Executive Committee (EC) to follow up on the proposal given in a motion from the Swedish Cartographic Society. An IMY Working Group (WG) was constituted - it defined the IMY goals and the activities required to reach them, and it proposed a suitable time period for the IMY to the ICA EC. IMY commenced in August 2015 and ended in December 2016. The success of IMY was dependent on all member nations of the ICA participating in an effort to broaden the knowledge of cartography and geographic information in society in general, especially among citizens and school children. Member nations of the ICA were responsible for organizing IMY activities, such as a national Map Day, through national IMY committees tasked to engage national organizations and spearheading collaboration. The IMY WG set up an IMY web site with general information on IMY, guidelines for how to organize Map Days, suggestions relating to activities aimed at general map awareness, and more. The web site also provides access to the electronic book The World of Maps, which has been translated from English into five other languages.

Vertex maps on graphs -- Perron-Frobenius Theory

OpenAIRE

Bernhardt, Chris

2015-01-01

The goal of this paper is to describe the connections between Perron-Frobenius theory and vertex maps on graphs. In particular, it is shown how Perron-Frobenius theory gives results about the sets of integers that can arise as periods of periodic orbits, about the concepts of transitivity and topological mixing, and about horseshoes and topological entropy. This is a preprint. The final version will appear in the Journal of Difference Equations and Applications.

Old maps in the GIS and Internet environment

Science.gov (United States)

Křováková, K.; Brůna, V.; Pacina, J.

2009-04-01

Old maps are moreover used as data layers in GIS environment, both in raster or vector form. By comparing data from several time periods we can identify the main trends in landscape development and its spatial structure. The Laboratory of geoinformatics at Jan Evangelista Purkyně University, Czech republic is working on several projects concerned about analysis and visualization of old maps. On the poster are presented results of some of the projects solved at the laboratory. One of the most successful project is the web-application http://oldmaps.geolab.cz - where are online presented old maps from the region of Bohemia, Moravia and Silesia. On this server are accessible maps of the 1st, 2nd and partially 3rd military mapping, Müller's map of Bohemia and a part of survey operator of Stabile cadastre. On the poster are as well presented results from the Historical atlas of Czech towns and results from project solved for the National Park of Šumava in the area of Chlum.

Schedule and complex motion of shuttle bus induced by periodic inflow of passengers

Science.gov (United States)

Nagatani, Takashi; Naito, Yuichi

2011-09-01

We have studied the dynamic behavior of a bus in the shuttle bus transportation with a periodic inflow. A bus schedule is closely related to the dynamics. We present the modified circle map model for the dynamics of the shuttle bus. The motion of the shuttle bus depends on the loading parameter and the inflow period. The shuttle bus displays the periodic, quasi-periodic, and chaotic motions with varying both loading parameter and inflow rate.

Mapping of the seasonal dynamic properties of building walls in actual periodic conditions and effects produced by solar radiation incident on the outer and inner surfaces of the wall

International Nuclear Information System (INIS)

Mazzeo, D.; Oliveti, G.; Arcuri, N.

2016-01-01

Highlights: • Dynamic thermal behaviour of building walls subjected to actual periodic loadings. • Dynamic parameters of wall in terms of energy and of heat flux are defined. • Different solar absorption coefficients and orientations of wall are considered. • On the internal surface is present or absent a shortwave radiant field. • Seasonal thermal characteristics for different plant operating regime are provided. - Abstract: In this work, the dynamic characteristics of the external walls of air-conditioned buildings subject to the joint action of periodic non-sinusoidal external and internal loadings are determined. The dynamic parameters used are the energy decrement factor, which is evaluated by means of the fluctuating heat flux in a semi-period exiting and entering the wall, the decrement factor of the maximum peak and minimum peak of the heat flux in a period and the relative time lags. The fluctuating heat flux in the wall in steady periodic regime conditions is determined with an analytical model obtained by resolving the equivalent electrical circuit. The preceding parameters are used for a study of the influence of solar radiation on the dynamic characteristics of the walls in summer and winter air-conditioning. Solar radiation is considered as operating on the external surface and on the internal surface due to the presence in the indoor environments of a shortwave radiant field. The absorbed solar heat flux by the external surface varies, modifying the solar absorption coefficient and wall orientation. Indoors, we considered a continuous operating regime of the plant and a regime with nocturnal attenuation. The results obtained, relating to 1152 different boundary conditions, were used for the construction of maps of dynamic characteristics, different on variation of the plant functioning regime and of the shortwave radiant load on the internal surface. The maps show the dependence of the decrement factors and of the time lags on variation of

Planetary Geologic Mapping Handbook - 2009

Science.gov (United States)

Tanaka, K. L.; Skinner, J. A.; Hare, T. M.

2009-01-01

. Terrestrial geologic maps published by the USGS now are primarily digital products using geographic information system (GIS) software and file formats. GIS mapping tools permit easy spatial comparison, generation, importation, manipulation, and analysis of multiple raster image, gridded, and vector data sets. GIS software has also permitted the development of project-specific tools and the sharing of geospatial products among researchers. GIS approaches are now being used in planetary geologic mapping as well (e.g., Hare and others, 2009). Guidelines or handbooks on techniques in planetary geologic mapping have been developed periodically (e.g., Wilhelms, 1972, 1990; Tanaka and others, 1994). As records of the heritage of mapping methods and data, these remain extremely useful guides. However, many of the fundamental aspects of earlier mapping handbooks have evolved significantly, and a comprehensive review of currently accepted mapping methodologies is now warranted. As documented in this handbook, such a review incorporates additional guidelines developed in recent years for planetary geologic mapping by the NASA Planetary Geology and Geophysics (PGG) Program s Planetary Cartography and Geologic Mapping Working Group s (PCGMWG) Geologic Mapping Subcommittee (GEMS) on the selection and use of map bases as well as map preparation, review, publication, and distribution. In light of the current boom in planetary exploration and the ongoing rapid evolution of available data for planetary mapping, this handbook is especially timely.

Transitions from phase-locked dynamics to chaos in a piecewise-linear map

DEFF Research Database (Denmark)

Zhusubaliyev, Z.T.; Mosekilde, Erik; De, S.

2008-01-01

place via border-collision fold bifurcations. We examine the transition to chaos through torus destruction in such maps. Considering a piecewise-linear normal-form map we show that this transition, by virtue of the interplay of border-collision bifurcations with period-doubling and homoclinic...

Poisson-Lie T-duality open strings and D-branes

CERN Document Server

Klimcik, C.

1996-01-01

Global issues of the Poisson-Lie T-duality are addressed. It is shown that oriented open strings propagating on a group manifold G are dual to D-brane - anti-D-brane pairs propagating on the dual group manifold \\ti G. The D-branes coincide with the symplectic leaves of the standard Poisson structure induced on the dual group \\ti G by the dressing action of the group G. T-duality maps the momentum of the open string into the mutual distance of the D-branes in the pair. The whole picture is then extended to the full modular space M(D) of the Poisson-Lie equivalent \\si-models which is the space of all Manin triples of a given Drinfeld double.T-duality rotates the zero modes of pairs of D-branes living on targets belonging to M(D). In this more general case the D-branes are preimages of symplectic leaves in certain Poisson homogeneous spaces of their targets and, as such, they are either all even or all odd dimensional.

Stabilization of the quasi-periodic motion of a Q-switched Nd:YAG laser

International Nuclear Information System (INIS)

Kim, Chil-Min; Rim, Sunghwan; Kye, Won-Ho; Kim, Jeong-Moog; Lee, Kang-Soo

2004-01-01

We have developed a stabilization method of quasi-periodicity based on a return map. The method is explained in the forced Van der Pol oscillator, and applied experimentally to a quasi-periodic output of a Q-switched Nd:YAG laser. Even though the attractors have no unstable periodic orbit, we were able to stabilize them to an arbitrarily chosen orbit by targeting the trajectory into it

What is an evidence map? A systematic review of published evidence maps and their definitions, methods, and products.

Science.gov (United States)

Miake-Lye, Isomi M; Hempel, Susanne; Shanman, Roberta; Shekelle, Paul G

2016-02-10

The need for systematic methods for reviewing evidence is continuously increasing. Evidence mapping is one emerging method. There are no authoritative recommendations for what constitutes an evidence map or what methods should be used, and anecdotal evidence suggests heterogeneity in both. Our objectives are to identify published evidence maps and to compare and contrast the presented definitions of evidence mapping, the domains used to classify data in evidence maps, and the form the evidence map takes. We conducted a systematic review of publications that presented results with a process termed "evidence mapping" or included a figure called an "evidence map." We identified publications from searches of ten databases through 8/21/2015, reference mining, and consulting topic experts. We abstracted the research question, the unit of analysis, the search methods and search period covered, and the country of origin. Data were narratively synthesized. Thirty-nine publications met inclusion criteria. Published evidence maps varied in their definition and the form of the evidence map. Of the 31 definitions provided, 67 % described the purpose as identification of gaps and 58 % referenced a stakeholder engagement process or user-friendly product. All evidence maps explicitly used a systematic approach to evidence synthesis. Twenty-six publications referred to a figure or table explicitly called an "evidence map," eight referred to an online database as the evidence map, and five stated they used a mapping methodology but did not present a visual depiction of the evidence. The principal conclusion of our evaluation of studies that call themselves "evidence maps" is that the implied definition of what constitutes an evidence map is a systematic search of a broad field to identify gaps in knowledge and/or future research needs that presents results in a user-friendly format, often a visual figure or graph, or a searchable database. Foundational work is needed to better

Meteorological circumstances during the 'Chernobyl-period'

International Nuclear Information System (INIS)

Ivens, R.; Lablans, W.N.; Wessels, H.R.A.

1987-01-01

The progress of the meteorological circumstances and air flows in Europe from 26th April up to 8th May 1986, which caused the spread of contaminated air originating from Chernobyl is outlined and mapped out. Furthermore a global survey is presented of the precipitation in the Netherlands during the period 2nd May to 10th May based on observations of various observation stations of the Royal Dutch Meteorologic Institute (KNMI). 11 figs.; 1 table (H.W.)

Advanced Map For Real-Time Process Control

Science.gov (United States)

Shiobara, Yasuhisa; Matsudaira, Takayuki; Sashida, Yoshio; Chikuma, Makoto

1987-10-01

MAP, a communications protocol for factory automation proposed by General Motors [1], has been accepted by users throughout the world and is rapidly becoming a user standard. In fact, it is now a LAN standard for factory automation. MAP is intended to interconnect different devices, such as computers and programmable devices, made by different manufacturers, enabling them to exchange information. It is based on the OSI intercomputer com-munications protocol standard under development by the ISO. With progress and standardization, MAP is being investigated for application to process control fields other than factory automation [2]. The transmission response time of the network system and centralized management of data exchanged with various devices for distributed control are import-ant in the case of a real-time process control with programmable controllers, computers, and instruments connected to a LAN system. MAP/EPA and MINI MAP aim at reduced overhead in protocol processing and enhanced transmission response. If applied to real-time process control, a protocol based on point-to-point and request-response transactions limits throughput and transmission response. This paper describes an advanced MAP LAN system applied to real-time process control by adding a new data transmission control that performs multicasting communication voluntarily and periodically in the priority order of data to be exchanged.

GIS-aided low flow mapping

Science.gov (United States)

Saghafian, B.; Mohammadi, A.

2003-04-01

Most studies involving water resources allocation, water quality, hydropower generation, and allowable water withdrawal and transfer require estimation of low flows. Normally, frequency analysis on at-station D-day low flow data is performed to derive various T-yr return period values. However, this analysis is restricted to the location of hydrometric stations where the flow discharge is measured. Regional analysis is therefore conducted to relate the at-station low flow quantiles to watershed characteristics. This enables the transposition of low flow quantiles to ungauged sites. Nevertheless, a procedure to map the regional regression relations for the entire stream network, within the bounds of the relations, is particularly helpful when one studies and weighs alternative sites for certain water resources project. In this study, we used a GIS-aided procedure for low flow mapping in Gilan province, part of northern region in Iran. Gilan enjoys a humid climate with an average of 1100 mm annual precipitation. Although rich in water resources, the highly populated area is quite dependent on minimum amount of water to sustain the vast rice farming and to maintain required flow discharge for quality purposes. To carry out the low flow analysis, a total of 36 hydrometric stations with sufficient and reliable discharge data were identified in the region. The average area of the watersheds was 250 sq. km. Log Pearson type 3 was found the best distribution for flow durations over 60 days, while log normal fitted well the shorter duration series. Low flows with return periods of 2, 5, 10, 25, 50, and 100 year were then computed. Cluster analysis identified two homogeneous areas. Although various watershed parameters were examined in factor analysis, the results showed watershed area, length of the main stream, and annual precipitation were the most effective low flow parameters. The regression equations were then mapped with the aid of GIS based on flow accumulation maps

Projective geometry for polarization in geometric quantization

International Nuclear Information System (INIS)

Campbell, P.; Dodson, C.T.J.

1976-12-01

It is important to know the extent to which the procedure of geometric quantization depends on a choice of polarization of the symplectic manifold that is the classical phase space. Published results have so far been restricted to real and transversal polarizations. Here we also consider these cases by presenting a formulation in terms of projective geometry. It turns out that there is a natural characterization of real transversal polarizations and maps among them using projective concepts. We give explicit constructions for Rsup(2n)

Planetary Geologic Mapping Handbook - 2010. Appendix

Science.gov (United States)

Tanaka, K. L.; Skinner, J. A., Jr.; Hare, T. M.

2010-01-01

the USGS now are primarily digital products using geographic information system (GIS) software and file formats. GIS mapping tools permit easy spatial comparison, generation, importation, manipulation, and analysis of multiple raster image, gridded, and vector data sets. GIS software has also permitted the development of projectspecific tools and the sharing of geospatial products among researchers. GIS approaches are now being used in planetary geologic mapping as well. Guidelines or handbooks on techniques in planetary geologic mapping have been developed periodically. As records of the heritage of mapping methods and data, these remain extremely useful guides. However, many of the fundamental aspects of earlier mapping handbooks have evolved significantly, and a comprehensive review of currently accepted mapping methodologies is now warranted. As documented in this handbook, such a review incorporates additional guidelines developed in recent years for planetary geologic mapping by the NASA Planetary Geology and Geophysics (PGG) Program's Planetary Cartography and Geologic Mapping Working Group's (PCGMWG) Geologic Mapping Subcommittee (GEMS) on the selection and use of map bases as well as map preparation, review, publication, and distribution. In light of the current boom in planetary exploration and the ongoing rapid evolution of available data for planetary mapping, this handbook is especially timely.

Symmetries of noncommutative scalar field theory

International Nuclear Information System (INIS)

De Goursac, Axel; Wallet, Jean-Christophe

2011-01-01

We investigate symmetries of the scalar field theory with a harmonic term on the Moyal space with the Euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on the symplectic structure. We find that the invariance under the orthogonal group can also be restored at the quantum level by restricting the symplectic structures to a particular orbit.

Analytical determination of bifurcations of periodic solution in three-degree-of-freedom vibro-impact systems with clearance

International Nuclear Information System (INIS)

Liu, Yongbao; Wang, Qiang; Xu, Huidong

2017-01-01

The smooth bifurcation and non-smooth grazing bifurcation of periodic solution of three-degree-of-freedom vibro-impact systems with clearance are studied in this paper. Firstly, six-dimensional Poincaré maps are established through choosing suitable Poincaré section and solving periodic solutions of vibro-impact system. Then, as the analytic expressions of all eigenvalues of Jacobi matrix of six-dimensional map are unavailable, the numerical calculations to search for the critical bifurcation values point by point is a laborious job based on the classical critical criterion described by the properties of eigenvalues. To overcome the difficulty from the classical bifurcation criteria, the explicit critical criterion without using eigenvalues calculation of high-dimensional map is applied to determine bifurcation points of Co-dimension-one bifurcations and Co-dimension-two bifurcations, and then local dynamical behaviors of these bifurcations are further analyzed. Finally, the existence of the grazing periodic solution of the vibro-impact system and grazing bifurcation point are analyzed, the discontinuous grazing bifurcation behavior is studied based on the compound normal form map near the grazing point, the discontinuous jumping phenomenon and the co-existing multiple solutions near the grazing bifurcation point are revealed.

Baecklund transformations as exact integrable time discretizations for the trigonometric Gaudin model

International Nuclear Information System (INIS)

Ragnisco, Orlando; Zullo, Federico

2010-01-01

We construct a two-parameter family of Baecklund transformations for the trigonometric classical Gaudin magnet. The approach follows closely the one introduced by Sklyanin and Kuznetsov (1998 J. Phys. A: Math. Gen. 31 2241-51) in a number of seminal papers and takes advantage of the intimate relation between the trigonometric and the rational case. As in the paper by Hone, Kuznetsov and one of the authors (OR) (2001 J. Phys. A: Math. Gen. 34 2477-90) the Baecklund transformations are presented as explicit symplectic maps, starting from their Lax representation. The (expected) connection with the xxz Heisenberg chain is established and the rational (xxx) case is recovered in a suitable limit. It is shown how to obtain a 'physical' transformation mapping real variables into real variables. The interpolating Hamiltonian flow is derived and some numerical iterations of the map are presented.

Mapped Fourier Methods for stiff problems in toroidal geometry

OpenAIRE

Guillard , Herve

2014-01-01

Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this makes the Fourier method unpractical in many cases. This work investigates the use of mapped Fourier method as a way to circumvent this problem. Mapped Fourier method uses instead of the usual Fourier interpolant the compositio...

Movie-maps of low-latitude magnetic storm disturbance

Science.gov (United States)

Love, Jeffrey J.; Gannon, Jennifer L.

2010-06-01

We present 29 movie-maps of low-latitude horizontal-intensity magnetic disturbance for the years 1999-2006: 28 recording magnetic storms and 1 magnetically quiescent period. The movie-maps are derived from magnetic vector time series data collected at up to 25 ground-based observatories. Using a technique similar to that used in the calculation of Dst, a quiet time baseline is subtracted from the time series from each observatory. The remaining disturbance time series are shown in a polar coordinate system that accommodates both Earth rotation and the universal time dependence of magnetospheric disturbance. Each magnetic storm recorded in the movie-maps is different. While some standard interpretations about the storm time equatorial ring current appear to apply to certain moments and certain phases of some storms, the movie-maps also show substantial variety in the local time distribution of low-latitude magnetic disturbance, especially during storm commencements and storm main phases. All movie-maps are available at the U.S. Geological Survey Geomagnetism Program Web site (http://geomag.usgs.gov).

Japanese Mapping of Asia-Pacific Areas, 1873-1945: An Overview

Directory of Open Access Journals (Sweden)

Shigeru Kobayashi

2012-03-01

Full Text Available Japanese mapping in the Asia-Pacific region up to 1945 calls for scrutiny, because its development was a multifaceted process with military, administrative, political, and cultural dimensions. This article traces the changes in Japanese mapping of overseas areas to the end of World War II and assesses the significance of the resulting maps, called gaihōzu, as sources for East Asian history. As implements of military operation and colonial administration, the gaihōzu were produced during a protracted period by various means under changing circumstances. Expanding military activity also promoted differentiation among the gaihōzu by increasing the use of maps originally produced in foreign countries. In conclusion, the need for detailed cataloging, in combination with chronologically arranged index mapping, is emphasized for the systematic use of the gaihōzu.

Analysis of family-wise error rates in statistical parametric mapping using random field theory.

Science.gov (United States)

Flandin, Guillaume; Friston, Karl J

2017-11-01

This technical report revisits the analysis of family-wise error rates in statistical parametric mapping-using random field theory-reported in (Eklund et al. []: arXiv 1511.01863). Contrary to the understandable spin that these sorts of analyses attract, a review of their results suggests that they endorse the use of parametric assumptions-and random field theory-in the analysis of functional neuroimaging data. We briefly rehearse the advantages parametric analyses offer over nonparametric alternatives and then unpack the implications of (Eklund et al. []: arXiv 1511.01863) for parametric procedures. Hum Brain Mapp, 2017. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Periodic-impact motions and bifurcations in dynamics of a plastic impact oscillator with a frictional slider

International Nuclear Information System (INIS)

Luo, G.W.; Lv, X.H.; Ma, L.

2008-01-01

A two-degree-of-freedom plastic impact oscillator with a frictional slider is considered. Dynamics of the plastic impact oscillator are analyzed by a three-dimensional map, which describes free flight and sticking solutions of two masses of the system, between impacts, supplemented by transition conditions at the instants of impacts. Piecewise property and singularity are found to exist in the impact Poincare map. The piecewise property of the map is caused by the transitions of free flight and sticking motions of two masses immediately after the impact, and the singularity of the map is generated via the grazing contact of two masses immediately before the impact. These properties of the map have been shown to exhibit particular types of sliding and grazing bifurcations of periodic-impact motions under parameter variation. The influence of piecewise property, grazing singularity and parameter variation on dynamics of the vibro-impact system is analyzed. The global bifurcation diagrams of before-impact velocity as a function of the excitation frequency are plotted to predict much of the qualitative behavior of the system. The global bifurcations of period-N single-impact motions of the plastic impact oscillator are found to exhibit extensive and systematic characteristics. Dynamics of the impact oscillator, in the elastic impact case, is also analyzed. This type of impact is modelled by using the conditions of conservation of momentum and an instantaneous coefficient of restitution rule. The differences in periodic-impact motions and bifurcations are found by making a comparison between dynamic behaviors of the plastic and elastic impact oscillators with a frictional slider. The best progression of the plastic impact oscillator is found to occur in period-1 single-impact sticking motion with large impact velocity. The largest progression of the elastic impact oscillator occurs in period-1 multi-impact motion. The simulative results show that the plastic impact

Experience mapping and multifunctional golf course development

DEFF Research Database (Denmark)

Caspersen, Ole H.; Jensen, Frank Søndergaard; Jensen, Anne Mette Dahl

This report describes the development of a method for mapping and describing recreational experiences on golf courses. The objective is to provide a planning tool that can facilitate development of a broader multifunctional use of the golf course landscape. The project has produced several results....... The main output is this report, which provides a detailed description of the mapping procedure. This process is illustrated using examples from five test golf courses. In addition to this mapping report, a catalogue has been developed providing hands-on guidance for adapting the method in a golf club...... without the use of a specialist. During the project period, the research team has participated in a number of workshops that included representatives from golf courses, STERF, the Norwegian Golf Federation and the Danish Golf Union. At these workshops, the method was presented and discussed. This has been...

Global Geological Map of Venus

Science.gov (United States)

Ivanov, M. A.

2008-09-01

bias [35], appear to affect the statistics of the smaller craters on Venus. For the larger craters, these factors appear to be less important and craters >8 km were used to estimate the crater density on mapped units. The shape and size of occurrences of units may also affect the crater statistics on Venus where the total number of craters is small. To minimize influence of this factor the crater density on large and contiguous units that have quasiequidimensional occurrences was estimated. Sometimes, the small total number of craters on Venus impels to combine some units into one in order to increase the crater statistics. The generally similar nature of the heavily tectonized units (t, pdl, pr, gb) and their consistent relationships with the vast plains units permit to combine them into one, the tectonized terrains unit. Both units of regional plains were also combined. Thus, craters were counted on five units: tt (tectonized terrains: t+pdl+pr+gb), psh, rp (rp1+rp2), pl, and rt that make up ~95.8% of the map area. The mean densities (craters per 106km2) of craters on these units are as follow: tt 1.70 (±0.27, two σ); psh: 1.62 (±0.28); rp: 1.63 (±0.18); pl: 0.84 (±0.29); rt: 0.98 (±0.40). The mean density of craters (>8 km) in the map area (all units) is 1.56. If the mean crater density corresponds to the mean surface age, T [19], then the ages of the above units as fractions of T are: tt: 1.09 (±0.17, two σ) T, psh: 1.04 (±0.18) T, rp: 1.05 (±0.12) T, pl: 0.54 (±0.19) T, rt: 0.63 (±0.26) T. These results are consistent with the observed stratigraphic relationships and suggest that the visible stratigraphic record consists of two periods: Fortunian, which includes units from tessera to regional plains (densely clustered around 1.06 T) and Atlian, during which smooth and lobate plains and rift zones were emplaced. These units formed during significantly longer time interval from ~1 T and perhaps to the present. The exposed (minimal) area of the Fortunian

Southern European ionospheric TEC maps based on Kriging technique to monitor ionosphere behavior

Science.gov (United States)

Rodríguez-Bouza, Marta; Paparini, Claudia; Otero, Xurxo; Herraiz, Miguel; Radicella, Sandro M.; Abe, Oladipo E.; Rodríguez-Caderot, Gracia

2017-10-01

Global or regional Maps of the ionospheric Total Electron Content (TEC) are an efficient tool to monitor the delay introduced by the ionosphere in the satellite signals. Ionospheric disturbance periods are of particular interest because these conditions can strongly affect satellite navigation range measurements. This work presents post-processing regional vertical TEC maps over Southern Europe ([35°N-50°N] latitude) obtained by applying Kriging interpolation to GPS derived TEC over more than 100 Global Navigation Satellite System (GNSS) stations. These maps are used to study the behavior of the ionosphere during space weather events and their effects. To validate these maps, hereafter called Southern European Ionospheric Maps (SEIMs), their TEC values have been compared with those obtained from EGNOS Message Server (EMS) and with direct experimental TEC data from GNSS stations. Ionospheric space weather events related to geomagnetic storms of March 17th, 2013, February 19th, 2014 and March 17th, 2015 have been selected. To test the methodology, one period of quiet days has been also analyzed. TEC values obtained by SEIMs in the Ionospheric Grid Points (IGPs) defined by EGNOS are very close to those given by EMS and in the period of major geomagnetic storms the difference does not exceed 6 TEC units. These results confirm the good performance of the technique used for obtaining the SEIMs that can be a useful tool to study the ionosphere behavior during geomagnetic storms and their effects in the region of interest.

Crime clocks and target performance maps

CSIR Research Space (South Africa)

Cooper, Antony K

1999-12-01

Full Text Available the period of analysis. Each segment of a pie chart represents a selected part of the day (eg: a two- or three-hour period) or a day of the week. The first and last segments in the day or week are then adjacent, ensuring that there is no artificial break... clocks We have also used crime clocks to map the proportion of crimes that occur during normal police working hours (07:00 to 16:00, Monday to Friday, in the case of the Johannesburg Area), against those that occur outside these hours. 3. Target...

Evaluation of flood hazard maps in print and web mapping services as information tools in flood risk communication

Science.gov (United States)

Hagemeier-Klose, M.; Wagner, K.

2009-04-01

Flood risk communication with the general public and the population at risk is getting increasingly important for flood risk management, especially as a precautionary measure. This is also underlined by the EU Flood Directive. The flood related authorities therefore have to develop adjusted information tools which meet the demands of different user groups. This article presents the formative evaluation of flood hazard maps and web mapping services according to the specific requirements and needs of the general public using the dynamic-transactional approach as a theoretical framework. The evaluation was done by a mixture of different methods; an analysis of existing tools, a creative workshop with experts and laymen and an online survey. The currently existing flood hazard maps or web mapping services or web GIS still lack a good balance between simplicity and complexity with adequate readability and usability for the public. Well designed and associative maps (e.g. using blue colours for water depths) which can be compared with past local flood events and which can create empathy in viewers, can help to raise awareness, to heighten the activity and knowledge level or can lead to further information seeking. Concerning web mapping services, a linkage between general flood information like flood extents of different scenarios and corresponding water depths and real time information like gauge levels is an important demand by users. Gauge levels of these scenarios are easier to understand than the scientifically correct return periods or annualities. The recently developed Bavarian web mapping service tries to integrate these requirements.

Evaluation of flood hazard maps in print and web mapping services as information tools in flood risk communication

Directory of Open Access Journals (Sweden)

M. Hagemeier-Klose

2009-04-01

Full Text Available Flood risk communication with the general public and the population at risk is getting increasingly important for flood risk management, especially as a precautionary measure. This is also underlined by the EU Flood Directive. The flood related authorities therefore have to develop adjusted information tools which meet the demands of different user groups. This article presents the formative evaluation of flood hazard maps and web mapping services according to the specific requirements and needs of the general public using the dynamic-transactional approach as a theoretical framework. The evaluation was done by a mixture of different methods; an analysis of existing tools, a creative workshop with experts and laymen and an online survey.

The currently existing flood hazard maps or web mapping services or web GIS still lack a good balance between simplicity and complexity with adequate readability and usability for the public. Well designed and associative maps (e.g. using blue colours for water depths which can be compared with past local flood events and which can create empathy in viewers, can help to raise awareness, to heighten the activity and knowledge level or can lead to further information seeking. Concerning web mapping services, a linkage between general flood information like flood extents of different scenarios and corresponding water depths and real time information like gauge levels is an important demand by users. Gauge levels of these scenarios are easier to understand than the scientifically correct return periods or annualities. The recently developed Bavarian web mapping service tries to integrate these requirements.

BAC-HAPPY mapping (BAP mapping: a new and efficient protocol for physical mapping.

Directory of Open Access Journals (Sweden)

Giang T H Vu

2010-02-01

Full Text Available Physical and linkage mapping underpin efforts to sequence and characterize the genomes of eukaryotic organisms by providing a skeleton framework for whole genome assembly. Hitherto, linkage and physical "contig" maps were generated independently prior to merging. Here, we develop a new and easy method, BAC HAPPY MAPPING (BAP mapping, that utilizes BAC library pools as a HAPPY mapping panel together with an Mbp-sized DNA panel to integrate the linkage and physical mapping efforts into one pipeline. Using Arabidopsis thaliana as an exemplar, a set of 40 Sequence Tagged Site (STS markers spanning approximately 10% of chromosome 4 were simultaneously assembled onto a BAP map compiled using both a series of BAC pools each comprising 0.7x genome coverage and dilute (0.7x genome samples of sheared genomic DNA. The resultant BAP map overcomes the need for polymorphic loci to separate genetic loci by recombination and allows physical mapping in segments of suppressed recombination that are difficult to analyze using traditional mapping techniques. Even virtual "BAC-HAPPY-mapping" to convert BAC landing data into BAC linkage contigs is possible.

Poincare' maps of impulsed oscillators and two-dimensional dynamics

International Nuclear Information System (INIS)

Lupini, R.; Lenci, S.; Gardini, L.; Urbino Univ.

1996-01-01

The Poincare' map of one-dimensional linear oscillators subject to periodic, non-linear and time-delayed impulses is shown to reduce to a family of plane maps with possible non-uniqueness of the inverse. By restricting the analysis to a convenient form of the impulse function, a variety of interesting dynamical behaviours in this family are pointed out, including multistability and homoclinic bifurcations. Critical curves of two-dimensional endomorphisms are used to identify the structure of absorbing areas and their bifurcations

Periodic motions and chaos for a damped mobile piston system in a high pressure gas cylinder with P control

International Nuclear Information System (INIS)

Wang, Donghua; Huang, Jianzhe

2017-01-01

In this paper, the complex motions for a moving piston in a closed gas cylinder will be analyzed using the discrete implicit maps method. The strong nonlinearity of such system will be observed due to the large quadratic and cubic stiffness. Period-1 motions which contain high order of harmonic components will be presented. The periodic motions will be discretized into multiple continuous mappings, and such mapping can be analyzed via Newton–Raphson iteration. The stability analysis will be given and the analytic conditions for the saddle-node and period-doubling bifurcation will be determined. From the semi-analytic solution route, the possible motions without considering the impact of the piston with the end wall of the cylinder will be obtained analytically. The scheme to reduce the vibration of the piston can be obtained through the parameter studies.

Mapping specific soil functions based on digital soil property maps

Science.gov (United States)

Pásztor, László; Fodor, Nándor; Farkas-Iványi, Kinga; Szabó, József; Bakacsi, Zsófia; Koós, Sándor

2016-04-01

climatic conditions in the Carpathian Basin. In addition to soil fertility, degradation risk due to N-leaching was also assessed by the model runs by taking into account the movement of nitrate in the profile during the simulated periods. Our paper will present the resulted national maps and some conclusions drawn from the experiences. Acknowledgement: Our work was supported by Iceland, Liechtenstein and Norway through the EEA Grants and the REC (Project No: EEA C12-12) and the Hungarian National Scientific Research Foundation (OTKA, Grant No. K105167).

Applications of polyfold theory I

CERN Document Server

Hofer, H; Zehnder, E

2017-01-01

In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyfold theory the authors use the results of the present paper to describe an alternative construction of the Gromov-Witten invariants for general compact symplectic manifolds.

Inland excess water mapping using hyperspectral imagery

Directory of Open Access Journals (Sweden)

Csendes Bálint

2016-01-01

Full Text Available Hyperspectral imaging combined with the potentials of airborne scanning is a powerful tool to monitor environmental processes. The aim of this research was to use high resolution remotely sensed data to map the spatial extent of inland excess water patches in a Hungarian study area that is known for its oil and gas production facilities. Periodic floodings show high spatial and temporal variability, nevertheless, former studies have proven that the affected soil surfaces can be accurately identified. Besides separability measurements, we performed spectral angle classification, which gave a result of 85% overall accuracy and we also compared the generated land cover map with LIDAR elevation data.

The topology of toric origami manifolds

OpenAIRE

Holm, Tara; Pires, Ana Rita

2012-01-01

A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin and Pires, who classified toric origami manifolds by combinatorial origami templates. In this paper, we examine the topology of toric origami manifolds that have acyclic origami template and co-orientable folding hypersurface. We prove that the cohomology i...

A sympletic formulation of relativistic particle dynamics

International Nuclear Information System (INIS)

Tulczyjew, W.M.

1977-01-01

Particle mechanics is formulated in terms of sympletic relations and infinitesimal symplectic relations. Generating functions of symplectic relations are shown to be classical counterparts of Green's functions of wave mechanics. (author)

Geological hazards investigation - relative slope stability map

Energy Technology Data Exchange (ETDEWEB)

Han, Dae Suk; Kim, Won Young; Yu, Il Hyon; Kim, Kyeong Su; Lee, Sa Ro; Choi, Young Sup [Korea Institute of Geology Mining and Materials, Taejon (Korea, Republic of)

1997-12-01

The Republic of Korea is a mountainous country; the mountains occupy about three quarters of her land area, an increasing urban development being taken place along the mountainside. For the reason, planners as well as developers and others must realize that some of the urban areas may be threaten by geologic hazards such as landslides and accelerated soil and rock creeps. For the purpose of environmental land-use planning, a mapping project on relative slope-stability was established in 1996. The selected area encompasses about 5,900 km{sup 2} including the topographic maps of Ulsan, Yongchon, Kyongju, Pulguksa, and Kampo, all at a scale of 1:50,000. Many disturbed and undisturbed soil samples, which were collected from the ares of the landslides and unstable slopes, were tested for their physical properties and shear strength. They were classified as GC, SP, SC, SM, SP-SM, SC-SM, CL, ML, and MH according to the Unified Soil Classification System, their liquid limit and plasticity index ranging from 25.3% to as high as 81.3% and from 4.1% to 41.5%, respectively. X-ray analysis revealed that many of the soils contained a certain amount of montmorillonite. Based on the available information as well as both field and laboratory investigation, it was found out that the most common types of slope failures in the study area were both debris and mud flows induced by the heavy rainfalls during the period of rainy season; the flows mostly occurred in the colluvial deposits at the middle and foot of mountains. Thus the deposits generally appear to be the most unstable slope forming materials in the study area. Produced for the study area were six different maps consisting of slope classification map, soil classification map, lineament density map, landslide distribution map, zonal map of rainfall, and geology map, most of them being stored as data base. Using the first four maps and GIS, two sheets of relative slope-stability maps were constructed, each at a scale of 1

Brain mapping in tumors: intraoperative or extraoperative?

Science.gov (United States)

Duffau, Hugues

2013-12-01

In nontumoral epilepsy surgery, the main goal for all preoperative investigation is to first determine the epileptogenic zone, and then to analyze its relation to eloquent cortex, in order to control seizures while avoiding adverse postoperative neurologic outcome. To this end, in addition to neuropsychological assessment, functional neuroimaging and scalp electroencephalography, extraoperative recording, and electrical mapping, especially using subdural strip- or grid-electrodes, has been reported extensively. Nonetheless, in tumoral epilepsy surgery, the rationale is different. Indeed, the first aim is rather to maximize the extent of tumor resection while minimizing postsurgical morbidity, in order to increase the median survival as well as to preserve quality of life. As a consequence, as frequently seen in infiltrating tumors such as gliomas, where these lesions not only grow but also migrate along white matter tracts, the resection should be performed according to functional boundaries both at cortical and subcortical levels. With this in mind, extraoperative mapping by strips/grids is often not sufficient in tumoral surgery, since in essence, it allows study of the cortex but cannot map subcortical pathways. Therefore, intraoperative electrostimulation mapping, especially in awake patients, is more appropriate in tumor surgery, because this technique allows real-time detection of areas crucial for cerebral functions--eloquent cortex and fibers--throughout the resection. In summary, rather than choosing one or the other of different mapping techniques, methodology should be adapted to each pathology, that is, extraoperative mapping in nontumoral epilepsy surgery and intraoperative mapping in tumoral surgery. Wiley Periodicals, Inc. © 2013 International League Against Epilepsy.

The necessity of flood risk maps on Timis River

International Nuclear Information System (INIS)

Aldescu, Geogr Catalin

2008-01-01

The paper aims to clarify the necessity of risk reduction in flood prone areas along the Timis River. Different methods to reduce risk in flood prone areas are analyzed as well. According to the EU Flood Directive it is mandatory for the European countries to develop flood maps and flood risk maps. The maps help to assess the vulnerable zones in the floodable (i.e. flood prone) areas. Many European countries have produced maps which identify areas prone to flooding events for specific known return periods. In Romania the flood risk maps have not been yet produced, but the process has been started to be implemented at the national and regional level, therefore the first results will be soon available. Banat Hydrographical Area was affected by severe floods on Timis River in 2000, 2005 and 2006. The 2005 flood was the most devastating one with large economic losses. As a result of these catastrophes the need for generating flood risk maps along the Timis. River was clearly stated. The water management experts can use these maps in order to identify the 'hot spots' in Timis catchment, give the people a better understanding of flood risk issues and help reducing flood risk more efficient in the identified vulnerable areas.

Maps & minds : mapping through the ages

Science.gov (United States)

,

1984-01-01

Throughout time, maps have expressed our understanding of our world. Human affairs have been influenced strongly by the quality of maps available to us at the major turning points in our history. "Maps & Minds" traces the ebb and flow of a few central ideas in the mainstream of mapping. Our expanding knowledge of our cosmic neighborhood stems largely from a small number of simple but grand ideas, vigorously pursued.

Flood Hazard Mapping using Hydraulic Model and GIS: A Case Study in Mandalay City, Myanmar

Directory of Open Access Journals (Sweden)

Kyu Kyu Sein

2016-01-01

Full Text Available This paper presents the use of flood frequency analysis integrating with 1D Hydraulic model (HECRAS and Geographic Information System (GIS to prepare flood hazard maps of different return periods in Ayeyarwady River at Mandalay City in Myanmar. Gumbel’s distribution was used to calculate the flood peak of different return periods, namely, 10 years, 20 years, 50 years, and 100 years. The flood peak from frequency analysis were input into HEC-RAS model to find the corresponding flood level and extents in the study area. The model results were used in integrating with ArcGIS to generate flood plain maps. Flood depths and extents have been identified through flood plain maps. Analysis of 100 years return period flood plain map indicated that 157.88 km2 with the percentage of 17.54% is likely to be inundated. The predicted flood depth ranges varies from greater than 0 to 24 m in the flood plains and on the river. The range between 3 to 5 m were identified in the urban area of Chanayetharzan, Patheingyi, and Amarapua Townships. The highest inundated area was 85 km2 in the Amarapura Township.

Roebuck Bay Invertebrate and bird Mapping 2006

NARCIS (Netherlands)

Piersma, Theunis; Pearson, Grant B.; Hickey, Robert; Dittmann, Sabine; Rogers, Danny I.; Folmer, Eelke; Honkoop, Pieter; Drent, Jan; Goeij, Petra de; Marsh, Loisette

2006-01-01

1. This is a report on a survey of the benthic ecology of the intertidal flats along the northern shores of Roebuck Bay in June 2006. In the period 11-20 June we mapped both the invertebrate macrobenthic animals (those retained by a 1 mm sieve) over the whole of the northern intertidal area of

Mapping innovation processes: Visual techniques for opening and presenting the black box of service innovation processes

DEFF Research Database (Denmark)

Olesen, Anne Rørbæk

2017-01-01

This chapter argues for the usefulness of visual mapping techniques for performing qualitative analysis of complex service innovation processes. Different mapping formats are presented, namely, matrices, networks, process maps, situational analysis maps and temporal situational analysis maps....... For the purpose of researching service innovation processes, the three latter formats are argued to be particularly interesting. Process maps can give an overview of different periods and milestones in a process in one carefully organized location. Situational analysis maps and temporal situational analysis maps...... can open up complexities of service innovation processes, as well as close them down for presentational purposes. The mapping formats presented are illustrated by displaying maps from an exemplary research project, and the chapter is concluded with a brief discussion of the limitations and pitfalls...

The Seismotectonic Map of Africa

Science.gov (United States)

Meghraoui, Mustapha

2015-04-01

We present the Seismotectonic Map of Africa based on a geological, geophysical and geodetic database including the instrumental seismicity and re-appraisal of large historical events with harmonization and homogenization of earthquake parameters in catalogues. Although the seismotectonic framework and mapping of the African continent is a difficult task, several previous and ongoing projects provide a wealth of data and outstanding results. The database of large and moderate earthquakes in different geological domains includes the coseismic and Quaternary faulting that reveals the complex nature of the active tectonics in Africa. The map also benefits from previous works on local and regional seismotectonic maps that needed to be integrated with the lithospheric and upper mantle structures from tomographic anisotropy and gravity anomaly into a continental framework. The synthesis of earthquake and volcanic studies with the analysis of long-term (late Quaternary) and short-term (last decades and centuries) active deformation observed with geodetic and other approaches presented along with the seismotectonic map serves as a basis for hazard calculations and the reduction of seismic risks. The map may also be very useful in the assessment of seismic hazard and mitigation of earthquake risk for significant infrastructures and their implications in the socio-economic impact in Africa. In addition, the constant population increase and infrastructure growth in the continent that exacerbate the earthquake risk justify the necessity for a continuous updating of the seismotectonic map. The database and related map are prepared in the framework of the IGC Project-601 "Seismotectonics and Seismic Hazards in Africa" of UNESCO-IUGS, funded by the Swedish International Development Agency and UNESCO-Nairobi for a period of 4 years (2011 - 2014), extended to 2016. * Mustapha Meghraoui (Coordinator) EOST - IPG Strasbourg CNRS-UMR 7516 m.meghraoui@unistra.fr corresponding author

Differential maps, difference maps, interpolated maps, and long term prediction

International Nuclear Information System (INIS)

Talman, R.

1988-06-01

Mapping techniques may be thought to be attractive for the long term prediction of motion in accelerators, especially because a simple map can approximately represent an arbitrarily complicated lattice. The intention of this paper is to develop prejudices as to the validity of such methods by applying them to a simple, exactly solveable, example. It is shown that a numerical interpolation map, such as can be generated in the accelerator tracking program TEAPOT, predicts the evolution more accurately than an analytically derived differential map of the same order. Even so, in the presence of ''appreciable'' nonlinearity, it is shown to be impractical to achieve ''accurate'' prediction beyond some hundreds of cycles of oscillation. This suggests that the value of nonlinear maps is restricted to the parameterization of only the ''leading'' deviation from linearity. 41 refs., 6 figs

Remote landslide mapping using a laser rangefinder binocular and GPS

Directory of Open Access Journals (Sweden)

M. Santangelo

2010-12-01

Full Text Available We tested a high-quality laser rangefinder binocular coupled with a GPS receiver connected to a Tablet PC running dedicated software to help recognize and map in the field recent rainfall-induced landslides. The system was tested in the period between March and April 2010, in the Monte Castello di Vibio area, Umbria, Central Italy. To test the equipment, we measured thirteen slope failures that were mapped previously during a visual reconnaissance field campaign conducted in February and March 2010. For reference, four slope failures were also mapped by walking the GPS receiver along the landslide perimeter. Comparison of the different mappings revealed that the geographical information obtained remotely for each landslide by the rangefinder binocular and GPS was comparable to the information obtained by walking the GPS around the landslide perimeter, and was superior to the information obtained through the visual reconnaissance mapping. Although our tests were not exhaustive, we maintain that the system is effective to map recent rainfall induced landslides in the field, and we foresee the possibility of using the same (or similar system to map landslides, and other geomorphological features, in other areas.

Multiple bifurcations and periodic 'bubbling' in a delay population model

International Nuclear Information System (INIS)

Peng Mingshu

2005-01-01

In this paper, the flip bifurcation and periodic doubling bifurcations of a discrete population model without delay influence is firstly studied and the phenomenon of Feigenbaum's cascade of periodic doublings is also observed. Secondly, we explored the Neimark-Sacker bifurcation in the delay population model (two-dimension discrete dynamical systems) and the unique stable closed invariant curve which bifurcates from the nontrivial fixed point. Finally, a computer-assisted study for the delay population model is also delved into. Our computer simulation shows that the introduction of delay effect in a nonlinear difference equation derived from the logistic map leads to much richer dynamic behavior, such as stable node → stable focus → an lower-dimensional closed invariant curve (quasi-periodic solution, limit cycle) or/and stable periodic solutions → chaotic attractor by cascading bubbles (the combination of potential period doubling and reverse period-doubling) and the sudden change between two different attractors, etc

Bifurcations and Periodic Solutions for an Algae-Fish Semicontinuous System

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Chuanjun Dai

2013-01-01

Full Text Available We propose an algae-fish semicontinuous system for the Zeya Reservoir to study the control of algae, including biological and chemical controls. The bifurcation and periodic solutions of the system were studied using a Poincaré map and a geometric method. The existence of order-1 periodic solution of the system is discussed. Based on previous analysis, we investigated the change in the location of the order-1 periodic solution with variable parameters and we described the transcritical bifurcation of the system. Finally, we provided a series of numerical results to illustrate the feasibility of the theoretical results. These results may help to facilitate a better understanding of algal control in the Zeya Reservoir.

On Building and Processing of Large Digitalized Map Archive

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Milan Simunek

2011-07-01

Full Text Available A tall list of problems needs to be solved during a long-time work on a virtual model of Prague aim of which is to show historical development of the city in virtual reality. This paper presents an integrated solution to digitalizing, cataloguing and processing of a large number of maps from different periods and from variety of sources. A specialized (GIS software application was developed to allow for a fast georeferencing (using an evolutionary algorithm, for cataloguing in an internal database, and subsequently for an easy lookup of relevant maps. So the maps could be processed further to serve as a main input for a proper modeling of a changing face of the city through times.

Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

International Nuclear Information System (INIS)

Common, Alan K; Hone, Andrew N W

2008-01-01

The Yablonskii-Vorob'ev polynomials y n (t), which are defined by a second-order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painleve equation (P II ). Here we define two-variable polynomials Y n (t, h) on a lattice with spacing h, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when h = 0. They also provide rational solutions for a particular discretization of P II , namely the so-called alternate discrete P II , and this connection leads to an expression in terms of the Umemura polynomials for the third Painleve equation (P III ). It is shown that the Baecklund transformation for the alternate discrete Painleve equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete P II , which recovers Jimbo and Miwa's Lax pair for P II in the continuum limit h → 0

Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle

Science.gov (United States)

Wang, Hong

2017-09-01

In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.

The Poincaré compactification of the MIC-Kepler problem with positive energies

CERN Document Server

Iwai, T

2001-01-01

The Poincare compactification and the symplectic reduction methods are first reviewed and then used to study the behaviour at infinity of the MIC (McIntosh-Cisneros)-Kepler problem at positive energies. The hyperbolic orbits leave the unstable equilibrium point set at infinity and tend eventually to the stable equilibrium point set at infinity. Both of these equilibrium point sets are diffeomorphic with S/sup 2/, the unit sphere in R/sup 3/. The hyperbolic orbits determine a map of the unstable equilibrium point set to the stable equilibrium point set in such a manner that the initial point (or the limit point as t to - infinity ) of an orbit is mapped to its final point (or the limit point as t to infinity ). This map is found explicitly as a rotation matrix which depends on the energy and the angular momentum of the orbits. (9 refs).

Frequently updated noise threat maps created with use of supercomputing grid

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Szczodrak Maciej

2014-09-01

Full Text Available An innovative supercomputing grid services devoted to noise threat evaluation were presented. The services described in this paper concern two issues, first is related to the noise mapping, while the second one focuses on assessment of the noise dose and its influence on the human hearing system. The discussed serviceswere developed within the PL-Grid Plus Infrastructure which accumulates Polish academic supercomputer centers. Selected experimental results achieved by the usage of the services proposed were presented. The assessment of the environmental noise threats includes creation of the noise maps using either ofline or online data, acquired through a grid of the monitoring stations. A concept of estimation of the source model parameters based on the measured sound level for the purpose of creating frequently updated noise maps was presented. Connecting the noise mapping grid service with a distributed sensor network enables to automatically update noise maps for a specified time period. Moreover, a unique attribute of the developed software is the estimation of the auditory effects evoked by the exposure to noise. The estimation method uses a modified psychoacoustic model of hearing and is based on the calculated noise level values and on the given exposure period. Potential use scenarios of the grid services for research or educational purpose were introduced. Presentation of the results of predicted hearing threshold shift caused by exposure to excessive noise can raise the public awareness of the noise threats.

Meso(topoclimatic maps and mapping

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Ladislav Plánka

2007-06-01

Full Text Available The atmospheric characteristics can be studied from many points of view, most often we talk about time and spatial standpoint. Application of time standpoint leads either to different kinds of the synoptic and prognostic maps production, which presents actual state of atmosphere in short time section in the past or in the near future or to the climatic maps production which presents longterm weather regime. Spatial standpoint then differs map works according to natural phenomenon proportions, whereas the scale of their graphic presentation can be different. It depends on production purpose of each work.In the paper there are analysed methods of mapping and climatic maps production, which display longterm regime of chosen atmospheric features. These athmosphere features are formed in interaction with land surface and also have direct influence on people and their activities throughout the country. At the same time they’re influenced by anthropogenic intervention to the landscape.

Pascal (Yang Hui) triangles and power laws in the logistic map

International Nuclear Information System (INIS)

Velarde, Carlos; Robledo, Alberto

2015-01-01

We point out the joint occurrence of Pascal triangle patterns and power-law scaling in the standard logistic map, or more generally, in unimodal maps. It is known that these features are present in its two types of bifurcation cascades: period and chaotic-band doubling of attractors. Approximate Pascal triangles are exhibited by the sets of lengths of supercycle diameters and by the sets of widths of opening bands. Additionally, power-law scaling manifests along periodic attractor supercycle positions and chaotic band splitting points. Consequently, the attractor at the mutual accumulation point of the doubling cascades, the onset of chaos, displays both Gaussian and power-law distributions. Their combined existence implies both ordinary and exceptional statistical-mechanical descriptions of dynamical properties. (paper)