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Sample records for period symplectic maps

  1. Period mappings with applications to symplectic complex spaces

    CERN Document Server

    Kirschner, Tim

    2015-01-01

    Extending Griffiths’ classical theory of period mappings for compact Kähler manifolds, this book develops and applies a theory of period mappings of “Hodge-de Rham type” for families of open complex manifolds. The text consists of three parts. The first part develops the theory. The second part investigates the degeneration behavior of the relative Frölicher spectral sequence associated to a submersive morphism of complex manifolds. The third part applies the preceding material to the study of irreducible symplectic complex spaces. The latter notion generalizes the idea of an irreducible symplectic manifold, dubbed an irreducible hyperkähler manifold in differential geometry, to possibly singular spaces. The three parts of the work are of independent interest, but intertwine nicely.

  2. Singularity theory and equivariant symplectic maps

    CERN Document Server

    Bridges, Thomas J

    1993-01-01

    The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate student...

  3. Symplectic Maps from Cluster Algebras

    Directory of Open Access Journals (Sweden)

    Allan P. Fordy

    2011-09-01

    Full Text Available We consider nonlinear recurrences generated from the iteration of maps that arise from cluster algebras. More precisely, starting from a skew-symmetric integer matrix, or its corresponding quiver, one can define a set of mutation operations, as well as a set of associated cluster mutations that are applied to a set of affine coordinates (the cluster variables. Fordy and Marsh recently provided a complete classification of all such quivers that have a certain periodicity property under sequences of mutations. This periodicity implies that a suitable sequence of cluster mutations is precisely equivalent to iteration of a nonlinear recurrence relation. Here we explain briefly how to introduce a symplectic structure in this setting, which is preserved by a corresponding birational map (possibly on a space of lower dimension. We give examples of both integrable and non-integrable maps that arise from this construction. We use algebraic entropy as an approach to classifying integrable cases. The degrees of the iterates satisfy a tropical version of the map.

  4. Symplectic maps for accelerator lattices

    International Nuclear Information System (INIS)

    Warnock, R.L.; Ruth, R.; Gabella, W.

    1988-05-01

    We describe a method for numerical construction of a symplectic map for particle propagation in a general accelerator lattice. The generating function of the map is obtained by integrating the Hamilton-Jacobi equation as an initial-value problem on a finite time interval. Given the generating function, the map is put in explicit form by means of a Fourier inversion technique. We give an example which suggests that the method has promise. 9 refs., 9 figs

  5. Strongly stable real infinitesimally symplectic mappings

    NARCIS (Netherlands)

    Cushman, R.; Kelley, A.

    We prove that a mapA εsp(σ,R), the set of infinitesimally symplectic maps, is strongly stable if and only if its centralizerC(A) insp(σ,R) contains only semisimple elements. Using the theorem that everyB insp(σ,R) close toA is conjugate by a real symplectic map to an element ofC(A), we give a new

  6. Rotation number of integrable symplectic mappings of the plane

    Energy Technology Data Exchange (ETDEWEB)

    Zolkin, Timofey [Fermilab; Nagaitsev, Sergei [Fermilab; Danilov, Viatcheslav [Oak Ridge

    2017-04-11

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

  7. Characterization and solvability of quasipolynomial symplectic mappings

    Energy Technology Data Exchange (ETDEWEB)

    Hernandez-Bermejo, Benito [ESCET (Edificio Departamental II), Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933-Mostoles-Madrid (Spain); Brenig, Leon [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles, Campus Plaine, CP 231, Boulevard du Triomphe, B-1050 Brussels (Belgium)

    2004-02-13

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

  8. Characterization and solvability of quasipolynomial symplectic mappings

    International Nuclear Information System (INIS)

    Hernandez-Bermejo, Benito; Brenig, Leon

    2004-01-01

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

  9. Characterization and solvability of quasipolynomial symplectic mappings

    Science.gov (United States)

    Hernández-Bermejo, Benito; Brenig, Léon

    2004-02-01

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

  10. Invariant metric for nonlinear symplectic maps

    Indian Academy of Sciences (India)

    In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree (≥ 3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we ...

  11. An algorithm for symplectic implicit Taylor-map tracking

    International Nuclear Information System (INIS)

    Yan, Y.; Channell, P.; Syphers, M.

    1992-10-01

    An algorithm has been developed for converting an ''order-by-order symplectic'' Taylor map that is truncated to an arbitrary order (thus not exactly symplectic) into a Courant-Snyder matrix and a symplectic implicit Taylor map for symplectic tracking. This algorithm is implemented using differential algebras, and it is numerically stable and fast. Thus, lifetime charged-particle tracking for large hadron colliders, such as the Superconducting Super Collider, is now made possible

  12. Smooth Maps of a Foliated Manifold in a Symplectic Manifold

    Indian Academy of Sciences (India)

    Let be a smooth manifold with a regular foliation F and a 2-form which induces closed forms on the leaves of F in the leaf topology. A smooth map f : ( M , F ) ⟶ ( N , ) in a symplectic manifold ( N , ) is called a foliated symplectic immersion if restricts to an immersion on each leaf of the foliation and further, the ...

  13. Smooth maps of a foliated manifold in a symplectic manifold

    Indian Academy of Sciences (India)

    Abstract. Let M be a smooth manifold with a regular foliation F and a 2-form ω which induces closed forms on the leaves of F in the leaf topology. A smooth map f : (M, F) −→ (N,σ) in a symplectic manifold (N,σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the.

  14. Fast symplectic mapping and quasi-invariants for the Large Hadron Collider

    International Nuclear Information System (INIS)

    Warnock, R.L.; Berg, J.S.; Forest, E.

    1995-05-01

    Beginning with a tracking code for the LHC, we construct the canonical generator of the full-turn map in polar coordinates. For very fast mapping we adopt a model in which the momentum is modulated sinusoidally with a period of 130 turns (very close to the synchrotron period). We achieve symplectic mapping of 10 7 turns in 3.6 hours on a workstation. Quasi-invariant tori are constructed on the Poincare section corresponding to multiples of the synchrotron period. The possible use of quasi-invariants in derivin, long-term bounds on the motion is discussed

  15. Symplectic maps and chromatic optics in particle accelerators

    Energy Technology Data Exchange (ETDEWEB)

    Cai, Yunhai

    2015-10-11

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

  16. Symmetric integrable-polynomial factorization for symplectic one-turn-map tracking

    International Nuclear Information System (INIS)

    Shi, Jicong

    1993-01-01

    It was found that any homogeneous polynomial can be written as a sum of integrable polynomials of the same degree which Lie transformations can be evaluated exactly. By utilizing symplectic integrators, an integrable-polynomial factorization is developed to convert a symplectic map in the form of Dragt-Finn factorization into a product of Lie transformations associated with integrable polynomials. A small number of factorization bases of integrable polynomials enable one to use high order symplectic integrators so that the high-order spurious terms can be greatly suppressed. A symplectic map can thus be evaluated with desired accuracy

  17. From symplectic integrator to Poincare map: Spline expansion of a map generator in Cartesian coordinates

    International Nuclear Information System (INIS)

    Warnock, R.L.; Ellison, J.A.; Univ. of New Mexico, Albuquerque, NM

    1997-08-01

    Data from orbits of a symplectic integrator can be interpolated so as to construct an approximation to the generating function of a Poincare map. The time required to compute an orbit of the symplectic map induced by the generator can be much less than the time to follow the same orbit by symplectic integration. The construction has been carried out previously for full-turn maps of large particle accelerators, and a big saving in time (for instance a factor of 60) has been demonstrated. A shortcoming of the work to date arose from the use of canonical polar coordinates, which precluded map construction in small regions of phase space near coordinate singularities. This paper shows that Cartesian coordinates can also be used, thus avoiding singularities. The generator is represented in a basis of tensor product B-splines. Under weak conditions the spline expansion converges uniformly as the mesh is refined, approaching the exact generator of the Poincare map as defined by the symplectic integrator, in some parallelepiped of phase space centered at the origin

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

    Science.gov (United States)

    Karabegov, Alexander V.

    2004-10-01

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

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

    Science.gov (United States)

    Frejlich, Pedro; Mărcuț, Ioan

    2018-01-01

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

  20. Full-turn symplectic map from a generator in a Fourier-spline basis

    International Nuclear Information System (INIS)

    Berg, J.S.; Warnock, R.L.; Ruth, R.D.; Forest, E.

    1993-04-01

    Given an arbitrary symplectic tracking code, one can construct a full-turn symplectic map that approximates the result of the code to high accuracy. The map is defined implicitly by a mixed-variable generating function. The implicit definition is no great drawback in practice, thanks to an efficient use of Newton's method to solve for the explicit map at each iteration. The generator is represented by a Fourier series in angle variables, with coefficients given as B-spline functions of action variables. It is constructed by using results of single-turn tracking from many initial conditions. The method has been appliedto a realistic model of the SSC in three degrees of freedom. Orbits can be mapped symplectically for 10 7 turns on an IBM RS6000 model 320 workstation, in a run of about one day

  1. 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

  2. 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

  3. 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.

  4. 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

  5. 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

  6. 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

  7. 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.

  8. 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...

  9. 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...

  10. 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)

  11. 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

  12. 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.

  13. 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)

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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)

  19. 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

  20. 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...

  1. 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...

  2. 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.

  3. 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 ...

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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)

  10. 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.)

  11. 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.

  12. 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...

  13. 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

  14. 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

  15. 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...

  16. 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

  17. 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.

  18. 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...

  19. 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.

  20. 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...

  1. 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

  2. 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.

  3. 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

  4. 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.

  5. 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

  6. 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

  7. 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....

  8. 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

  9. 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

  10. 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...

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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)

  18. 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.

  19. 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

  20. 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

  1. 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...

  2. 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.

  3. 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

  4. 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.

  5. 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

  6. 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

  7. 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.

  8. 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

  9. 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

  10. 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.

  11. 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 .

  12. 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)

  13. 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)}.

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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....

  19. 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.

  20. 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

  1. 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

  2. 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.

  3. 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)

  4. 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.

  5. 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)

  6. 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

  7. 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.

  8. 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

  9. 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...

  10. 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.

  11. 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.

  12. 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.

  13. 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 ...

  14. 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

  15. 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...

  16. 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

  17. 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)

  18. 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.

  19. 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

  20. 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.

  1. 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....

  2. 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

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. 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)

  8. 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)

  9. 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.)

  10. 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.)

  11. 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.

  12. 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

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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)

  1. 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.

  2. 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)

  3. 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

  4. 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)

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.)

  13. 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.

  14. 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.

  15. 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.

  16. 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)

  17. 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.``

  18. 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.

  19. 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

  20. 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

  1. 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.

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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)

  7. 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.

  8. 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.

  9. 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)

  10. 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

  11. 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)

  12. 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)].

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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)

  20. 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.

  1. 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

  2. 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.

  3. 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)

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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)

  9. 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.

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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,...

  15. 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.

  16. 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.

  17. 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

  18. 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.

  19. 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)

  20. 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.

  1. 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.

  2. 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.

  3. 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)

  4. 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.

  5. 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.)

  6. 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.

  7. 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

  8. 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

  9. 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.

  10. 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.

  11. 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.)

  12. 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.

  13. 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)

  14. 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)

  15. 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.

  16. 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.

  17. 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....

  18. 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.

  19. Phenotypic Characterization and Genetic Dissection of Growth Period Traits in Soybean (Glycine max Using Association Mapping.

    Directory of Open Access Journals (Sweden)

    Zhangxiong Liu

    Full Text Available The growth period traits are important traits that affect soybean yield. The insights into the genetic basis of growth period traits can provide theoretical basis for cultivated area division, rational distribution, and molecular breeding for soybean varieties. In this study, genome-wide association analysis (GWAS was exploited to detect the quantitative trait loci (QTL for number of days to flowering (ETF, number of days from flowering to maturity (FTM, and number of days to maturity (ETM using 4032 single nucleotide polymorphism (SNP markers with 146 cultivars mainly from Northeast China. Results showed that abundant phenotypic variation was presented in the population, and variation explained by genotype, environment, and genotype by environment interaction were all significant for each trait. The whole accessions could be clearly clustered into two subpopulations based on their genetic relatedness, and accessions in the same group were almost from the same province. GWAS based on the unified mixed model identified 19 significant SNPs distributed on 11 soybean chromosomes, 12 of which can be consistently detected in both planting densities, and 5 of which were pleotropic QTL. Of 19 SNPs, 7 SNPs located in or close to the previously reported QTL or genes controlling growth period traits. The QTL identified with high resolution in this study will enrich our genomic understanding of growth period traits and could then be explored as genetic markers to be used in genomic applications in soybean breeding.

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. Mapping of the quasi-periodic oscillations at the flank magnetopause into the ionosphere

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    E. R. Dougal

    2013-11-01

    Full Text Available We have estimated the ionospheric location, area, and travel time of quasi-periodic oscillations originating from the magnetospheric flanks. This was accomplished by utilizing global and local MHD models and Tsyganenko semi-empirical magnetic field model on multiple published and four new cases believed to be caused by the Kelvin–Helmholtz Instability. Finally, we used auroral, magnetometer, and radar instruments to observe the ionospheric signatures. The ionospheric magnetic latitude determined using global MHD and Tsyganenko models ranged from 58.3–80.2 degrees in the Northern Hemisphere and −59.6 degrees to −83.4 degrees in the Southern Hemisphere. The ionospheric magnetic local time ranged between 5.0–13.8 h in the Northern Hemisphere and 1.3–11.9 h in the Southern Hemisphere. Typical Alfvén wave travel time from spacecraft location to the closest ionosphere ranged between 0.6–3.6 min. The projected ionospheric size calculated at an altitude of 100 km ranged from 47–606 km, the same order of magnitude as previously determined ionospheric signature sizes. Stationary and traveling convection vortices were observed in SuperDARN radar data in both hemispheres. The vortices were between 1000–1800 km in size. Some events were located within the ionospheric footprint ranges. Pc5 magnetic oscillations were observed in SuperMAG magnetometer data in both hemispheres. The oscillations had periods between 4–10 min with amplitudes of 3–25 nT. They were located within the ionospheric footprint ranges. Some ground magnetometer data power spectral density peaked at frequencies within one tenth of a mHz of the peaks found in the corresponding Cluster data. These magnetometer observations were consistent with previously published results.

  5. 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

  6. 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.

  7. 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)

  8. Mapping of Chagas disease research: analysis of publications in the period between 1940 and 2009

    Directory of Open Access Journals (Sweden)

    José Manuel Ramos

    2011-12-01

    Full Text Available INTRODUCTION: Publications are often used as a measure of success in research work. Chagas disease occurs in Central and Southern America. However, during the past years, the disease has been occurring outside Latin America due to migration from endemic zones. This article describes a bibliometric review of the literature on Chagas disease research indexed in PubMed during a 70-year period. METHODS: Medline was used via the PubMed online service of the U.S. National Library of Medicine from 1940 to 2009. The search strategy was: Chagas disease [MeSH] OR Trypanosoma cruzi [MeSH]. RESULTS: A total of 13,989 references were retrieved. The number of publications increased steadily over time from 1,361 (1940-1969 to 5,430 (2000-2009 (coefficient of determination for linear fit, R²=0.910. Eight journals contained 25% of the Chagas disease literature. Of the publications, 64.2% came from endemic countries. Brazil was the predominant country (37%, followed by the United States (17.6% and Argentina (14%. The ranking in production changed when the number of publications was normalized by estimated cases of Chagas disease (Panama and Uruguay, population (Argentina and Uruguay, and gross domestic product (Bolivia and Brazil. CONCLUSIONS: Several Latin American countries, where the prevalence of T. cruzi infection was not very high, were the main producers of the Chagas disease literature, after adjusting for economic and population indexes. The countries with more estimated cases of Chagas disease produced less research on Chagas disease than some developed countries.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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).

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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

  19. 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

  20. 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

  1. 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

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.)

  8. 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

  9. 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

  10. 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.

  11. 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.

  12. 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

  13. 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.

  14. 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

  15. 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.

  16. 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

  17. 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.

  18. 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

  19. 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)

  20. 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

  1. 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.

  2. 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.

  3. 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

  4. 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

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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)

  10. 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.

  11. 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.

  12. 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)

  13. A Forecasting Approach Combining Self-Organizing Map with Support Vector Regression for Reservoir Inflow during Typhoon Periods

    Directory of Open Access Journals (Sweden)

    Gwo-Fong Lin

    2016-01-01

    Full Text Available This study describes the development of a reservoir inflow forecasting model for typhoon events to improve short lead-time flood forecasting performance. To strengthen the forecasting ability of the original support vector machines (SVMs model, the self-organizing map (SOM is adopted to group inputs into different clusters in advance of the proposed SOM-SVM model. Two different input methods are proposed for the SVM-based forecasting method, namely, SOM-SVM1 and SOM-SVM2. The methods are applied to an actual reservoir watershed to determine the 1 to 3 h ahead inflow forecasts. For 1, 2, and 3 h ahead forecasts, improvements in mean coefficient of efficiency (MCE due to the clusters obtained from SOM-SVM1 are 21.5%, 18.5%, and 23.0%, respectively. Furthermore, improvement in MCE for SOM-SVM2 is 20.9%, 21.2%, and 35.4%, respectively. Another SOM-SVM2 model increases the SOM-SVM1 model for 1, 2, and 3 h ahead forecasts obtained improvement increases of 0.33%, 2.25%, and 10.08%, respectively. These results show that the performance of the proposed model can provide improved forecasts of hourly inflow, especially in the proposed SOM-SVM2 model. In conclusion, the proposed model, which considers limit and higher related inputs instead of all inputs, can generate better forecasts in different clusters than are generated from the SOM process. The SOM-SVM2 model is recommended as an alternative to the original SVR (Support Vector Regression model because of its accuracy and robustness.

  14. 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

  15. 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.

  16. 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)

  17. EVOLUTIONS OF THE OLYMPIC MOVEMENT UNDER THE INFLUENCE OF THE CHANGES ON THE WORLD POLITICAL MAP IN THE INTERWAR PERIOD

    Directory of Open Access Journals (Sweden)

    Vasile GRAMA

    2016-11-01

    Full Text Available The use of sports and politics has had both positive and negative implications over history. Sports competitions or activities have had the intention to bring about change in certain cases. Nationalistic fervor is sometimes linked to victories or losses to some sport on sports fields. Also, new independent countries need to be recognized on international arena, so participating at the Olympic Games, they become more visible and marginalization is broken. National feelings are boosted by some of the finest sports performances. The interwar period took politics to the sporting arena; when governments decided to control the sport and politics became more authoritative and states went on to find new ways to dominate the thinking process and imagination of their citizens. Fascist regimes developed techniques that allowed them to use achievements made in sporting arena to inspire people within their geographical boundaries and impress those beyond these boundaries. A fanatic love with sports was developed and through it, symbols of nationalist socialism were entrenched.

  18. 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.

  19. 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

  20. 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

  1. 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.

  2. 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

  3. 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

  4. 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.

  5. 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".

  6. 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.

  7. 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.

  8. 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)

  9. 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)

  10. 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.

  11. 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.

  12. 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.

  13. Mapping Annual Precipitation across Mainland China in the Period 2001–2010 from TRMM3B43 Product Using Spatial Downscaling Approach

    Directory of Open Access Journals (Sweden)

    Yuli Shi

    2015-05-01

    Full Text Available Spatially explicit precipitation data is often responsible for the prediction accuracy of hydrological and ecological models. Several statistical downscaling approaches have been developed to map precipitation at a high spatial resolution, which are mainly based on the valid conjugations between satellite-driven precipitation data and geospatial predictors. Performance of the existing approaches should be first evaluated before applying them to larger spatial extents with a complex terrain across different climate zones. In this paper, we investigate the statistical downscaling algorithms to derive the high spatial resolution maps of precipitation over continental China using satellite datasets, including the Normalized Distribution Vegetation Index (NDVI from the Moderate Resolution Imaging Spectroradiometer (MODIS, the Global Digital Elevation Model (GDEM from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER, and the rainfall product from the Tropical Rainfall Monitoring Mission (TRMM. We compare three statistical techniques (multiple linear regression, exponential regression, and Random Forest regression trees for modeling precipitation to better understand how the selected model types affect the prediction accuracy. Then, those models are implemented to downscale the original TRMM product (3B43; 0.25° resolution onto the finer grids (1 × 1 km2 of precipitation. Finally we validate the downscaled annual precipitation (a wet year 2001 and a dry year 2010 against the ground rainfall observations from 596 rain gauge stations over continental China. The result indicates that the downscaling algorithm based on the Random Forest regression outperforms, when compared to the linear regression and the exponential regression. It also shows that the addition of the residual terms does not significantly improve the accuracy of results for the RF model. The analysis of the variable importance reveals the NDVI related predictors

  14. 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

  15. 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.

  16. 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.

  17. Map showing Features and Displacements of the Scenic Drive Landslide, La Honda, California, During the Period March 31, 2005-November 5, 2006

    Science.gov (United States)

    Wells, Ray E.; Rymer, Michael J.; Prentice, Carol S.; Wheeler, Karen L.

    2006-01-01

    The Scenic Drive landslide in La Honda, San Mateo County, California began movement during the El Ni?o winter of 1997-98. Recurrent motion occurred during the mild El Ni?o winter of 2004-2005 and again during the winter of 2005-06. This report documents the changing geometry and motion of the Scenic Drive landslide in 2005-2006, and it documents changes and persistent features that we interpret to reflect underlying structural control of the landslide. We have also compared the displacement history to near-real time rainfall history at a continuously recording gauge for the period October 2004-November 2006.

  18. 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...

  19. 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.

  20. 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

  1. 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....

  2. 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.

  3. Problem Periods

    Science.gov (United States)

    ... ovary syndrome. Read our information on PCOS for teens , and see your doctor if you think you may have PCOS. Major weight loss. Girls who have anorexia will often stop having periods. When to see ...

  4. 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.

  5. 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.

  6. (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

  7. 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.

  8. 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...

  9. 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

  10. 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.

  11. 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.

  12. Topographic mapping

    Science.gov (United States)

    ,

    2008-01-01

    The U.S. Geological Survey (USGS) produced its first topographic map in 1879, the same year it was established. Today, more than 100 years and millions of map copies later, topographic mapping is still a central activity for the USGS. The topographic map remains an indispensable tool for government, science, industry, and leisure. Much has changed since early topographers traveled the unsettled West and carefully plotted the first USGS maps by hand. Advances in survey techniques, instrumentation, and design and printing technologies, as well as the use of aerial photography and satellite data, have dramatically improved mapping coverage, accuracy, and efficiency. Yet cartography, the art and science of mapping, may never before have undergone change more profound than today.

  13. 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.

  14. 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

  15. 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

  16. 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.

  17. Participatory Maps

    DEFF Research Database (Denmark)

    Salovaara-Moring, Inka

    2016-01-01

    practice. In particular, mapping environmental damage, endangered species, and human-made disasters has become one focal point for environmental knowledge production. This type of digital map has been highlighted as a processual turn in critical cartography, whereas in related computational journalism...... of a geo-visualization within information mapping that enhances embodiment in the experience of the information. InfoAmazonia is defined as a digitally created map-space within which journalistic practice can be seen as dynamic, performative interactions between journalists, ecosystems, space, and species...

  18. 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.

  19. Concept Mapping

    Science.gov (United States)

    Technology & Learning, 2005

    2005-01-01

    Concept maps are graphical ways of working with ideas and presenting information. They reveal patterns and relationships and help students to clarify their thinking, and to process, organize and prioritize. Displaying information visually--in concept maps, word webs, or diagrams--stimulates creativity. Being able to think logically teaches…

  20. Mapping racism.

    Science.gov (United States)

    Moss, Donald B

    2006-01-01

    The author uses the metaphor of mapping to illuminate a structural feature of racist thought, locating the degraded object along vertical and horizontal axes. These axes establish coordinates of hierarchy and of distance. With the coordinates in place, racist thought begins to seem grounded in natural processes. The other's identity becomes consolidated, and parochialism results. The use of this kind of mapping is illustrated via two patient vignettes. The author presents Freud's (1905, 1927) views in relation to such a "mapping" process, as well as Adorno's (1951) and Baldwin's (1965). Finally, the author conceptualizes the crucial status of primitivity in the workings of racist thought.

  1. Genetic Mapping

    Science.gov (United States)

    ... greatly advanced genetics research. The improved quality of genetic data has reduced the time required to identify a ... cases, a matter of months or even weeks. Genetic mapping data generated by the HGP's laboratories is freely accessible ...

  2. 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...

  3. MAPPING FLOW LOCALIZATION PROCESSES IN DEFORMATION OF IRRADIATED REACTOR STRUCTURAL ALLOYS - FINAL REPORT. Nuclear Energy Research Initiative Program No. MSF99-0072. Period: August 1999 through September 2002. (ORNL/TM-2003/63)

    Energy Technology Data Exchange (ETDEWEB)

    Farrell, K.

    2003-09-26

    Metals that can sustain plastic deformation homogeneously throughout their bulk tend to be tough and malleable. Often, however, if a metal has been hardened it will no longer deform uniformly. Instead, the deformation occurs in narrow bands on a microscopic scale wherein stresses and strains become concentrated in localized zones. This strain localization degrades the mechanical properties of the metal by causing premature plastic instability failure or by inducing the formation of cracks. Irradiation with neutrons hardens a metal and makes it more prone to deformation by strain localization. Although this has been known since the earliest days of radiation damage studies, a full measure of the connection between neutron irradiation hardening and strain localization is wanting, particularly in commercial alloys used in the construction of nuclear reactors. Therefore, the goal of this project is to systematically map the extent of involvement of strain localization processes in plastic deformation of three reactor alloys that have been neutron irradiated. The deformation processes are to be identified and related to changes in the tensile properties of the alloys as functions of neutron fluence (dose) and degree of plastic strain. The intent is to define the role of strain localization in radiation embrittlement phenomena. The three test materials are a tempered bainitic A533B steel, representing reactor pressure vessel steel, an annealed 316 stainless steel and annealed Zircaloy-4 representing reactor internal components. These three alloys cover the range of crystal structures usually encountered in structural alloys, i.e. body-centered cubic (bcc), face-centered cubic (fcc), and close-packed hexagonal (cph), respectively. The experiments were conducted in three Phases, corresponding to the three years duration of the project. Phases 1 and 2 addressed irradiations and tensile tests made at near-ambient temperatures, and covered a wide range of neutron fluences

  4. 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.

  5. Projective mapping

    DEFF Research Database (Denmark)

    Dehlholm, Christian; Brockhoff, Per B.; Bredie, Wender Laurentius Petrus

    2012-01-01

    by the practical testing environment. As a result of the changes, a reasonable assumption would be to question the consequences caused by the variations in method procedures. Here, the aim is to highlight the proven or hypothetic consequences of variations of Projective Mapping. Presented variations will include...... instructions and influence heavily the product placements and the descriptive vocabulary (Dehlholm et.al., 2012b). The type of assessors performing the method influences results with an extra aspect in Projective Mapping compared to more analytical tests, as the given spontaneous perceptions are much dependent......Projective Mapping (Risvik et.al., 1994) and its Napping (Pagès, 2003) variations have become increasingly popular in the sensory field for rapid collection of spontaneous product perceptions. It has been applied in variations which sometimes are caused by the purpose of the analysis and sometimes...

  6. Affective Maps

    DEFF Research Database (Denmark)

    Salovaara-Moring, Inka

    . In particular, mapping environmental damage, endangered species, and human made disasters has become one of the focal point of affective knowledge production. These ‘more-than-humangeographies’ practices include notions of species, space and territory, and movement towards a new political ecology. This type...... of digital cartographies has been highlighted as the ‘processual turn’ in critical cartography, whereas in related computational journalism it can be seen as an interactive and iterative process of mapping complex and fragile ecological developments. This paper looks at computer-assisted cartography as part...

  7. Energetic map

    International Nuclear Information System (INIS)

    2012-01-01

    This report explains the energetic map of Uruguay as well as the different systems that delimits political frontiers in the region. The electrical system importance is due to the electricity, oil and derived , natural gas, potential study, biofuels, wind and solar energy

  8. Necklace maps

    NARCIS (Netherlands)

    Speckmann, B.; Verbeek, K.A.B.

    2010-01-01

    Statistical data associated with geographic regions is nowadays globally available in large amounts and hence automated methods to visually display these data are in high demand. There are several well-established thematic map types for quantitative data on the ratio-scale associated with regions:

  9. Participatory maps

    DEFF Research Database (Denmark)

    Salovaara-Moring, Inka

    towards a new political ecology. This type of digital cartographies has been highlighted as the ‘processual turn’ in critical cartography, whereas in related computational journalism it can be seen as an interactive and iterative process of mapping complex and fragile ecological developments. This paper...

  10. Evolution of periodicity in periodical cicadas.

    Science.gov (United States)

    Ito, Hiromu; Kakishima, Satoshi; Uehara, Takashi; Morita, Satoru; Koyama, Takuya; Sota, Teiji; Cooley, John R; Yoshimura, Jin

    2015-09-14

    Periodical cicadas (Magicicada spp.) in the USA are famous for their unique prime-numbered life cycles of 13 and 17 years and their nearly perfectly synchronized mass emergences. Because almost all known species of cicada are non-periodical, periodicity is assumed to be a derived state. A leading hypothesis for the evolution of periodicity in Magicicada implicates the decline in average temperature during glacial periods. During the evolution of periodicity, the determinant of maturation in ancestral cicadas is hypothesized to have switched from size dependence to time (period) dependence. The selection for the prime-numbered cycles should have taken place only after the fixation of periodicity. Here, we build an individual-based model of cicadas under conditions of climatic cooling to explore the fixation of periodicity. In our model, under cold environments, extremely long juvenile stages lead to extremely low adult densities, limiting mating opportunities and favouring the evolution of synchronized emergence. Our results indicate that these changes, which were triggered by glacial cooling, could have led to the fixation of periodicity in the non-periodical ancestors.

  11. 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

  12. 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

  13. MAPPING INNOVATION

    DEFF Research Database (Denmark)

    Thuesen, Christian Langhoff; Koch, Christian

    2011-01-01

    By adopting a theoretical framework from strategic niche management research (SNM) this paper presents an analysis of the innovation system of the Danish Construction industry. The analysis shows a multifaceted landscape of innovation around an existing regime, built around existing ways of working...... and developed over generations. The regime is challenged from various niches and the socio-technical landscape through trends as globalization. Three niches (Lean Construction, BIM and System Deliveries) are subject to a detailed analysis showing partly incompatible rationales and various degrees of innovation...... potential. The paper further discusses how existing policymaking operates in a number of tensions one being between government and governance. Based on the concepts from SNM the paper introduces an innovation map in order to support the development of meta-governance policymaking. By mapping some...

  14. Mapping filmmaking

    DEFF Research Database (Denmark)

    Gilje, Øystein; Frølunde, Lisbeth; Lindstrand, Fredrik

    2010-01-01

    This chapter concerns mapping patterns in regards to how young filmmakers (age 15 – 20) in the Scandinavian countries learn about filmmaking. To uncover the patterns, we present portraits of four young filmmakers who participated in the Scandinavian research project Making a filmmaker. The focus ...... is on their learning practices and how they create ‘learning paths’ in relation to resources in diverse learning contexts, whether formal, non-formal and informal contexts.......This chapter concerns mapping patterns in regards to how young filmmakers (age 15 – 20) in the Scandinavian countries learn about filmmaking. To uncover the patterns, we present portraits of four young filmmakers who participated in the Scandinavian research project Making a filmmaker. The focus...

  15. 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.

  16. 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.

  17. Quadratic brackets from symplectic forms

    International Nuclear Information System (INIS)

    Alekseev, Anton Yu.; Todorov, Ivan T.

    1994-01-01

    We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))

  18. 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...

  19. Mapping Resilience

    DEFF Research Database (Denmark)

    Carruth, Susan

    2015-01-01

    by planners when aiming to construct resilient energy plans. It concludes that a graphical language has the potential to be a significant tool, flexibly facilitating cross-disciplinary communication and decision-making, while emphasising that its role is to support imaginative, resilient planning rather than...... the relationship between resilience and energy planning, suggesting that planning in, and with, time is a core necessity in this domain. It then reviews four examples of graphically mapping with time, highlighting some of the key challenges, before tentatively proposing a graphical language to be employed...

  20. 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.

  1. Mapping of

    Directory of Open Access Journals (Sweden)

    Sayed M. Arafat

    2014-06-01

    Full Text Available Land cover map of North Sinai was produced based on the FAO-Land Cover Classification System (LCCS of 2004. The standard FAO classification scheme provides a standardized system of classification that can be used to analyze spatial and temporal land cover variability in the study area. This approach also has the advantage of facilitating the integration of Sinai land cover mapping products to be included with the regional and global land cover datasets. The total study area is covering a total area of 20,310.4 km2 (203,104 hectare. The landscape classification was based on SPOT4 data acquired in 2011 using combined multispectral bands of 20 m spatial resolution. Geographic Information System (GIS was used to manipulate the attributed layers of classification in order to reach the maximum possible accuracy. GIS was also used to include all necessary information. The identified vegetative land cover classes of the study area are irrigated herbaceous crops, irrigated tree crops and rain fed tree crops. The non-vegetated land covers in the study area include bare rock, bare soils (stony, very stony and salt crusts, loose and shifting sands and sand dunes. The water bodies were classified as artificial perennial water bodies (fish ponds and irrigated canals and natural perennial water bodies as lakes (standing. The artificial surfaces include linear and non-linear features.

  2. The Periodic Pyramid

    Science.gov (United States)

    Hennigan, Jennifer N.; Grubbs, W. Tandy

    2013-01-01

    The chemical elements present in the modern periodic table are arranged in terms of atomic numbers and chemical periodicity. Periodicity arises from quantum mechanical limitations on how many electrons can occupy various shells and subshells of an atom. The shell model of the atom predicts that a maximum of 2, 8, 18, and 32 electrons can occupy…

  3. Book Reviews in Periodicals.

    Science.gov (United States)

    Ettelt, Harold J.

    All recent issues of periodicals found which contain indexed book reviews are listed in this compilation from Drake Memorial Library at the New York State University at Brockport. The periodicals are listed by 29 subject headings in this informal guide designed to be used at Drake Library. The number of reviews in the periodical in a recent year…

  4. Human Mind Maps

    Science.gov (United States)

    Glass, Tom

    2016-01-01

    When students generate mind maps, or concept maps, the maps are usually on paper, computer screens, or a blackboard. Human Mind Maps require few resources and little preparation. The main requirements are space where students can move around and a little creativity and imagination. Mind maps can be used for a variety of purposes, and Human Mind…

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. Lunar Map Catalog

    Data.gov (United States)

    National Aeronautics and Space Administration — The Lunar Map Catalog includes various maps of the moon's surface, including Apollo landing sites; earthside, farside, and polar charts; photography index maps; zone...

  10. Baby Brain Map

    Science.gov (United States)

    ... a Member Home Resources & Services Professional Resource Baby Brain Map Mar 17, 2016 The Brain Map was adapted in 2006 by ZERO TO ... supports Adobe Flash Player. To view the Baby Brain Map, please visit this page on a browser ...

  11. Snapshots for Semantic Maps

    National Research Council Canada - National Science Library

    Nielsen, Curtis W; Ricks, Bob; Goodrich, Michael A; Bruemmer, David; Few, Doug; Walton, Miles

    2004-01-01

    .... Semantic maps are a relatively new approach to information presentation. Semantic maps provide more detail about an environment than typical maps because they are augmented by icons or symbols that provide meaning for places or objects of interest...

  12. Painful menstrual periods

    Science.gov (United States)

    Menstruation - painful; Dysmenorrhea; Periods - painful; Cramps - menstrual; Menstrual cramps ... into two groups, depending on the cause: Primary dysmenorrhea Secondary dysmenorrhea Primary dysmenorrhea is menstrual pain that ...

  13. Middle Helladic Period

    DEFF Research Database (Denmark)

    Sarri, Kalliopi

    1999-01-01

    and their quality was improved considerably toward the end of this period. The profound cultural innovations of the Middle Helladic period were initially interpreted as a result of violent population movement and troubles provoked by the coming of the first Indo-European races. However, this matter does no more...... Helladic period is considered as a period of economic and social decline it was the time during which the mainland features merged with the insular influence, that is all the Aegean elements which led to the creation of the Mycenaean civilization were mixed in a creative way....

  14. On some periodicity effects

    DEFF Research Database (Denmark)

    Sorokin, Sergey V.

    2015-01-01

    The talk is concerned with the modelling of wave propagation in and vibration of periodic elastic structures. Although analysis of wave-guide properties of infinite periodic structures is a well establish research subject, some issues have not yet been fully addressed in the literature. The aim o...

  15. The Living Periodic Table

    Science.gov (United States)

    Nahlik, Mary Schrodt

    2005-01-01

    To help make the abstract world of chemistry more concrete eighth-grade students, the author has them create a living periodic table that can be displayed in the classroom or hallway. This display includes information about the elements arranged in the traditional periodic table format, but also includes visual real-world representations of the…

  16. Periods and Nori motives

    CERN Document Server

    Huber, Annette

    2017-01-01

    This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori’s unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a to...

  17. Long Period Seismic Waves

    Science.gov (United States)

    1976-08-01

    Geoffsica, TPHM. No. 5 , p. 161. Vargas, Freddy (To he published in 1976) 1 .-DTSCRP1TNACTON DE EVENTO«; NATHDALE«; Y ARTTFTCT ALES. 2.- CALCULO DEL...seismic risk, bv de - fininn relative weiqht of maximum MM intensity at a pivon distance ponulation density, area feolupy and attenuation of intensity wit...Population densitv, area peolopv and attenuation of intensitv with distance, is presented topether with a map anplvinp theorv to Bo- livia. ^«^a

  18. 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)

  19. 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.)

  20. 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...

  1. Mean-periodic functions

    Directory of Open Access Journals (Sweden)

    Carlos A. Berenstein

    1980-01-01

    Full Text Available We show that any mean-periodic function f can be represented in terms of exponential-polynomial solutions of the same convolution equation f satisfies, i.e., u∗f=0(μ∈E′(ℝn. This extends to n-variables the work of L. Schwartz on mean-periodicity and also extends L. Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. We also answer a number of open questions about mean-periodic functions of one variable. The basic ingredient is our work on interpolation by entire functions in one and several complex variables.

  2. 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

  3. 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.)

  4. Mapping the Heart

    Science.gov (United States)

    Hulse, Grace

    2012-01-01

    In this article, the author describes how her fourth graders made ceramic heart maps. The impetus for this project came from reading "My Map Book" by Sara Fanelli. This book is a collection of quirky, hand-drawn and collaged maps that diagram a child's world. There are maps of her stomach, her day, her family, and her heart, among others. The…

  5. Painful periods (dysmenorrhea) (image)

    Science.gov (United States)

    Primary dysmenorrhea is a normal cramping of the lower abdomen caused by hormone-induced uterine contractions before the period. Secondary dysmenorrhea may be caused by abnormal conditions such as ...

  6. Vaginal bleeding between periods

    Science.gov (United States)

    ... this page: //medlineplus.gov/ency/article/003156.htm Vaginal bleeding between periods To use the sharing features ... this page, please enable JavaScript. This article discusses vaginal bleeding that occurs between a woman's monthly menstrual ...

  7. Super periodic potential

    Science.gov (United States)

    Hasan, Mohammd; Mandal, Bhabani Prasad

    2018-04-01

    In this paper we introduce the concept of super periodic potential (SPP) of arbitrary order n, n ∈I+, in one dimension. General theory of wave propagation through SPP of order n is presented and the reflection and transmission coefficients are derived in their closed analytical form by transfer matrix formulation. We present scattering features of super periodic rectangular potential and super periodic delta potential as special cases of SPP. It is found that the symmetric self-similarity is the special case of super periodicity. Thus by identifying a symmetric fractal potential as special cases of SPP, one can obtain the tunnelling amplitude for a particle from such fractal potential. By using the formalism of SPP we obtain the close form expression of tunnelling amplitude of a particle for general Cantor and Smith-Volterra-Cantor potentials.

  8. Establishing contract periods

    International Nuclear Information System (INIS)

    Huffman, F.C.

    1978-01-01

    The lead time for executing the Adjustable Fixed-Commitment (AFC) contract and exceptions which may be considered are discussed. The initial delivery period is also discussed. Delays, deferrals, and schedule adjustment charges are finally considered

  9. The Periodic Table CD.

    Science.gov (United States)

    Banks, Alton J.; Holmes, Jon L.

    1995-01-01

    Describes the characteristics of the digitized version of The Periodic Table Videodisc. Provides details about the organization of information and access to the data via Macintosh and Windows computers. (DDR)

  10. Setting the Periodic Table.

    Science.gov (United States)

    Saturnelli, Annette

    1985-01-01

    Examines problems resulting from different forms of the periodic table, indicating that New York State schools use a form reflecting the International Union of Pure and Applied Chemistry's 1984 recommendations. Other formats used and reasons for standardization are discussed. (DH)

  11. 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

  12. USGS Map Indices Overlay Map Service from The National Map

    Data.gov (United States)

    U.S. Geological Survey, Department of the Interior — The USGS Map Indices service from The National Map (TNM) consists of 1x1 Degree, 30x60 Minute (100K), 15 Minute (63K), 7.5 Minute (24K), and 3.75 Minute grid...

  13. Supersymmetrically transformed periodic potentials

    OpenAIRE

    C, David J. Fernandez

    2003-01-01

    The higher order supersymmetric partners of a stationary periodic potential are studied. The transformation functions associated to the band edges do not change the spectral structure. However, when the transformation is implemented for factorization energies inside of the forbidden bands, the final potential will have again the initial band structure but it can have bound states encrusted into the gaps, giving place to localized periodicity defects.

  14. Thyrotoxic periodic paralysis

    OpenAIRE

    Rojith Karandode Balakrishnan; Suresh Rama Chandran; Geetha Thirumalnesan; Nedumaran Doraisamy

    2011-01-01

    This article aims at highlighting the importance of suspecting thyrotoxicosis in cases of recurrent periodic flaccid paralysis; especially in Asian men to facilitate early diagnosis of the former condition. A case report of a 28 year old male patient with recurrent periodic flaccid paralysis has been presented. Hypokalemia secondary to thyrotoxicosis was diagnosed as the cause of the paralysis. The patient was given oral potassium intervention over 24 hours. The patient showed complete recove...

  15. 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)

  16. 7. Annex II: Maps

    OpenAIRE

    Aeberli, Annina

    2012-01-01

    Map 1: States of South Sudan UN OCHA (2012) Republic of South Sudan – States, as of 15 July 2012, Reliefweb http://reliefweb.int/map/south-sudan-republic/republic-south-sudan-states-15-july-2012-reference-map, accessed 31 July 2012. Map 2: Counties of South Sudan UN OCHA (2012) Republic of South Sudan – Counties, as of 16 July 2012, Reliefweb http://reliefweb.int/map/south-sudan-republic/republic-south-sudan-counties-16-july-2012-reference-map, accessed 31 July 2012. Map 3: Eastern Equato...

  17. Applicability of vulnerability maps

    International Nuclear Information System (INIS)

    Andersen, L.J.; Gosk, E.

    1989-01-01

    A number of aspects to vulnerability maps are discussed: the vulnerability concept, mapping purposes, possible users, and applicability of vulnerability maps. Problems associated with general-type vulnerability mapping, including large-scale maps, universal pollutant, and universal pollution scenario are also discussed. An alternative approach to vulnerability assessment - specific vulnerability mapping for limited areas, specific pollutant, and predefined pollution scenario - is suggested. A simplification of the vulnerability concept is proposed in order to make vulnerability mapping more objective and by this means more comparable. An extension of the vulnerability concept to the rest of the hydrogeological cycle (lakes, rivers, and the sea) is proposed. Some recommendations regarding future activities are given

  18. 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

  19. 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.

  20. VEGETATION MAPPING IN WETLANDS

    Directory of Open Access Journals (Sweden)

    F. PEDROTTI

    2004-01-01

    Full Text Available The current work examines the main aspects of wetland vegetation mapping, which can be summarized as analysis of the ecological-vegetational (ecotone gradients; vegetation complexes; relationships between vegetation distribution and geomorphology; vegetation of the hydrographic basin lo which the wetland in question belongs; vegetation monitoring with help of four vegetation maps: phytosociological map of the real and potential vegetation, map of vegetation dynamical tendencies, map of vegetation series.

  1. Periodic table of elements

    International Nuclear Information System (INIS)

    Fluck, E.; Heumann, K.G.

    1985-01-01

    Following a recommendation by the International Union for Pure and Applied Chemistry (IUPAC), the groups of the periodic table shall be numbered from 1 to 18, instead of I to VIII as before. The recommendations has been approved of by the Committee on Nomenclature of the American Chemical Society. The new system abandons the distinction between main groups (a) and auxiliary groups (b), which in the past frequently has been the reason for misunderstandings between European and American chemists, due to different handling. The publishing house VCH Verlagsgesellschaft recently produced a new periodic table that shows the old and the new numbering system together at a glance, so that chemists will have time to get familiar with the new system. In addition the new periodic table represents an extensive data compilation arranged by elements. The front page lists the chemical properties of elements, the back page their physical properties. (orig./EF) [de

  2. Thyrotoxic periodic paralysis

    Directory of Open Access Journals (Sweden)

    Rojith Karandode Balakrishnan

    2011-01-01

    Full Text Available This article aims at highlighting the importance of suspecting thyrotoxicosis in cases of recurrent periodic flaccid paralysis; especially in Asian men to facilitate early diagnosis of the former condition. A case report of a 28 year old male patient with recurrent periodic flaccid paralysis has been presented. Hypokalemia secondary to thyrotoxicosis was diagnosed as the cause of the paralysis. The patient was given oral potassium intervention over 24 hours. The patient showed complete recovery after the medical intervention and was discharged after 24 hours with no residual paralysis. Thyrotoxic periodic paralysis (TPP is a complication of thyrotoxicosis, more common amongst males in Asia. It presents as acute flaccid paralysis in a case of hyperthyroidism with associated hypokalemia. The features of thyrotoxicosis may be subtle or absent. Thus, in cases of recurrent or acute flaccid muscle paralysis, it is important to consider thyrotoxicosis as one of the possible causes, and take measures accordingly.

  3. Expanding Thurston maps

    CERN Document Server

    Bonk, Mario

    2017-01-01

    This monograph is devoted to the study of the dynamics of expanding Thurston maps under iteration. A Thurston map is a branched covering map on a two-dimensional topological sphere such that each critical point of the map has a finite orbit under iteration. It is called expanding if, roughly speaking, preimages of a fine open cover of the underlying sphere under iterates of the map become finer and finer as the order of the iterate increases. Every expanding Thurston map gives rise to a fractal space, called its visual sphere. Many dynamical properties of the map are encoded in the geometry of this visual sphere. For example, an expanding Thurston map is topologically conjugate to a rational map if and only if its visual sphere is quasisymmetrically equivalent to the Riemann sphere. This relation between dynamics and fractal geometry is the main focus for the investigations in this work.

  4. Periodically poled silicon

    Science.gov (United States)

    Hon, Nick K.; Tsia, Kevin K.; Solli, Daniel R.; Khurgin, Jacob B.; Jalali, Bahram

    2010-02-01

    Bulk centrosymmetric silicon lacks second-order optical nonlinearity χ(2) - a foundational component of nonlinear optics. Here, we propose a new class of photonic device which enables χ(2) as well as quasi-phase matching based on periodic stress fields in silicon - periodically-poled silicon (PePSi). This concept adds the periodic poling capability to silicon photonics, and allows the excellent crystal quality and advanced manufacturing capabilities of silicon to be harnessed for devices based on χ(2)) effects. The concept can also be simply achieved by having periodic arrangement of stressed thin films along a silicon waveguide. As an example of the utility, we present simulations showing that mid-wave infrared radiation can be efficiently generated through difference frequency generation from near-infrared with a conversion efficiency of 50% based on χ(2) values measurements for strained silicon reported in the literature [Jacobson et al. Nature 441, 199 (2006)]. The use of PePSi for frequency conversion can also be extended to terahertz generation. With integrated piezoelectric material, dynamically control of χ(2)nonlinearity in PePSi waveguide may also be achieved. The successful realization of PePSi based devices depends on the strength of the stress induced χ(2) in silicon. Presently, there exists a significant discrepancy in the literature between the theoretical and experimentally measured values. We present a simple theoretical model that produces result consistent with prior theoretical works and use this model to identify possible reasons for this discrepancy.

  5. Hereditary periodic fever syndromes

    NARCIS (Netherlands)

    McDermott, MF; Frenkel, J

    Hereditary periodic fever syndromes are defined by recurrent attacks of generalised inflammation for which no infectious or auto-immune cause can be identified. For most of these disorders, the molecular basis has recently been elucidated. This has opened the prospect of novel therapeutic

  6. Almost periodic Schroedinger operators

    International Nuclear Information System (INIS)

    Bellissard, J.; Lima, R.

    1984-01-01

    These lectures are devoted to recent developments in the theory of almost-periodic Schroedinger Operators. We specially describe the algebraic point of view, with applications to gap-labelling theorems. Particular models are also presented which exhibit various spectral properties. (orig.)

  7. Astrophysical implications of periodicity

    International Nuclear Information System (INIS)

    Muller, R.A.

    1988-01-01

    Two remarkable discoveries of the last decade have profound implications for astrophysics and for geophysics. These are the discovery by Alvarez et al., that certain mass extinctions are caused by the impact on the earth of a large asteroid or comet, and the discovery by Raup and Sepkoski that such extinctions are periodic, with a cycle time of 26 to 30 million years. The validity of both of these discoveries is assumed and the implications are examined. Most of the phenomena described depend not on periodicity, but just on the weaker assumption that the impacts on the earth take place primarily in showers. Proposed explanations for the periodicity include galactic oscillations, the Planet X model, and the possibility of Nemesis, a solar companion star. These hypotheses are critically examined. Results of the search for the solar companion are reported. The Deccan flood basalts of India have been proposed as the impact site for the Cretaceous impact, but this hypotheisis is in contradiction with the conclusion of Courtillot et al., that the magma flow began during a period of normal magnetic field. A possible resolution of this contradiction is proposed

  8. Periodic Table of Students.

    Science.gov (United States)

    Johnson, Mike

    1998-01-01

    Presents an exercise in which an eighth-grade science teacher decorated the classroom with a periodic table of students. Student photographs were arranged according to similarities into vertical columns. Students were each assigned an atomic number according to their placement in the table. The table is then used to teach students about…

  9. A Modern Periodic Table.

    Science.gov (United States)

    Herrenden-Harker, B. D.

    1997-01-01

    Presents a modern Periodic Table based on the electron distribution in the outermost shell and the order of filling of the sublevels within the shells. Enables a student to read off directly the electronic configuration of the element and the order in which filling occurs. (JRH)

  10. Mapping in the cloud

    CERN Document Server

    Peterson, Michael P

    2014-01-01

    This engaging text provides a solid introduction to mapmaking in the era of cloud computing. It takes students through both the concepts and technology of modern cartography, geographic information systems (GIS), and Web-based mapping. Conceptual chapters delve into the meaning of maps and how they are developed, covering such topics as map layers, GIS tools, mobile mapping, and map animation. Methods chapters take a learn-by-doing approach to help students master application programming interfaces and build other technical skills for creating maps and making them available on the Internet. Th

  11. Mapping with Drupal

    CERN Document Server

    Palazzolo, Alan

    2011-01-01

    Build beautiful interactive maps on your Drupal website, and tell engaging visual stories with your data. This concise guide shows you how to create custom geographical maps from top to bottom, using Drupal 7 tools and out-of-the-box modules. You'll learn how mapping works in Drupal, with examples on how to use intuitive interfaces to map local events, businesses, groups, and other custom data. Although building maps with Drupal can be tricky, this book helps you navigate the system's complexities for creating sophisticated maps that match your site design. Get the knowledge and tools you ne

  12. Meso(topoclimatic maps and mapping

    Directory of Open Access Journals (Sweden)

    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.

  13. 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

  14. 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.

  15. Thyrotoxic periodic paralysis

    International Nuclear Information System (INIS)

    Ferreiro, J.E.; Arguelles, D.J.; Rams, H. Jr.

    1986-01-01

    A case of thyrotoxic periodic paralysis is reported in a Hispanic man with an unusual recurrence six weeks after radioactive iodine treatment. Thyrotoxic periodic paralysis has now been well characterized in the literature: it occurs primarily in Orientals with an overwhelming male preponderance and a higher association of specific HLA antigens. Clinical manifestations include onset after high carbohydrate ingestion or heavy exertion, with progressive symmetric weakness leading to flaccid paralysis of the extremities and other muscle groups, lasting several hours. If hypokalemia is present, potassium administration may help abort the attack. Although propranolol can be efficacious in preventing further episodes, the only definitive treatment is establishing a euthyroid state. The pathophysiology is still controversial, but reflects altered potassium and calcium dynamics as well as certain morphologic characteristics within the muscle unit itself

  16. Active Fire Mapping Program

    Science.gov (United States)

    Active Fire Mapping Program Current Large Incidents (Home) New Large Incidents Fire Detection Maps MODIS Satellite Imagery VIIRS Satellite Imagery Fire Detection GIS Data Fire Data in Google Earth ...

  17. Using maps in genealogy

    Science.gov (United States)

    ,

    2002-01-01

    In genealogical research, maps can provide clues to where our ancestors may have lived and where to look for written records about them. Beginners should master basic genealogical research techniques before starting to use topographic maps.

  18. NGS Survey Control Map

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — The NGS Survey Control Map provides a map of the US which allows you to find and display geodetic survey control points stored in the database of the National...

  19. National Pipeline Mapping System

    Data.gov (United States)

    Department of Transportation — The NPMS Public Map Viewer allows the general public to view maps of transmission pipelines, LNG plants, and breakout tanks in one selected county. Distribution and...

  20. NAIP Status Maps Gallery

    Data.gov (United States)

    Farm Service Agency, Department of Agriculture — NAIP Status Maps Gallery. These maps illustrate what aerial imagery collection is planned, whats been collected, when it is available and how it is available. These...

  1. Mapping Medicare Disparities Tool

    Data.gov (United States)

    U.S. Department of Health & Human Services — The CMS Office of Minority Health has designed an interactive map, the Mapping Medicare Disparities Tool, to identify areas of disparities between subgroups of...

  2. Recovery Action Mapping Tool

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — The Recovery Action Mapping Tool is a web map that allows users to visually interact with and query actions that were developed to recover species listed under the...

  3. Letter of Map Revision

    Data.gov (United States)

    Earth Data Analysis Center, University of New Mexico — The National Flood Hazard Layer (NFHL) data incorporates all Digital Flood Insurance Rate Map(DFIRM) databases published by FEMA, and any Letters Of Map Revision...

  4. 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.

  5. 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.

  6. Branched polynomial covering maps

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    1999-01-01

    A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch...... set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere....

  7. Multi-moment maps

    DEFF Research Database (Denmark)

    Swann, Andrew Francis; Madsen, Thomas Bruun

    2012-01-01

    We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold. Such maps are also shown to exist for all groups whose second...

  8. Diffusion Based Photon Mapping

    DEFF Research Database (Denmark)

    Schjøth, Lars; Fogh Olsen, Ole; Sporring, Jon

    2007-01-01

    . To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....

  9. Diffusion Based Photon Mapping

    DEFF Research Database (Denmark)

    Schjøth, Lars; Olsen, Ole Fogh; Sporring, Jon

    2006-01-01

    . To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....

  10. Digitised Maps in the Danish Map Collection

    OpenAIRE

    Annie Lenschau-Teglers; Vivi Gade Rønsberg

    2005-01-01

    As in the rest of the library world, The Royal Library in Copenhagen is in the process of digitising its collections. At the moment we are mainly working on the handwritten manual catalogue - but digitising the material is also a major working assignment. The Map Collection at The Royal Library has today divided the effort in digitising its materials into 3 groups: 1. Digitised maps as a vital addition to the records in our bibliographic database REX 2. Digitised maps presented as a Digital F...

  11. 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

  12. 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

  13. 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

  14. 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

  15. Polysheroidal periodic functions

    International Nuclear Information System (INIS)

    Truskova, N.F.

    1985-01-01

    Separation of variables in the Helmholtz N-dimensional (N≥4) equation in polyspheroidal coordinate systems leads to the necessity of solving equations going over into equations for polyspheroidal periodic functions used for solving the two-centre problem in quantum mechanics, the three-body problem with Coulomb interaction, etc. For these functions the expansions are derived in terms of the Jacobi polynomials and Bessel functions. Their basic properties, asymptotics are considered. The algorithm of their computer calculations is developed. The results of numerical calculations are given

  16. Deciphering Periodic Methanol Masers

    Science.gov (United States)

    Stecklum, Bringfried; Caratti o Garatti, Alessio; Henning, Thomas; Hodapp, Klaus; Hopp, Ulrich; Kraus, Alex; Linz, Hendrik; Sanna, Alberto; Sobolev, Andrej; Wolf, Verena

    2018-05-01

    Impressive progress has been made in recent years on massive star formation, yet the involved high optical depths even at submm/mm wavelengths make it difficult to reveal its details. Recently, accretion bursts of massive YSOs have been identified to cause flares of Class II methanol masers (methanol masers for short) due to enhanced mid-IR pumping. This opens a new window to protostellar accretion variability, and implies that periodic methanol masers hint at cyclic accretion. Pinning down the cause of the periodicity requires joint IR and radio monitoring. We derived the first IR light curve of a periodic maser host from NEOWISE data. The source, G107.298+5.639, is an intermediate-mass YSO hosting methanol and water masers which flare every 34.5 days. Our recent joint K-band and radio observations yielded first but marginal evidence for a phase lag between the rise of IR and maser emission, respectively, and revealed that both NEOWISE and K-band light curves are strongly affected by the light echo from the ambient dust. Both the superior resolution of IRAC over NEOWISE and the longer wavelengths compared to our ground-based imaging are required to inhibit the distractive contamination by the light echo. Thus, we ask for IRAC monitoring of G107 to cover one flare cycle, in tandem with 100-m Effelsberg and 2-m Wendelstein radio and NIR observations to obtain the first high-quality synoptic measurements of this kind of sources. The IR-maser phase lag, the intrinsic shape of the IR light curves and their possible color variation during the cycle allow us to constrain models for the periodic maser excitation. Since methanol masers are signposts of intermediate-mass and massive YSOs, deciphering their variability offers a clue to the dynamics of the accretion-mediated growth of massive stars and their feedback onto the immediate natal environment. The Spitzer light curve of such a maser-hosting YSO would be a legacy science product of the mission.

  17. Mapping of wine industry

    OpenAIRE

    Віліна Пересадько; Надія Максименко; Катерина Біла

    2016-01-01

    Having reviewed a variety of approaches to understanding the essence of wine industry, having studied the modern ideas about the future of wine industry, having analyzed more than 50 maps from the Internet we have set the trends and special features of wine industry mapping in the world, such as: - the vast majority of maps displays the development of the industry at regional or national level, whereas there are practically no world maps; - wine-growing regions are represented on maps very un...

  18. Maps of the Auditory Cortex.

    Science.gov (United States)

    Brewer, Alyssa A; Barton, Brian

    2016-07-08

    One of the fundamental properties of the mammalian brain is that sensory regions of cortex are formed of multiple, functionally specialized cortical field maps (CFMs). Each CFM comprises two orthogonal topographical representations, reflecting two essential aspects of sensory space. In auditory cortex, auditory field maps (AFMs) are defined by the combination of tonotopic gradients, representing the spectral aspects of sound (i.e., tones), with orthogonal periodotopic gradients, representing the temporal aspects of sound (i.e., period or temporal envelope). Converging evidence from cytoarchitectural and neuroimaging measurements underlies the definition of 11 AFMs across core and belt regions of human auditory cortex, with likely homology to those of macaque. On a macrostructural level, AFMs are grouped into cloverleaf clusters, an organizational structure also seen in visual cortex. Future research can now use these AFMs to investigate specific stages of auditory processing, key for understanding behaviors such as speech perception and multimodal sensory integration.

  19. Rainfall erosivity map for Ghana

    International Nuclear Information System (INIS)

    Oduro Afriyie, K.

    1995-10-01

    Monthly rainfall data, spanning over a period of more than thirty years, were used to compute rainfall erosivity indices for various stations in Ghana, using the Fournier index, c, defined as p 2 /P, where p is the rainfall amount in the wettest month and P is the annual rainfall amount. Values of the rainfall erosivity indices ranged from 24.5 mm at Sunyani in the mid-portion of Ghana to 180.9 mm at Axim in the south western coastal portion. The indices were used to construct a rainfall erosivity map for the country. The map revealed that Ghana may be broadly divided into five major erosion risk zones. The middle sector of Ghana is generally in the low erosion risk zone; the northern sector is in the moderate to severe erosion risk zone, while the coastal sector is in the severe to extreme severe erosion risk zone. (author). 11 refs, 1 fig., 1 tab

  20. 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

  1. 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

  2. Branched polynomial covering maps

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    2002-01-01

    A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch ...... set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere. (C) 2001 Elsevier Science B.V. All rights reserved.......A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch...

  3. Mapping Earth's electromagnetic dimensionality

    Science.gov (United States)

    Love, J. J.; Kelbert, A.; Bedrosian, P.

    2017-12-01

    The form of a magnetotelluric impedance tensor, obtained for a given geographic site through simultaneous measurement of geomagnetic and geoelectric field variation, is affected by electrical conductivity structure beneath the measurement site. Building on existing methods for characterizing the symmetry of magnetotelluric impedance tensors, a simple scalar measure is developed for measuring the (frequency dependent) proportion of the impedance tensor that is not just a one-dimensional (1D) function of depth ("non-1D-ness"). These measures are applied to nearly 1000 impedance tensors obtained during magnetotelluric surveys, those for the continental United States and obtained principally through the National Science Foundation's EarthScope project. Across geomagnetic/geoelectric variational periods ranging from 30 s to 3,000 s, corresponding to crustal and upper mantle depths, it is shown that local Earth structure is very often not simply 1D-depth-dependent - often less than 50% of magnetotelluric impedance is 1D. For selected variational frequencies, non-1D-ness is mapped and the relationship between electromagnetic dimensionality and known geological and tectonic structures is discussed. The importance of using realistic surface impedances to accurately evaluate magnetic-storm geoelectric hazards is emphasized.

  4. Periodically modulated dark states

    Science.gov (United States)

    Han, Yingying; Zhang, Jun; Zhang, Wenxian

    2018-04-01

    Phenomena of electromagnetically induced transparency (PEIT) may be interpreted by the Autler-Townes Splitting (ATS), where the coupled states are split by the coupling laser field, or by the quantum destructive interference (QDI), where the atomic phases caused by the coupling laser and the probe laser field cancel. We propose modulated experiments to explore the PEIT in an alternative way by periodically modulating the coupling and the probe fields in a Λ-type three-level system initially in a dark state. Our analytical and numerical results rule out the ATS interpretation and show that the QDI interpretation is more appropriate for the modulated experiments. Interestingly, dark state persists in the double-modulation situation where control and probe fields never occur simultaneously, which is significant difference from the traditional dark state condition. The proposed experiments are readily implemented in atomic gases, artificial atoms in superconducting quantum devices, or three-level meta-atoms in meta-materials.

  5. 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.

  6. Mapping Urban Social Divisions

    Directory of Open Access Journals (Sweden)

    Susan Ball

    2010-05-01

    Full Text Available Against the background of increased levels of interest in space and images beyond the field of geography, this article (re- introduces earlier work on the semiotics of maps undertaken by geographers in the 1960s. The data limitations, purpose and cultural context in which a user interprets a map's codes and conventions are highlighted in this work, which remains relevant to the interpretation of maps—new and old—forty years later. By means of drawing on geography's contribution to the semiotics of maps, the article goes on to examine the concept of urban social divisions as represented in map images. Using a small number of map images, including two of the most widely known maps of urban social division in Europe and North America, the roles of context, data and purpose in the production and interpretation of maps are discussed. By presenting the examples chronologically the article shows that although advances in data collection and manipulation have allowed researchers to combine different social variables in maps of social division, and to interact with map images, work by geographers on the semiotics of maps is no less relevant today than when it was first proposed forty years ago. URN: urn:nbn:de:0114-fqs1002372

  7. [Childhood periodic syndromes].

    Science.gov (United States)

    Cuvellier, J-C; Lépine, A

    2010-01-01

    This review focuses on the so-called "periodic syndromes of childhood that are precursors to migraine", as included in the Second Edition of the International Classification of Headache Disorders. Three periodic syndromes of childhood are included in the Second Edition of the International Classification of Headache Disorders: abdominal migraine, cyclic vomiting syndrome and benign paroxysmal vertigo, and a fourth, benign paroxysmal torticollis is presented in the Appendix. The key clinical features of this group of disorders are the episodic pattern and intervals of complete health. Episodes of benign paroxysmal torticollis begin between 2 and 8 months of age. Attacks are characterized by an abnormal inclination and/or rotation of the head to one side, due to cervical dystonia. They usually resolve by 5 years. Benign paroxysmal vertigo presents as sudden attacks of vertigo, accompanied by inability to stand without support, and lasting seconds to minutes. Age at onset is between 2 and 4 years, and the symptoms disappear by the age of 5. Cyclic vomiting syndrome is characterized in young infants and children by repeated stereotyped episodes of pernicious vomiting, at times to the point of dehydration, and impacting quality of life. Mean age of onset is 5 years. Abdominal migraine remains a controversial issue and presents in childhood with repeated stereotyped episodes of unexplained abdominal pain, nausea and vomiting occurring in the absence of headache. Mean age of onset is 7 years. Both cyclic vomiting syndrome and abdominal migraine are noted for the absence of pathognomonic clinical features but also for the large number of other conditions to be considered in their differential diagnoses. Diagnostic criteria, such as those of the Second Edition of the International Classification of Headache Disorders and the North American Society for Pediatric Gastroenterology, Hepatology and Nutrition, have made diagnostic approach and management easier. Their diagnosis

  8. Nonparametric Inference for Periodic Sequences

    KAUST Repository

    Sun, Ying; Hart, Jeffrey D.; Genton, Marc G.

    2012-01-01

    the periodogram, a widely used tool for period estimation. The CV method is computationally simple and implicitly penalizes multiples of the smallest period, leading to a "virtually" consistent estimator of integer periods. This estimator is investigated both

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. Mapping of wine industry

    Directory of Open Access Journals (Sweden)

    Віліна Пересадько

    2016-10-01

    Full Text Available Having reviewed a variety of approaches to understanding the essence of wine industry, having studied the modern ideas about the future of wine industry, having analyzed more than 50 maps from the Internet we have set the trends and special features of wine industry mapping in the world, such as: - the vast majority of maps displays the development of the industry at regional or national level, whereas there are practically no world maps; - wine-growing regions are represented on maps very unevenly; - all existing maps of the industry could be classified as analytical ascertaining inventory type; - the dominant ways of cartographic representation are area method and qualitative background method, sign method and collation maps are rarely used; - basically all the Internet maps have low quality as they are scanned images with poor resolution; - the special feature of maps published lately is lack of geographical basis (except for state borders and coastline. We created wine production and consumption world map «Wine Industry» in the scale of 1:60 000 000 with simple geographical basis (state names, state borders, major rivers, coastline. It was concluded that from the methodological point of view it is incorrect not to show geographical basis on maps of wine industry. Analysis of this map allowed us to identify areas of traditional wine-making, potential wine-making areas and countries which claim to be the world leaders in the field of wine production. We found disbalans between wine production and wine consumption - increasing wine production in South America, China and the United States and increasing wine consumption (mainly due to the import products in countries where the grape is not the primary agricultural product.

  14. 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...

  15. Introduction to "Mapping Vietnameseness"

    OpenAIRE

    Hue-Tam Ho Tai

    2016-01-01

    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 o...

  16. North America pipeline map

    International Nuclear Information System (INIS)

    Anon.

    2005-01-01

    This map presents details of pipelines currently in place throughout North America. Fifty-nine natural gas pipelines are presented, as well as 16 oil pipelines. The map also identifies six proposed natural gas pipelines. Major cities, roads and highways are included as well as state and provincial boundaries. The National Petroleum Reserve is identified, as well as the Arctic National Wildlife Refuge. The following companies placed advertisements on the map with details of the services they provide relating to pipeline management and construction: Ferus Gas Industries Trust; Proline; SulfaTreat Direct Oxidation; and TransGas. 1 map

  17. Open land use map

    OpenAIRE

    Mildorf, T.; Charvát, K.; Jezek, J.; Templer, Simon; Malewski, Christian

    2014-01-01

    Open Land Use Map is an initiative that has been started by the Plan4business project and that will be extended as part of the SDI4Apps project in the future. This service aims to create an improved worldwide land use map. The initial map will be prepared using the CORINE Land Cover, Global Cover dataset and Open Street Map. Contributors, mainly volunteers, will able to change the geometry and assign up-to-date land use according to the HILUCS specification. For certain regions more detailed ...

  18. 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

  19. 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).

  20. 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.

  1. 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.

  2. 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

  3. Testing periodically integrated autoregressive models

    NARCIS (Netherlands)

    Ph.H.B.F. Franses (Philip Hans); M.J. McAleer (Michael)

    1997-01-01

    textabstractPeriodically integrated time series require a periodic differencing filter to remove the stochastic trend. A non-periodic integrated time series needs the first-difference filter for similar reasons. When the changing seasonal fluctuations for the non-periodic integrated series can be

  4. On circle map coupled map lattice

    CERN Document Server

    Ahmed, E

    2002-01-01

    Circle map in one and two dimensions is studied. Both its stability, synchronization using bounded control and persistence is discussed. This work is expected to be applicable in ecology where spatial effects are known to be important. Also it will be relevant to systems where delay effects are not negligible.

  5. Sodium Velocity Maps on Mercury

    Science.gov (United States)

    Potter, A. E.; Killen, R. M.

    2011-01-01

    The objective of the current work was to measure two-dimensional maps of sodium velocities on the Mercury surface and examine the maps for evidence of sources or sinks of sodium on the surface. The McMath-Pierce Solar Telescope and the Stellar Spectrograph were used to measure Mercury spectra that were sampled at 7 milliAngstrom intervals. Observations were made each day during the period October 5-9, 2010. The dawn terminator was in view during that time. The velocity shift of the centroid of the Mercury emission line was measured relative to the solar sodium Fraunhofer line corrected for radial velocity of the Earth. The difference between the observed and calculated velocity shift was taken to be the velocity vector of the sodium relative to Earth. For each position of the spectrograph slit, a line of velocities across the planet was measured. Then, the spectrograph slit was stepped over the surface of Mercury at 1 arc second intervals. The position of Mercury was stabilized by an adaptive optics system. The collection of lines were assembled into an images of surface reflection, sodium emission intensities, and Earthward velocities over the surface of Mercury. The velocity map shows patches of higher velocity in the southern hemisphere, suggesting the existence of sodium sources there. The peak earthward velocity occurs in the equatorial region, and extends to the terminator. Since this was a dawn terminator, this might be an indication of dawn evaporation of sodium. Leblanc et al. (2008) have published a velocity map that is similar.

  6. 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.

  7. 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

  8. 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.

  9. Mapping online consumer search

    NARCIS (Netherlands)

    Bronnenberg, B.J.; Kim, J.; Albuquerque, P.

    2011-01-01

    The authors propose a new method to visualize browsing behavior in so-called product search maps. Manufacturers can use these maps to understand how consumers search for competing products before choice, including how information acquisition and product search are organized along brands, product

  10. Map of Nasca Geoglyphs

    Science.gov (United States)

    Hanzalová, K.; Pavelka, K.

    2013-07-01

    The Czech Technical University in Prague in the cooperation with the University of Applied Sciences in Dresden (Germany) work on the Nasca Project. The cooperation started in 2004 and much work has been done since then. All work is connected with Nasca lines in southern Peru. The Nasca project started in 1995 and its main target is documentation and conservation of the Nasca lines. Most of the project results are presented as WebGIS application via Internet. In the face of the impending destruction of the soil drawings, it is possible to preserve this world cultural heritage for the posterity at least in a digital form. Creating of Nasca lines map is very useful. The map is in a digital form and it is also available as a paper map. The map contains planimetric component of the map, map lettering and altimetry. Thematic folder in this map is a vector layer of the geoglyphs in Nasca/Peru. Basis for planimetry are georeferenced satellite images, altimetry is created from digital elevation model. This map was created in ArcGis software.

  11. Mapping of Outdoor Classrooms.

    Science.gov (United States)

    Horvath, Victor G.

    Mapping symbols adopted by the Michigan Department of Natural Resources are presented with their explanations. In an effort to provide standardization and familiarity teachers and other school people involved in an outdoor education program are encouraged to utilize the same symbols in constructing maps. (DK)

  12. MAP OF NASCA GEOGLYPHS

    Directory of Open Access Journals (Sweden)

    K. Hanzalová

    2013-07-01

    Full Text Available The Czech Technical University in Prague in the cooperation with the University of Applied Sciences in Dresden (Germany work on the Nasca Project. The cooperation started in 2004 and much work has been done since then. All work is connected with Nasca lines in southern Peru. The Nasca project started in 1995 and its main target is documentation and conservation of the Nasca lines. Most of the project results are presented as WebGIS application via Internet. In the face of the impending destruction of the soil drawings, it is possible to preserve this world cultural heritage for the posterity at least in a digital form. Creating of Nasca lines map is very useful. The map is in a digital form and it is also available as a paper map. The map contains planimetric component of the map, map lettering and altimetry. Thematic folder in this map is a vector layer of the geoglyphs in Nasca/Peru. Basis for planimetry are georeferenced satellite images, altimetry is created from digital elevation model. This map was created in ArcGis software.

  13. Diffusion Based Photon Mapping

    DEFF Research Database (Denmark)

    Schjøth, Lars; Sporring, Jon; Fogh Olsen, Ole

    2008-01-01

    . To address this problem, we introduce a photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way, we preserve important illumination features, while...

  14. Maps between Grassmann manifolds

    Indian Academy of Sciences (India)

    Parameswaran Sankaran Institute of Mathematical Sciences Chennai, India sankaran@imsc.res.in Indian Academy of Sciences Platinum Jubilee Meeting Hyderabad

    2009-07-02

    Jul 2, 2009 ... Classification of all manifolds (or maps between them) is an impossible task. The coarser, homotopical classification, is relatively easier–but only relatively! Homotopy is, roughly speaking, the study of properties of spaces and maps invariant under continuous deformations. Denote by [X, Y ] the set of all ...

  15. Constructing Maps Collaboratively.

    Science.gov (United States)

    Leinhardt, Gaea; Stainton, Catherine; Bausmith, Jennifer Merriman

    1998-01-01

    Summarizes a study that maintains that students who work together in small groups had a better understanding of map concepts. Discusses why making maps in groups can enhance students' conceptual geographic understanding and offers suggestions for improving geography instructions using small group configurations. Includes statistical and graphic…

  16. Algorithms for necklace maps

    NARCIS (Netherlands)

    Speckmann, B.; Verbeek, K.A.B.

    2015-01-01

    Necklace maps visualize quantitative data associated with regions by placing scaled symbols, usually disks, without overlap on a closed curve (the necklace) surrounding the map regions. Each region is projected onto an interval on the necklace that contains its symbol. In this paper we address the

  17. Text 2 Mind Map

    OpenAIRE

    Iona, John

    2017-01-01

    This is a review of the web resource 'Text 2 Mind Map' www.Text2MindMap.com. It covers what the resource is, and how it might be used in Library and education context, in particular for School Librarians.

  18. Formal genetic maps

    African Journals Online (AJOL)

    Mohammad Saad Zaghloul Salem

    2014-12-24

    Dec 24, 2014 ... ome/transcriptome/proteome, experimental induced maps that are intentionally designed and con- ... genetic maps imposed their application in nearly all fields of medical genetics including ..... or genes located adjacent to, or near, them. ...... types of markers, e.g., clinical markers (eye color), genomic.

  19. Bodily maps of emotions.

    Science.gov (United States)

    Nummenmaa, Lauri; Glerean, Enrico; Hari, Riitta; Hietanen, Jari K

    2014-01-14

    Emotions are often felt in the body, and somatosensory feedback has been proposed to trigger conscious emotional experiences. Here we reveal maps of bodily sensations associated with different emotions using a unique topographical self-report method. In five experiments, participants (n = 701) were shown two silhouettes of bodies alongside emotional words, stories, movies, or facial expressions. They were asked to color the bodily regions whose activity they felt increasing or decreasing while viewing each stimulus. Different emotions were consistently associated with statistically separable bodily sensation maps across experiments. These maps were concordant across West European and East Asian samples. Statistical classifiers distinguished emotion-specific activation maps accurately, confirming independence of topographies across emotions. We propose that emotions are represented in the somatosensory system as culturally universal categorical somatotopic maps. Perception of these emotion-triggered bodily changes may play a key role in generating consciously felt emotions.

  20. Application of ecological mapping

    International Nuclear Information System (INIS)

    Sherk, J.A.

    1982-01-01

    The US Fish and Wildlife Service has initiated the production of a comprehensive ecological inventory map series for use as a major new planning tool. Important species data along with special land use designations are displayed on 1:250,000 scale topographic base maps. Sets of maps have been published for the Atlantic and Pacific coastal areas of the United States. Preparation of a map set for the Gulf of Mexico is underway at the present time. Potential application of ecological inventory map series information to a typical land disposal facility could occur during the narrowing of the number of possible disposal sites, the design of potential disposal site studies of ecological resources, the preparation of the environmental report, and the regulatory review of license applications. 3 figures, 3 tables

  1. The projective heat map

    CERN Document Server

    Schwartz, Richard Evan

    2017-01-01

    This book introduces a simple dynamical model for a planar heat map that is invariant under projective transformations. The map is defined by iterating a polygon map, where one starts with a finite planar N-gon and produces a new N-gon by a prescribed geometric construction. One of the appeals of the topic of this book is the simplicity of the construction that yet leads to deep and far reaching mathematics. To construct the projective heat map, the author modifies the classical affine invariant midpoint map, which takes a polygon to a new polygon whose vertices are the midpoints of the original. The author provides useful background which makes this book accessible to a beginning graduate student or advanced undergraduate as well as researchers approaching this subject from other fields of specialty. The book includes many illustrations, and there is also a companion computer program.

  2. 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.

  3. 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

  4. 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

  5. USGS Topo Base Map from The National Map

    Data.gov (United States)

    U.S. Geological Survey, Department of the Interior — The USGS Topographic Base Map from The National Map. This tile cached web map service combines the most current data services (Boundaries, Names, Transportation,...

  6. Analyzing thematic maps and mapping for accuracy

    Science.gov (United States)

    Rosenfield, G.H.

    1982-01-01

    Two problems which exist while attempting to test the accuracy of thematic maps and mapping are: (1) evaluating the accuracy of thematic content, and (2) evaluating the effects of the variables on thematic mapping. Statistical analysis techniques are applicable to both these problems and include techniques for sampling the data and determining their accuracy. In addition, techniques for hypothesis testing, or inferential statistics, are used when comparing the effects of variables. A comprehensive and valid accuracy test of a classification project, such as thematic mapping from remotely sensed data, includes the following components of statistical analysis: (1) sample design, including the sample distribution, sample size, size of the sample unit, and sampling procedure; and (2) accuracy estimation, including estimation of the variance and confidence limits. Careful consideration must be given to the minimum sample size necessary to validate the accuracy of a given. classification category. The results of an accuracy test are presented in a contingency table sometimes called a classification error matrix. Usually the rows represent the interpretation, and the columns represent the verification. The diagonal elements represent the correct classifications. The remaining elements of the rows represent errors by commission, and the remaining elements of the columns represent the errors of omission. For tests of hypothesis that compare variables, the general practice has been to use only the diagonal elements from several related classification error matrices. These data are arranged in the form of another contingency table. The columns of the table represent the different variables being compared, such as different scales of mapping. The rows represent the blocking characteristics, such as the various categories of classification. The values in the cells of the tables might be the counts of correct classification or the binomial proportions of these counts divided by

  7. 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.

  8. 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

  9. Color on emergency mapping

    Science.gov (United States)

    Jiang, Lili; Qi, Qingwen; Zhang, An

    2007-06-01

    There are so many emergency issues in our daily life. Such as typhoons, tsunamis, earthquake, fires, floods, epidemics, etc. These emergencies made people lose their lives and their belongings. Every day, every hour, even every minute people probably face the emergency, so how to handle it and how to decrease its hurt are the matters people care most. If we can map it exactly before or after the emergencies; it will be helpful to the emergency researchers and people who live in the emergency place. So , through the emergency map, before emergency is occurring we can predict the situation, such as when and where the emergency will be happen; where people can refuge, etc. After disaster, we can also easily assess the lost, discuss the cause and make the lost less. The primary effect of mapping is offering information to the people who care about the emergency and the researcher who want to study it. Mapping allows the viewers to get a spatial sense of hazard. It can also provide the clues to study the relationship of the phenomenon in emergency. Color, as the basic element of the map, it can simplify and clarify the phenomenon. Color can also affects the general perceptibility of the map, and elicits subjective reactions to the map. It is to say, structure, readability, and the reader's psychological reactions can be affected by the use of color.

  10. Cognitive maps and attention.

    Science.gov (United States)

    Hardt, Oliver; Nadel, Lynn

    2009-01-01

    Cognitive map theory suggested that exploring an environment and attending to a stimulus should lead to its integration into an allocentric environmental representation. We here report that directed attention in the form of exploration serves to gather information needed to determine an optimal spatial strategy, given task demands and characteristics of the environment. Attended environmental features may integrate into spatial representations if they meet the requirements of the optimal spatial strategy: when learning involves a cognitive mapping strategy, cues with high codability (e.g., concrete objects) will be incorporated into a map, but cues with low codability (e.g., abstract paintings) will not. However, instructions encouraging map learning can lead to the incorporation of cues with low codability. On the other hand, if spatial learning is not map-based, abstract cues can and will be used to encode locations. Since exploration appears to determine what strategy to apply and whether or not to encode a cue, recognition memory for environmental features is independent of whether or not a cue is part of a spatial representation. In fact, when abstract cues were used in a way that was not map-based, or when they were not used for spatial navigation at all, they were nevertheless recognized as familiar. Thus, the relation between exploratory activity on the one hand and spatial strategy and memory on the other appears more complex than initially suggested by cognitive map theory.

  11. Periodic feedback stabilization for linear periodic evolution equations

    CERN Document Server

    Wang, Gengsheng

    2016-01-01

    This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.

  12. 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

  13. 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.

  14. 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.

  15. Crowdsourcing The National Map

    Science.gov (United States)

    McCartney, Elizabeth; Craun, Kari J.; Korris, Erin M.; Brostuen, David A.; Moore, Laurence R.

    2015-01-01

    Using crowdsourcing techniques, the US Geological Survey’s (USGS) Volunteered Geographic Information (VGI) project known as “The National Map Corps (TNMCorps)” encourages citizen scientists to collect and edit data about man-made structures in an effort to provide accurate and authoritative map data for the USGS National Geospatial Program’s web-based The National Map. VGI is not new to the USGS, but past efforts have been hampered by available technologies. Building on lessons learned, TNMCorps volunteers are successfully editing 10 different structure types in all 50 states as well as Puerto Rico and the US Virgin Islands.

  16. Region & Gateway Mapping

    OpenAIRE

    Schröter, Derik

    2007-01-01

    State-of-the-art robot mapping approaches are capable of acquiring impressively accurate 2D and 3D models of their environments. To the best of our knowledge, few of them represent structure or acquire models of task-relevant objects. In this work, a new approach to mapping of indoor environments is presented, in which the environment structure in terms of regions and gateways is automatically extracted, while the robot explores. Objects, both in 2D and 3D, are modeled explicitly in those map...

  17. MUTYH Associated Polyposis (MAP)

    DEFF Research Database (Denmark)

    Poulsen, Marie Louise Mølgaard; Bisgaard, M L

    2008-01-01

    Adenomatous Polyposis (FAP) and to a lesser extend Lynch Syndrome, which are caused by germline mutations in the APC and Mismatch Repair (MMR) genes, respectively.Here we review research findings regarding MUTYH interactions, genotypic and phenotypic characteristics of MAP, as well as surveillance......MUTYH Associated Polyposis (MAP), a Polyposis predisposition caused by biallelic mutations in the Base Excision Repair (BER) gene MUTYH, confers a marked risk of colorectal cancer (CRC). The MAP phenotype is difficult to distinguish from other hereditary CRC syndromes. Especially from Familial...

  18. 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

  19. The redoubtable ecological periodic table

    Science.gov (United States)

    Ecological periodic tables are repositories of reliable information on quantitative, predictably recurring (periodic) habitat–community patterns and their uncertainty, scaling and transferability. Their reliability derives from their grounding in sound ecological principle...

  20. Elevation data for floodplain mapping

    National Research Council Canada - National Science Library

    Committee on Floodplain Mapping Technologies; National Research Council; Division on Earth and Life Studies; National Research Council

    2007-01-01

    .... Elevation Data for Floodplain Mapping shows that there is sufficient two-dimensional base map imagery to meet FEMA's flood map modernization goals, but that the three-dimensional base elevation data...

  1. Northern Hemisphere Synoptic Weather Maps

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — Daily Series of Synoptic Weather Maps. Part I consists of plotted and analyzed daily maps of sea-level and 500-mb maps for 0300, 0400, 1200, 1230, 1300, and 1500...

  2. DOT Official County Highway Map

    Data.gov (United States)

    Minnesota Department of Natural Resources — The County Highway Map theme is a scanned and rectified version of the original MnDOT County Highway Map Series. The cultural features on some of these maps may be...

  3. Tools for mapping ecosystem services

    Science.gov (United States)

    Palomo, Ignacio; Adamescu, Mihai; Bagstad, Kenneth J.; Cazacu, Constantin; Klug, Hermann; Nedkov, Stoyan; Burkhard, Benjamin; Maes, Joachim

    2017-01-01

    Mapping tools have evolved impressively in recent decades. From early computerised mapping techniques to current cloud-based mapping approaches, we have witnessed a technological evolution that has facilitated the democratisation of Geographic Information

  4. 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.

  5. Programming with Hierarchical Maps

    DEFF Research Database (Denmark)

    Ørbæk, Peter

    This report desribes the hierarchical maps used as a central data structure in the Corundum framework. We describe its most prominent features, ague for its usefulness and briefly describe some of the software prototypes implemented using the technology....

  6. Haz-Map

    Data.gov (United States)

    U.S. Department of Health & Human Services — Haz-Map is an occupational health database designed for health and safety professionals and for consumers seeking information about the adverse effects of workplace...

  7. TOXMAP®: Environmental Health Maps

    Data.gov (United States)

    U.S. Department of Health & Human Services — TOXMAP® is a Geographic Information System (GIS) that uses maps of the United States and Canada to help users visually explore data primarily from the EPA's Toxics...

  8. The CPD Maps System

    Data.gov (United States)

    Department of Housing and Urban Development — CPD Maps includes data on the locations of existing CDBG, HOME, public housing and other HUD-funded community assets, so that users can view past investments...

  9. MetaMap

    Data.gov (United States)

    U.S. Department of Health & Human Services — MetaMap is a highly configurable application developed by the Lister Hill National Center for Biomedical Communications at the National Library of Medicine (NLM) to...

  10. FLOODPLAIN MAPPING, Bandera, TEXAS

    Data.gov (United States)

    Federal Emergency Management Agency, Department of Homeland Security — The Floodplain Mapping/Redelineation study deliverables depict and quantify the flood risks for the study area. The primary risk classifications used are the...

  11. FLOODPLAIN MAPPING, Atascosa, TEXAS

    Data.gov (United States)

    Federal Emergency Management Agency, Department of Homeland Security — The Floodplain Mapping/Redelineation study deliverables depict and quantify the flood risks for the study area. The primary risk classifications used are the...

  12. Public Waters Inventory Maps

    Data.gov (United States)

    Minnesota Department of Natural Resources — This theme is a scanned and rectified version of the Minnesota DNR - Division of Waters "Public Waters Inventory" (PWI) maps. DNR Waters utilizes a small scale...

  13. Daily Weather Maps

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — Several different government offices have published the Daily weather maps over its history. The publication has also gone by different names over time. The U.S....

  14. Mapping Intermediality in Performance

    NARCIS (Netherlands)

    2010-01-01

    Mapping Intermediality in Performance benadert het vraagstuk van intermedialiteit met betrekking tot performance (vooral theater) vanuit vijf verschillende invalshoeken: performativiteit en lichaam; tijd en ruimte; digitale cultuur en posthumanisme; netwerken; pedagogiek en praxis. In deze boeiende

  15. NOS Bathymetric Maps

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — This collection of bathymetric contour maps which represent the seafloor topography includes over 400 individual titles and covers US offshore areas including Hawaii...

  16. Survey on Ontology Mapping

    Science.gov (United States)

    Zhu, Junwu

    To create a sharable semantic space in which the terms from different domain ontology or knowledge system, Ontology mapping become a hot research point in Semantic Web Community. In this paper, motivated factors of ontology mapping research are given firstly, and then 5 dominating theories and methods, such as information accessing technology, machine learning, linguistics, structure graph and similarity, are illustrated according their technology class. Before we analyses the new requirements and takes a long view, the contributions of these theories and methods are summarized in details. At last, this paper suggest to design a group of semantic connector with the ability of migration learning for OWL-2 extended with constrains and the ontology mapping theory of axiom, so as to provide a new methodology for ontology mapping.

  17. Interest rates mapping

    Science.gov (United States)

    Kanevski, M.; Maignan, M.; Pozdnoukhov, A.; Timonin, V.

    2008-06-01

    The present study deals with the analysis and mapping of Swiss franc interest rates. Interest rates depend on time and maturity, defining term structure of the interest rate curves (IRC). In the present study IRC are considered in a two-dimensional feature space-time and maturity. Exploratory data analysis includes a variety of tools widely used in econophysics and geostatistics. Geostatistical models and machine learning algorithms (multilayer perceptron and Support Vector Machines) were applied to produce interest rate maps. IR maps can be used for the visualisation and pattern perception purposes, to develop and to explore economical hypotheses, to produce dynamic asset-liability simulations and for financial risk assessments. The feasibility of an application of interest rates mapping approach for the IRC forecasting is considered as well.

  18. National Coastal Mapping Program

    Data.gov (United States)

    Army Corps of Engineers, Department of the Army, Department of Defense — The U. S. Army Corps of Engineers (USACE) National Coastal Mapping Program (NCMP) is designed to provide high-resolution elevation and imagery data along U.S....

  19. BaseMap

    Data.gov (United States)

    California Natural Resource Agency — The goal of this project is to provide a convenient base map that can be used as a starting point for CA projects. It's simple, but designed to work at a number of...

  20. Stochasticity in the Josephson map

    International Nuclear Information System (INIS)

    Nomura, Y.; Ichikawa, Y.H.; Filippov, A.T.

    1996-04-01

    The Josephson map describes nonlinear dynamics of systems characterized by standard map with the uniform external bias superposed. The intricate structures of the phase space portrait of the Josephson map are examined on the basis of the tangent map associated with the Josephson map. Numerical observation of the stochastic diffusion in the Josephson map is examined in comparison with the renormalized diffusion coefficient calculated by the method of characteristic function. The global stochasticity of the Josephson map occurs at the values of far smaller stochastic parameter than the case of the standard map. (author)