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
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)
The endoscopic classification of representations orthogonal and symplectic groups
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
Introduction to orthogonal, symplectic and unitary representations of finite groups
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
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
The real symplectic groups quantum mechanics and optics
International Nuclear Information System (INIS)
Arvind; Mukunda, N.
1995-01-01
We present a utilitarian review of the family of matrix groups Sp(2n,R), in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of Sp(2n,R). Global decomposition theorems, interesting subgroups and their generators are described. Turning to n-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and developed a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under Sp(2n,R) action are delineated. (author). 22 refs
Symplectic Group Representation of the Two-Mode Squeezing Operator in the Coherent State Basis
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
Lectures on Symplectic Geometry
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...
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)
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
Contact and symplectic topology
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.
Function theory on symplectic manifolds
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...
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.)
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...
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
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
Singularity theory and equivariant symplectic maps
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...
International Nuclear Information System (INIS)
Deenen, J.; Quesne, C.
1985-01-01
Both non-Hermitian Dyson and Hermitian Holstein--Primakoff representations of the Sp(2d,R) algebra are obtained when the latter is restricted to a positive discrete series irreducible representation 1 +n/2>. For such purposes, some results for boson representations, recently deduced from a study of the Sp(2d,R) partially coherent states, are combined with some standard techniques of boson expansion theories. The introduction of Usui operators enables the establishment of useful relations between the various boson representations. Two Dyson representations of the Sp(2d,R) algebra are obtained in compact form in terms of ν = d(d+1)/2 pairs of boson creation and annihilation operators, and of an extra U(d) spin, characterized by the irreducible representation [lambda 1 xxxlambda/sub d/]. In contrast to what happens when lambda 1 = xxx = lambda/sub d/ = lambda, it is shown that the Holstein--Primakoff representation of the Sp(2d,R) algebra cannot be written in such a compact form for a generic irreducible representation. Explicit expansions are, however, obtained by extending the Marumori, Yamamura, and Tokunaga method of boson expansion theories. The Holstein--Primakoff representation is then used to prove that, when restricted to the Sp(2d,R) irreducible representation 1 +n/2>, the dn-dimensional harmonic oscillator Hamiltonian has a U(ν) x SU(d) symmetry group
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...
Supersymmetric symplectic quantum mechanics
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.
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
Complex and symplectic geometry
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.
Conformal transformation and symplectic structure of self-dual fields
International Nuclear Information System (INIS)
Yang Kongqing; Luo Yan
1996-01-01
Considered two dimensional self-dual fields, the symplectic structure on the space of solutions is given. It is shown that this structure is Poincare invariant. The Lagrangian of two dimensional self-dual field is invariant under infinite one component conformal group, then this symplectic structure is also invariant under this conformal group. The conserved currents in geometrical formalism are also obtained
Symplectic 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 ...
Symplectic geometry and Fourier analysis
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.
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
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.
Spherical complexes attached to symplectic lattices
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
International Nuclear Information System (INIS)
Quesne, C.
1986-01-01
In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations 1 +n/2> encountered in physical applications, are analyzed in detail with special emphasis on those of Sp(4,R) and Sp(6,R). The present paper discusses the unitary-operator coherent states, as defined by Klauder, Perelomov, and Gilmore. These states are parametrized by the points of the coset space Sp(2d,R)/H, where H is the stability group of the Sp(2d,R) irreducible representation lowest weight state, chosen as the reference state, and depends upon the relative values of lambda 1 ,...,lambda/sub d/, subject to the conditions lambda 1 > or =lambda 2 > or = x x x > or =lambda/sub d/> or =0. A parametrization of Sp(2d,R)/H corresponding to a factorization of the latter into a product of coset spaces Sp(2d,R)/U(d) and U(d)/H is chosen. The overlap of two coherent states is calculated, the action of the Sp(2d,R) generators on the coherent states is determined, and the explicit form of the unity resolution relation satisfied by the coherent states in the representation space of the irreducible representation is obtained. The Hilbert space of analytic functions arising from the coherent state representation is studied in detail. Finally, some applications of the formalism developed in the present paper are outlined
Poisson traces, D-modules, and symplectic resolutions.
Etingof, Pavel; Schedler, Travis
2018-01-01
We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.
Poisson traces, D-modules, and symplectic resolutions
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.
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)
Bianchi type A hyper-symplectic and hyper-K\\"ahler metrics in 4D
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.
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)
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...
Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics
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.
Formal Symplectic Groupoid of a Deformation Quantization
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.
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....
Elementary symplectic topology and mechanics
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...
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.
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
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)
Symplectic Geometric Algorithms for Hamiltonian Systems
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
The Maslov index in symplectic Banach spaces
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Zhu, Chaofeng
. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all...... for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds....
Symplectic 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
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
Symplectic and semiclassical aspects of the Schläfli identity
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.
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.
The Maslov index in symplectic Banach spaces
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...
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.
On local invariants of singular symplectic forms
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.
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.
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
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...
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.
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
Strongly stable real infinitesimally symplectic mappings
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
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
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.
Composite particles and symplectic (Semi-) groups
International Nuclear Information System (INIS)
Kramer, P.
1978-01-01
Nuclear composits particle dynamics is intimately related to the fermion character of nucleons. This property is implemented via the permutational structure of nuclear states, leading to the concept of exchange and to the quantum number of the orbital partition. We review Weyl operators and representations of linear canonical transformations in Bargmann Hilbert space. In section 4 we use canonical transformations to describe the general n-body dynamics. In section 5 we derive the composite particle dynamics and discuss an algorithm to obtain the interaction of composite particles whose constituents are assumed to be in harmonic oscillator states. As a first example we treat in section 6 composite particles with unexcited internal oscillator states. In section 7 we deal with composite particles of internal oscillator shell configurations. (orig.) [de
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
Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
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.
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 .
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)
Infinitesimal Deformations of a Formal Symplectic Groupoid
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)}.
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.
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
Characterization and solvability of quasipolynomial symplectic mappings
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.
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.
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.
Infinitesimal deformations of a formal symplectic groupoid
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...
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
Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties
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,...
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....
Wigner functions on non-standard symplectic vector spaces
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.
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 ...
Symplectic integrators with adaptive time steps
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.
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)
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)
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
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.
Stochastic deformation of a thermodynamic symplectic structure
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...
Symplectic multi-particle tracking on GPUs
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.
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 ...
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 ...
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
The Maslov index in weak symplectic functional analysis
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Zhu, Chaofeng
2013-01-01
We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach...
Lorentz covariant canonical symplectic algorithms for dynamics of charged particles
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.
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
Higher-order force gradient symplectic algorithms
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.
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.))
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)
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
Symplectic invariants, entropic measures and correlations of Gaussian states
Energy Technology Data Exchange (ETDEWEB)
Serafini, Alessio; Illuminati, Fabrizio; Siena, Silvio De [Dipartimento di Fisica ' E R Caianiello' , Universita di Salerno, INFM UdR Salerno, INFN Sezione di Napoli, Gruppo Collegato di Salerno, Via S Allende, 84081 Baronissi, SA (Italy)
2004-01-28
We present a derivation of the Von Neumann entropy and mutual information of arbitrary two-mode Gaussian states, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different hierarchies of mixed Gaussian states. A comparison between mutual information and entanglement of formation for symmetric states is considered, taking note of the crucial role of the symplectic eigenvalues in qualifying and quantifying the correlations present in a generic state. (letter to the editor)
Symplectic invariants, entropic measures and correlations of Gaussian states
International Nuclear Information System (INIS)
Serafini, Alessio; Illuminati, Fabrizio; Siena, Silvio De
2004-01-01
We present a derivation of the Von Neumann entropy and mutual information of arbitrary two-mode Gaussian states, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different hierarchies of mixed Gaussian states. A comparison between mutual information and entanglement of formation for symmetric states is considered, taking note of the crucial role of the symplectic eigenvalues in qualifying and quantifying the correlations present in a generic state. (letter to the editor)
The GL(1 vertical stroke 1)-symplectic fermion correspondence
International Nuclear Information System (INIS)
Creutzig, Thomas; Roenne, Peter B.
2008-12-01
In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1 vertical stroke 1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1 vertical stroke 1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1 vertical stroke 1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition. (orig.)
The GL(1 vertical stroke 1)-symplectic fermion correspondence
Energy Technology Data Exchange (ETDEWEB)
Creutzig, Thomas; Roenne, Peter B.
2008-12-15
In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1 vertical stroke 1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1 vertical stroke 1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1 vertical stroke 1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition. (orig.)
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
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
Fedosov’s formal symplectic groupoids and contravariant connections
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.
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.
Symmetries of the Space of Linear Symplectic Connections
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.
A modified symplectic PRK scheme for seismic wave modeling
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.
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
A symplectic integration method for elastic filaments
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.
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
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)
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.
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.
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.
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.
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.
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.)
Symplectic and Hamiltonian structures of nonlinear evolution equations
International Nuclear Information System (INIS)
Dorfman, I.Y.
1993-01-01
A Hamiltonian structure on a finite-dimensional manifold can be introduced either by endowing it with a (pre)symplectic structure, or by describing the Poisson bracket with the help of a tensor with two upper indices named the Poisson structure. Under the assumption of nondegeneracy, the Poisson structure is nothing else than the inverse of the symplectic structure. Also in the degenerate case the distinction between the two approaches is almost insignificant, because both presymplectic and Poisson structures split into symplectic structures on leaves of appropriately chosen foliations. Hamiltonian structures that arise in the theory of evolution equations demonstrate something new in this respect: trying to operate in local terms, one is induced to develop both approaches independently. Hamiltonian operators, being the infinite-dimensional counterparts of Poisson structures, were the first to become the subject of investigations. A considerable period of time passed before the papers initiated research in the theory of symplectic operators, being the counterparts of presymplectic structures. In what follows, we focus on the main achievements in this field
Symplectic 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)
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.``
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.
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
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
Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds
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.
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)
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)
Period mappings with applications to symplectic complex spaces
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.
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.
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.
Symplectic tomography of nonclassical states of trapped ion
International Nuclear Information System (INIS)
Man'ko, O.
1996-03-01
The marginal distribution for two types of nonclassical states of trapped ion - for squeezed and correlated states and for squeezed even and odd coherent states (squeezed Schroedinger cat states) is studied. The obtained marginal distribution for the two types of states is shown to satisfy classical dynamical equation equivalent to standard quantum evolution equation for density matrix (wave function) derived in symplectic tomography scheme. (author). 20 refs
Symplectic 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)
Gauge properties of the guiding center variational symplectic integrator
International Nuclear Information System (INIS)
Squire, J.; Tang, W. M.; Qin, H.
2012-01-01
Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008); H. Qin, X. Guan, and W. Tang, Phys. Plasmas (2009); J. Li, H. Qin, Z. Pu, L. Xie, and S. Fu, Phys. Plasmas 18, 052902 (2011)]. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms, an instability arises because the discrete symplectic structure does not become the continuous structure in the t→0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the “antisymmetric discretization gauge,” in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and φ are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss’s law [J. Squire, H. Qin, and W. Tang (to be published)].
Global symplectic structure-preserving integrators for spinning compact binaries
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.
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
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.
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
Examples of integrable and non-integrable systems on singular symplectic manifolds
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.
A new multi-symplectic scheme for the generalized Kadomtsev-Petviashvili equation
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.
Differential and symplectic topology of knots and curves
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
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
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
The group of Hamiltonian automorphisms of a star product
La Fuente-Gravy, Laurent
2015-01-01
We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
An hp symplectic pseudospectral method for nonlinear optimal control
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.
Explicit symplectic algorithms based on generating functions for charged particle dynamics
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.
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.
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)
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.)
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.
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.
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
An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
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
Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.
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.
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.
Variational and symplectic integrators for satellite relative orbit propagation including drag
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.
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.)
On the Inverse Mapping of the Formal Symplectic Groupoid of a Deformation Quantization
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.
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)
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)
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.
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.
Coherent states associated to the Jacobi group
International Nuclear Information System (INIS)
Berceanu, S.
2007-01-01
.The coherent states (CS) offer a useful connection between classical and quantum mechanics. In several previous works we have constructed CS attached to the Jacobi group. It is well known that the Jacobi group appears in Quantum Mechanics, Geometric Quantization, Optics. The mathematicians have given the name 'Jacobi group' to the semidirect product of the Heisenberg-Weyl group and the symplectic group. The same group is known to physicists under other names, as the Schroedinger group. Also the name 'Weyl-symplectic' group is used for the same semi-direct product of the Heisenberg-Weyl group and the symplectic group. In this paper we review and discuss some properties of the coherent states associated to the Jacobi group. (author)
Highly accurate symplectic element based on two variational principles
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.
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
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.
Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method
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.
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.
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.
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
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
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.
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)
Karpilovsky, G
1994-01-01
This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory
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.
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.
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
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
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.
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
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
Directory of Open Access Journals (Sweden)
You Gao
2011-01-01
Full Text Available A new construction of authentication codes with arbitration and multireceiver from singular symplectic geometry over finite fields is given. The parameters are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities of success for different types of deception are also computed.
Symplectic homoclinic tangles of the ideal separatrix of the DIII-D from type I ELMs
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.
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
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.
Classification of the linear canonical transformation and its associated real symplectic matrix
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
The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies
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
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
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
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
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.
Orthogonal and symplectic Yangians and Yang–Baxter R-operators
International Nuclear Information System (INIS)
Isaev, A.P.; Karakhanyan, D.; Kirschner, R.
2016-01-01
Yang–Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalized L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.
Orthogonal and symplectic Yangians and Yang–Baxter R-operators
Energy Technology Data Exchange (ETDEWEB)
Isaev, A.P., E-mail: isaevap@theor.jinr.ru [Bogoliubov Lab., Joint Institute of Nuclear Research, Dubna (Russian Federation); Karakhanyan, D., E-mail: karakhan@yerphi.am [Yerevan Physics Institute, 2 Alikhanyan br., 0036 Yerevan (Armenia); Kirschner, R., E-mail: Roland.Kirschner@itp.uni-leipzig.de [Institut für Theoretische Physik, Universität Leipzig, PF 100 920, D-04009 Leipzig (Germany)
2016-03-15
Yang–Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalized L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.
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.)
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
Symplectic Tracking of Multi-Isotopic Heavy-Ion Beams in SixTrack
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.
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
An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
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.
An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
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.
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
Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces
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.
Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation
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.
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
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
The Group of Hamiltonian Automorphisms of a Star Product
Energy Technology Data Exchange (ETDEWEB)
La Fuente-Gravy, Laurent, E-mail: lfuente@ulg.ac.be [Université de Liège, Département de Mathématique (Belgium)
2016-09-15
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
The Group of Hamiltonian Automorphisms of a Star Product
International Nuclear Information System (INIS)
La Fuente-Gravy, Laurent
2016-01-01
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
Infinite dimensional groups and algebras in quantum physics
International Nuclear Information System (INIS)
Ottesen, J.T.
1995-01-01
This book is an introduction to the application of infite-dimensional groups and algebras in quantum physics. Especially considered are the spin representation of the infinite-dimensional orthogonal group, the metaplectic representation of the infinite-dimensional symplectic groups, and Loop and Virasoro algebras. (HSI)
Strict deformation quantization for actions of a class of symplectic lie groups
International Nuclear Information System (INIS)
Bieliavsky, Pierre; Massar, Marc
2002-01-01
We present explicit universal strict deformation quantization formulae for actions of Iwasawa subgroups AN of SN(1, n). This answers a question raised by Rieffel in [Contemp. Math. 228 (1998), 315]. (author)
Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes
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
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.
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.
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.
From Stein to Weinstein and back symplectic geometry of affine complex manifolds
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
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
Construction of nonlinear symplectic six-dimensional thin-lens maps by exponentiation
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...
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
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
Jones, Brandon A.; Anderson, Rodney L.
2012-01-01
Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.
Symplectic no-core shell-model approach to intermediate-mass nuclei
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.
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.
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.
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.
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)
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
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.
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.
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.
An introduction to Lie group integrators – basics, new developments and applications
International Nuclear Information System (INIS)
Celledoni, Elena; Marthinsen, Håkon; Owren, Brynjulf
2014-01-01
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion of discrete gradient methods is generalised to Lie groups
Symplectic finite element scheme: application to a driven problem with a regular singularity
Energy Technology Data Exchange (ETDEWEB)
Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-02-01
A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear `tent` elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs.
Symplectic finite element scheme: application to a driven problem with a regular singularity
International Nuclear Information System (INIS)
Pletzer, A.
1996-02-01
A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear 'tent' elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs
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
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
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.
On a group of the form 2 14 : Sp (6,2) | Basheer | Quaestiones ...
African Journals Online (AJOL)
The symplectic group Sp(6,2) has a 14-dimensional absolutely irreducible module over F2: Hence a split extension group of the form G = 214:Sp(6,2) does exist. In this paper we first determine the conjugacy classes of G using the coset analysis technique. The structures of inertia factor groups were determined. The inertia ...
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
Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
International Nuclear Information System (INIS)
Xiao, Jianyuan; Liu, Jian; He, Yang; Zhang, Ruili; Qin, Hong; Sun, Yajuan
2015-01-01
Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave
Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
Energy Technology Data Exchange (ETDEWEB)
Xiao, Jianyuan [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Qin, Hong [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA; Liu, Jian [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; He, Yang [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Zhang, Ruili [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Sun, Yajuan [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, China
2015-11-01
Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint arXiv: 1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. (C) 2015 AIP Publishing LLC.
Section sigma models coupled to symplectic duality bundles on Lorentzian four-manifolds
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".
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
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.
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.
Group theoretical construction of planar noncommutative phase spaces
Energy Technology Data Exchange (ETDEWEB)
Ngendakumana, Ancille, E-mail: nancille@yahoo.fr; Todjihoundé, Leonard, E-mail: leonardt@imsp.uac.org [Institut de Mathématiques et des Sciences Physiques (IMSP), Porto-Novo (Benin); Nzotungicimpaye, Joachim, E-mail: kimpaye@kie.ac.rw [Kigali Institute of Education (KIE), Kigali (Rwanda)
2014-01-15
Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.
Group theoretical construction of planar noncommutative phase spaces
International Nuclear Information System (INIS)
Ngendakumana, Ancille; Todjihoundé, Leonard; Nzotungicimpaye, Joachim
2014-01-01
Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given
Group and representation theory
Vergados, J D
2017-01-01
This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables. This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elemen...
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.
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.
The Poincare group as the symmetry group of canonical general relativity
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Beig, R.; Murchadha, N. o
1986-01-01
This work reconsiders the formulation, due to Regge and Teitelboim, of the phase space approach to General Relativity in the asymptotically flat context, phrasing it in the language of symplectic geometry. The necessary boundary conditions at spatial infinity are spelled out in detail. Precise meaning is given to the statement that, as a result of these boundary conditions, the Poincare group acts as a symmetry group on the phase space of G.R. This situation is compared with the spi-picture of Ashtekar and Hansen, where a larger asymptotic symmetry group is obtained. (Author)
The symplectic fermion ribbon quasi-Hopf algebra and the SL(2,Z)-action on its centre
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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.
Topological Poisson Sigma models on Poisson-Lie groups
International Nuclear Information System (INIS)
Calvo, Ivan; Falceto, Fernando; Garcia-Alvarez, David
2003-01-01
We solve the topological Poisson Sigma model for a Poisson-Lie group G and its dual G*. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of both models in the open geometry reveals that there exists a map from the reduced phase of each model (P and P*) to the main symplectic leaf of the Heisenberg double (D 0 ) such that the symplectic forms on P, P* are obtained as the pull-back by those maps of the symplectic structure on D 0 . This uncovers a duality between P and P* under the exchange of bulk degrees of freedom of one model with boundary degrees of freedom of the other one. We finally solve the Poisson Sigma model for the Poisson structure on G given by a pair of r-matrices that generalizes the Poisson-Lie case. The Hamiltonian analysis of the theory requires the introduction of a deformation of the Heisenberg double. (author)
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
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.
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.
Gelfand-Dikii Hamiltonian operator and co-ad joint representation of the Volterra group
International Nuclear Information System (INIS)
Lebedev, D.R.; Manin, Yu.I.
1978-01-01
It is shown that the Gelfand-Dikii Hamiltonian structure is an analogue of a very special class of finite-dimensional symplectic structures, namely, the Kirillow structures on the orbits of the co-adjoint representation of the Lie groups. The Lie group is represented by the Volterra operators. The main interest lies in the possibility of application of the ideology of ''geometric quantization'' to the Lax equations
International Nuclear Information System (INIS)
Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Ventriglia, F
2009-01-01
A natural extension of the Wigner function to the space of irreducible unitary representations of the Weyl-Heisenberg group is discussed. The action of the automorphisms group of the Weyl-Heisenberg group onto Wigner functions and their generalizations and onto symplectic tomograms is elucidated. Some examples of physical systems are considered to illustrate some aspects of the characterization of the Wigner functions as solutions of differential equations
The Hopf algebra structure of the character rings of classical groups
International Nuclear Information System (INIS)
Fauser, Bertfried; Jarvis, Peter D; King, Ronald C
2013-01-01
The character ring Char-GL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra Symm-Λ of symmetric functions. Here we study the character rings Char-O and Char-Sp of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions. We show that Char-O and Char-Sp also admit natural Hopf algebra structures that are isomorphic to that of Char-GL, and hence to Symm-Λ. The isomorphisms are determined explicitly, along with the specification of standard bases for Char-O and Char-Sp analogous to those used for Symm-Λ. A major structural change arising from the adoption of these bases is the introduction of new orthogonal and symplectic Schur–Hall scalar products. Significantly, the adjoint with respect to multiplication no longer coincides, as it does in the Char-GL case, with a Foulkes derivative or skew operation. The adjoint and Foulkes derivative now require separate definitions, and their properties are explored here in the orthogonal and symplectic cases. Moreover, the Hopf algebras Char-O and Char-Sp are not self-dual. The dual Hopf algebras Char-O * and Char-Sp are identified. Finally, the Hopf algebra of the universal rational character ring Char-GLrat of mixed irreducible tensor representations of the general linear group is introduced and its structure maps identified. (paper)
Classical r-matrices and Poisson bracket structures on infinite-dimensional groups
International Nuclear Information System (INIS)
Aratyn, H.; Nissimov, E.; Pacheva, S.
1992-01-01
Starting with a canonical symplectic structure defined on the contangent bundle T * G we derive, via Dirac hamiltonian reduction, Poisson brackets (PBs) on an arbitrary infinite-dimensional group G (admitting central extension). The PB structures are given in terms of an r-operator kernel related to the two-cocycle of the underlying Lie algebra and satisfying a differential classical Yang-Baxter equation. The explicit expressions of the PBs among the group variables for the (N, 0) for N=0, 1, ..., 4 (super-) Virasoro groups and the group of area-preserving diffeomorphisms on the torus are presented. (orig.)
Quantum dressing orbits on compact groups
Energy Technology Data Exchange (ETDEWEB)
Jurco, B. (Technische Univ. Clausthal, Clausthal-Zellerfeld (Germany). Sommerfeld Inst.); Stovicek, P. (Prague Univ. (Czechoslovakia). Dept. of Mathematics)
1993-02-01
The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decomposition in the general case. Quantum dressing orbits are describing explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient 'coherent states' are introduced and a correspondence between classical and quantum observables is given. (orig.).
Quantum dressing orbits on compact groups
International Nuclear Information System (INIS)
Jurco, B.; Stovicek, P.
1993-01-01
The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decomposition in the general case. Quantum dressing orbits are describing explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient 'coherent states' are introduced and a correspondence between classical and quantum observables is given. (orig.)
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
On the group theoretical meaning of conformal field theories in the framework of coadjoint orbits
International Nuclear Information System (INIS)
Aratyn, H.; Nissimov, E.; Pacheva, S.
1990-01-01
We present a unifying approach to conformal field theories and other geometric models within the formalism of coadjoint orbits of infinite dimensional Lie groups with central extensions. Starting from the previously obtained general formula for the symplectic action in terms of two fundamental group one-cocycles, we derive the most general form of the Polyakov-Wiegmann composition laws for any geometric model. These composition laws are succinct expressions of all pertinent Noether symmetries. As a basic consequence we obtain Ward identities allowing for the exact quantum solvability of any geometric model. (orig.)
New insights in particle dynamics from group cohomology
International Nuclear Information System (INIS)
Aldaya, V; Jaramillo, J L; Guerrero, J
2002-01-01
The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterizing the particle appear as central extension parameters of a group which is obtained from a centrally extended kinematical group (Poincare or Galilei) by making some subgroup local. The corresponding dynamics is generated by a vector field inside the kernel of a pre-symplectic form which is derived from the canonical left-invariant 1-form on the extended group. A non-relativistic limit is derived from the geodesic motion via an Inoenue-Wigner contraction. A deeper analysis of the cohomological structure reveals the possibility of a new force associated with a non-trivial mixing of gravity and electromagnetism leading to, in principle, testable predictions. (letter to the editor)
Quantum group and quantum symmetry
International Nuclear Information System (INIS)
Chang Zhe.
1994-05-01
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum group is primarily introduced as a systematic method for solving the Yang-Baxter equation. Quantum group theory is presented within the framework of quantum double through quantizing Lie bi-algebra. Both the highest weight and the cyclic representations are investigated for the quantum group and emphasis is laid on the new features of representations for q being a root of unity. Quantum symmetries are explored in selected topics of modern physics. For a Hamiltonian system the quantum symmetry is an enlarged symmetry that maintains invariance of equations of motion and allows a deformation of the Hamiltonian and symplectic form. The configuration space of the integrable lattice model is analyzed in terms of the representation theory of quantum group. By means of constructing the Young operators of quantum group, the Schroedinger equation of the model is transformed to be a set of coupled linear equations that can be solved by the standard method. Quantum symmetry of the minimal model and the WZNW model in conformal field theory is a hidden symmetry expressed in terms of screened vertex operators, and has a deep interplay with the Virasoro algebra. In quantum group approach a complete description for vibrating and rotating diatomic molecules is given. The exact selection rules and wave functions are obtained. The Taylor expansion of the analytic formulas of the approach reproduces the famous Dunham expansion. (author). 133 refs, 20 figs
Directory of Open Access Journals (Sweden)
Frédéric Barbaresco
2016-11-01
Full Text Available We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using geometric Planck temperature of Souriau model and symplectic cocycle notion, the Fisher metric is identified as a Souriau geometric heat capacity. The Souriau model is based on affine representation of Lie group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie group thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant–Kirillov–Souriau 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of information geometry for the action of an affine group for exponential families, and provide some illustrations of use cases for multivariate gaussian densities. Information geometry is presented in the context of the seminal work of Fréchet and his Clairaut-Legendre equation. The Souriau model of statistical physics is validated as compatible with the Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.
Group theoretical methods in physics. [Tuebingen, July 18-22, 1977
Energy Technology Data Exchange (ETDEWEB)
Kramer, P; Rieckers, A
1978-01-01
This volume comprises the proceedings of the 6th International Colloquium on Group Theoretical Methods in Physics, held at Tuebingen in July 1977. Invited papers were presented on the following topics: supersymmetry and graded Lie algebras; concepts of order and disorder arising from molecular physics; symplectic structures and many-body physics; symmetry breaking in statistical mechanics and field theory; automata and systems as examples of applied (semi-) group theory; renormalization group; and gauge theories. Summaries are given of the contributed papers, which can be grouped as follows: supersymmetry, symmetry in particles and relativistic physics; symmetry in molecular and solid state physics; broken symmetry and phase transitions; structure of groups and dynamical systems; representations of groups and Lie algebras; and general symmetries, quantization. Those individual papers in scope for the TIC data base are being entered from ATOMINDEX tapes. (RWR)
Convexity properties of Hamiltonian group actions
Guillemin, Victor
2005-01-01
This is a monograph on convexity properties of moment mappings in symplectic geometry. The fundamental result in this subject is the Kirwan convexity theorem, which describes the image of a moment map in terms of linear inequalities. This theorem bears a close relationship to perplexing old puzzles from linear algebra, such as the Horn problem on sums of Hermitian matrices, on which considerable progress has been made in recent years following a breakthrough by Klyachko. The book presents a simple local model for the moment polytope, valid in the "generic&rdquo case, and an elementary Morse-theoretic argument deriving the Klyachko inequalities and some of their generalizations. It reviews various infinite-dimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu). Finally, it gives an account of a new convexity theorem for moment map images of orbits of a Borel sub...
Algebras of functions on compact quantum groups, Schubert cells and quantum tori
International Nuclear Information System (INIS)
Levendorskij, S.; Soibelman, Ya.
1991-01-01
The structure of Poisson Lie groups on a simple compact group are parametrized by pairs (a, u), where aelement ofR, uelement ofΛ 2 f R , and f R is a real Cartan subalgebra of complexification of Lie algebra of the group in question. In the present article the description of the symplectic leaves for all pairs (a, u) is given. Also, the corresponding quantized algebras of functions are constructed and their irreducible representations are described. In the course of investigation Schubert cells and quantum tori appear. At the end of the article the quantum analog of the Weyl group is constructed and some of its applications, among them the formula for the universal R-matrix, are given. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Mei, Lijie, E-mail: bxhanm@126.com; Wu, Xinyuan, E-mail: xywu@nju.edu.cn
2016-10-15
In general, extended Runge–Kutta–Nyström (ERKN) methods are more effective than traditional Runge–Kutta–Nyström (RKN) methods in dealing with oscillatory Hamiltonian systems. However, the theoretical analysis for ERKN methods, such as the order conditions, the symplectic conditions and the symmetric conditions, becomes much more complicated than that for RKN methods. Therefore, it is a bottleneck to construct high-order ERKN methods efficiently. In this paper, we first establish the ERKN group Ω for ERKN methods and the RKN group G for RKN methods, respectively. We then rigorously show that ERKN methods are a natural extension of RKN methods, that is, there exists an epimorphism η of the ERKN group Ω onto the RKN group G. This epimorphism gives a global insight into the structure of the ERKN group by the analysis of its kernel and the corresponding RKN group G. Meanwhile, we establish a particular mapping φ of G into Ω so that each image element is an ideal representative element of the congruence class in Ω. Furthermore, an elementary theoretical analysis shows that this map φ can preserve many structure-preserving properties, such as the order, the symmetry and the symplecticity. From the epimorphism η together with its section φ, we may gain knowledge about the structure of the ERKN group Ω via the RKN group G. In light of the theoretical analysis of this paper, we obtain high-order structure-preserving ERKN methods in an effective way for solving oscillatory Hamiltonian systems. Numerical experiments are carried out and the results are very promising, which strongly support our theoretical analysis presented in this paper.
Quantization and harmonic analysis on nilpotent Lie groups
International Nuclear Information System (INIS)
Wildberger, N.J.
1983-01-01
Weyl Quantization is a procedure for associating a function on which the canonical commutation relations are realized. If G is a simply-connected, connected nilpotent Lie group with Lie algebra g and dual g/sup */, it is shown how to inductively construct symplectic isomorphisms between every co-adjoint orbit O and the bundle in Hilbert Space for some m. Weyl Quantization can then be used to associate to each orbit O a unitary representation rho 0 of G, recovering the classification of the unitary dual by Kirillov. It is used to define a geometric Fourier transform, F : L 1 (G) → functions on g/sup */, and it is shown that the usual operator-valued Fourier transform can be recovered from F, characters are inverse Fourier transforms of invariant measures on orbits, and matrix coefficients are inverse Fourier transforms of non-invariant measures supported on orbits. Realizations of the representations rho 0 in subspaces of L 2 (O) are obtained.. Finally, the kernel function is computed for the upper triangular unipotent group and one other example
Energy Technology Data Exchange (ETDEWEB)
Fields, Susannah
2007-08-16
This project is currently under contract for research through the Department of Homeland Security until 2011. The group I was responsible for studying has to remain confidential so as not to affect the current project. All dates, reference links and authors, and other distinguishing characteristics of the original group have been removed from this report. All references to the name of this group or the individual splinter groups has been changed to 'Group X'. I have been collecting texts from a variety of sources intended for the use of recruiting and radicalizing members for Group X splinter groups for the purpose of researching the motivation and intent of leaders of those groups and their influence over the likelihood of group radicalization. This work included visiting many Group X websites to find information on splinter group leaders and finding their statements to new and old members. This proved difficult because the splinter groups of Group X are united in beliefs, but differ in public opinion. They are eager to tear each other down, prove their superiority, and yet remain anonymous. After a few weeks of intense searching, a list of eight recruiting texts and eight radicalizing texts from a variety of Group X leaders were compiled.
Sawyer, Keith
2015-01-01
Keith Sawyer views the spontaneous collaboration of group creativity and improvisation actions as "group flow," which organizations can use to function at optimum levels. Sawyer establishes ideal conditions for group flow: group goals, close listening, complete concentration, being in control, blending egos, equal participation, knowing…
Passman, Donald S
2012-01-01
This volume by a prominent authority on permutation groups consists of lecture notes that provide a self-contained account of distinct classification theorems. A ready source of frequently quoted but usually inaccessible theorems, it is ideally suited for professional group theorists as well as students with a solid background in modern algebra.The three-part treatment begins with an introductory chapter and advances to an economical development of the tools of basic group theory, including group extensions, transfer theorems, and group representations and characters. The final chapter feature
Group devaluation and group identification
Leach, C.W.; Rodriguez Mosquera, P.M.; Vliek, M.L.W.; Hirt, E.
2010-01-01
In three studies, we showed that increased in-group identification after (perceived or actual) group devaluation is an assertion of a (preexisting) positive social identity that counters the negative social identity implied in societal devaluation. Two studies with real-world groups used order
Lie groups and algebraic groups
Indian Academy of Sciences (India)
We give an exposition of certain topics in Lie groups and algebraic groups. This is not a complete ... of a polynomial equation is equivalent to the solva- bility of the equation ..... to a subgroup of the group of roots of unity in k (in particular, it is a ...
Wilson, Kristy J.; Brickman, Peggy; Brame, Cynthia J.
2018-01-01
Science, technology, engineering, and mathematics faculty are increasingly incorporating both formal and informal group work in their courses. Implementing group work can be improved by an understanding of the extensive body of educational research studies on this topic. This essay describes an online, evidence-based teaching guide published by…
International Nuclear Information System (INIS)
Eggermont, G.
2006-01-01
In 2005, PISA organised proactive meetings of reflection groups on involvement in decision making, expert culture and ethical aspects of radiation protection.All reflection group meetings address particular targeted audiences while the output publication in book form is put forward
Scott, W R
2010-01-01
Here is a clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.
Adams, Karen
2015-01-01
In this article Karen Adams demonstrates how to incorporate group grammar techniques into a classroom activity. In the activity, students practice using the target grammar to do something they naturally enjoy: learning about each other.
International Nuclear Information System (INIS)
Bauer, H.; Black, I.; Heusler, A.; Hoeptner, G.; Krafft, F.; Lang, R.; Moellenkamp, R.; Mueller, W.; Mueller, W.F.; Schati, C.; Schmidt, A.; Schwind, D.; Weber, G.
1983-01-01
The computer groups has been reorganized to take charge for the general purpose computers DEC10 and VAX and the computer network (Dataswitch, DECnet, IBM - connections to GSI and IPP, preparation for Datex-P). (orig.)
DEFF Research Database (Denmark)
Pimentel, Ricardo; Noguira, Eloy Eros da Silva; Elkjær, Bente
The article presents a study that aims at the apprehension of the group learning in a top management team composed by teachers in a Brazilian Waldorf school whose management is collective. After deciding to extend the school, they had problems recruiting teachers who were already trained based...... on the Steiner´s ideas, which created practical problems for conducting management activities. The research seeks to understand how that group of teachers collectively manage the school, facing the lack of resources, a significant heterogeneity in the relationships, and the conflicts and contradictions......, and they are interrelated to the group learning as the construction, maintenance and reconstruction of the intelligibility of practices. From this perspective, it can be said that learning is a practice and not an exceptional phenomenon. Building, maintaining and rebuilding the intelligibility is the group learning...
International Nuclear Information System (INIS)
Rome, C.P.
1976-01-01
Group Technology has been conceptually applied to the manufacture of batch-lots of 554 machined electromechanical parts which now require 79 different types of metal-removal tools. The products have been grouped into 7 distinct families which require from 8 to 22 machines in each machine-cell. Throughput time can be significantly reduced and savings can be realized from tooling, direct-labor, and indirect-labor costs
Fuchs, László
2015-01-01
Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah’s seminal work on the undecidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, th...
Scandiffio, A L
1990-12-01
Group dynamics play a significant role within any organization, culture, or unit. The important thing to remember with any of these structures is that they are made up of people--people with different ideas, motivations, background, and sometimes different agendas. Most groups, formal or informal, look for a leader in an effort to maintain cohesiveness of the unit. At times, that cultural bond must be developed; once developed, it must be nurtured. There are also times that one of the group no longer finds the culture comfortable and begins to act out behaviorally. It is these times that become trying for the leader as she or he attempts to remain objective when that which was once in the building phase of group cohesiveness starts to fall apart. At all times, the manager must continue to view the employee creating the disturbance as an integral part of the group. It is at this time that it is beneficial to perceive the employee exhibiting problem behaviors as a special employee, as one who needs the benefit of your experience and skills, as one who is still part of the group. It is also during this time that the manager should focus upon her or his own views in the area of power, communication, and the corporate culture of the unit that one has established before attempting to understand another's point of view. Once we understand our own motivation and accept ourselves, it is then that we may move on to offer assistance to another. Once we understand our insecurities recognizing staff dysfunction as a symptom of system dysfunction will not be so threatening to the concept of the manager that we perceive ourselves to be. It takes a secure person to admit that she or he favors staff before deciding to do something to change things. The important thing to know is that it can be done. The favored staff can find a new way of relating to others, the special employee can find new modes of behavior (and even find self-esteem in the process), the group can find new ways
DEFF Research Database (Denmark)
Møller Larsen, Marcus; Pedersen, Torben; Slepniov, Dmitrij
2010-01-01
The last years’ rather adventurous journey from 2004 to 2009 had taught the fifth-largest toy-maker in the world - the LEGO Group - the importance of managing the global supply chain effectively. In order to survive the largest internal financial crisis in its roughly 70 years of existence......, the management had, among many initiatives, decided to offshore and outsource a major chunk of its production to Flextronics. In this pursuit of rapid cost-cutting sourcing advantages, the LEGO Group planned to license out as much as 80 per cent of its production besides closing down major parts...
E. van den Berg; P. van Houwelingen; J. de Hart
2011-01-01
Original title: Informele groepen Going out running with a group of friends, rather than joining an official sports club. Individuals who decide to take action themselves rather than giving money to good causes. Maintaining contact with others not as a member of an association, but through an
L. Taylor
2011-01-01
The CMS Communications Group, established at the start of 2010, has been busy in all three areas of its responsibility: (1) Communications Infrastructure, (2) Information Systems, and (3) Outreach and Education. Communications Infrastructure There are now 55 CMS Centres worldwide that are well used by physicists working on remote CMS shifts, Computing operations, data quality monitoring, data analysis and outreach. The CMS Centre@CERN in Meyrin, is the centre of the CMS offline and computing operations, hosting dedicated analysis efforts such as during the CMS Heavy Ion lead-lead running. With a majority of CMS sub-detectors now operating in a “shifterless” mode, many monitoring operations are now routinely performed from there, rather than in the main Control Room at P5. The CMS Communications Group, CERN IT and the EVO team are providing excellent videoconferencing support for the rapidly-increasing number of CMS meetings. In parallel, CERN IT and ...
International Nuclear Information System (INIS)
Anon.
1993-01-01
Full text: In his review 'Genesis of Unified Gauge Theories' at the symposium in Honour of Abdus Salam (June, page 23), Tom Kibble of Imperial College, London, looked back to the physics events around Salam from 1959-67. He described how, in the early 1960s, people were pushing to enlarge the symmetry of strong interactions beyond the SU(2) of isospin and incorporate the additional strangeness quantum number. Kibble wrote - 'Salam had students working on every conceivable symmetry group. One of these was Yuval Ne'eman, who had the good fortune and/or prescience to work on SU(3). From that work, and of course from the independent work of Murray Gell- Mann, stemmed the Eightfold Way, with its triumphant vindication in the discovery of the omega-minus in 1964.' Yuval Ne'eman writes - 'I was the Defence Attaché at the Israeli Embassy in London and was admitted by Salam as a part-time graduate student when I arrived in 1958. I started research after resigning from the Embassy in May 1960. Salam suggested a problem: provide vector mesons with mass - the problem which was eventually solved by Higgs, Guralnik, Kibble,.... (as described by Kibble in his article). I explained to Salam that I had become interested in symmetry. Nobody at Imperial College at the time, other than Salam himself, was doing anything in groups, and attention further afield was focused on the rotation - SO(N) - groups. Reacting to my own half-baked schemes, Salam told me to forget about the rotation groups he taught us, and study group theory in depth, directing me to Eugene Dynkin's classification of Lie subalgebras, about which he had heard from Morton Hamermesh. I found Dynkin incomprehensible without first learning about Lie algebras from Henri Cartan's thesis, which luckily had been reproduced by Dynkin in his 1946 thesis, using his diagram method. From a copy of a translation of Dynkin's thesis which I found in the British Museum Library, I
L. Taylor
2010-01-01
The CMS Communications Group, established at the start of 2010, has been strengthening the activities in all three areas of its responsibility: (1) Communications Infrastructure, (2) Information Systems, and (3) Outreach and Education. Communications Infrastructure The Communications Group has invested a lot of effort to support the operations needs of CMS. Hence, the CMS Centres where physicists work on remote CMS shifts, Data Quality Monitoring, and Data Analysis are running very smoothly. There are now 55 CMS Centres worldwide, up from just 16 at the start of CMS data-taking. The latest to join are Imperial College London, the University of Iowa, and the Università di Napoli. The CMS Centre@CERN in Meyrin, which is now full repaired after the major flooding at the beginning of the year, has been at the centre of CMS offline and computing operations, most recently hosting a large fraction of the CMS Heavy Ion community during the lead-lead run. A number of sub-detector shifts can now take pla...
DEFF Research Database (Denmark)
Tychsen, Anders; Hitchens, Michael; Brolund, Thea
2008-01-01
Role-playing games (RPGs) are a well-known game form, existing in a number of formats, including tabletop, live action, and various digital forms. Despite their popularity, empirical studies of these games are relatively rare. In particular there have been few examinations of the effects of the v......Role-playing games (RPGs) are a well-known game form, existing in a number of formats, including tabletop, live action, and various digital forms. Despite their popularity, empirical studies of these games are relatively rare. In particular there have been few examinations of the effects...... of the various formats used by RPGs on the gaming experience. This article presents the results of an empirical study, examining how multi-player tabletop RPGs are affected as they are ported to the digital medium. Issues examined include the use of disposition assessments to predict play experience, the effect...... of group dynamics, the influence of the fictional game characters and the comparative play experience between the two formats. The results indicate that group dynamics and the relationship between the players and their digital characters, are integral to the quality of the gaming experience in multiplayer...
L. Taylor
2011-01-01
The CMS Communications Group has been busy in all three areas of its responsibility: (1) Communications Infrastructure, (2) Information Systems, and (3) Outreach and Education. Communications Infrastructure The 55 CMS Centres worldwide are well used by physicists working on remote CMS shifts, Computing operations, data quality monitoring, data analysis and outreach. The CMS Centre@CERN in Meyrin, is the centre of the CMS Offline and Computing operations, and a number of subdetector shifts can now take place there, rather than in the main Control Room at P5. A new CMS meeting room has been equipped for videoconferencing in building 42, next to building 40. Our building 28 meeting room and the facilities at P5 will be refurbished soon and plans are underway to steadily upgrade the ageing equipment in all 15 CMS meeting rooms at CERN. The CMS evaluation of the Vidyo tool indicates that it is not yet ready to be considered as a potential replacement for EVO. The Communications Group provides the CMS-TV (web) cha...
L. Taylor
2010-01-01
The recently established CMS Communications Group, led by Lucas Taylor, has been busy in all three of its main are areas of responsibility: Communications Infrastructure, Information Systems, and Outreach and Education Communications Infrastructure The damage caused by the flooding of the CMS Centre@CERN on 21st December has been completely repaired and all systems are back in operation. Major repairs were made to the roofs, ceilings and one third of the floor had to be completely replaced. Throughout these works, the CMS Centre was kept operating and even hosted a major press event for first 7 TeV collisions, as described below. Incremental work behind the scenes is steadily improving the quality of the CMS communications infrastructure, particularly Webcasting, video conferencing, and meeting rooms at CERN. CERN/IT is also deploying a pilot service of a new videoconference tool called Vidyo, to assess whether it might provide an enhanced service at a lower cost, compared to the EVO tool currently in w...
L. Taylor
2011-01-01
Communications Infrastructure The 55 CMS Centres worldwide are well used by physicists working on remote CMS shifts, Computing operations, data quality monitoring, data analysis and outreach. The CMS Centre@CERN in Meyrin is particularly busy at the moment, hosting about 50 physicists taking part in the heavy-ion data-taking and analysis. Three new CMS meeting room will be equipped for videoconferencing in early 2012: 40/5B-08, 42/R-031, and 28/S-029. The CMS-TV service showing LHC Page 1, CMS Page 1, etc. (http://cmsdoc.cern.ch/cmscc/projector/index.jsp) is now also available for mobile devices: http://cern.ch/mcmstv. Figure 12: Screenshots of CMS-TV for mobile devices Information Systems CMS has a new web site: (http://cern.ch/cms) using a modern web Content Management System to ensure content and links are managed and updated easily and coherently. It covers all CMS sub-projects and groups, replacing the iCMS internal pages. It also incorporates the existing CMS public web site (http:/...
L. Taylor
2012-01-01
Outreach and Education We are fortunate that our research has captured the public imagination, even though this inevitably puts us under the global media spotlight, as we saw with the Higgs seminar at CERN in December, which had 110,000 distinct webcast viewers. The media interest was huge with 71 media organisations registering to come to CERN to cover the Higgs seminar, which was followed by a press briefing with the DG and Spokespersons. This event resulted in about 2,000 generally positive stories in the global media. For this seminar, the CMS Communications Group prepared up-to-date news and public material, including links to the CMS results, animations and event displays [http://cern.ch/go/Ch8thttp://cern.ch/go/Ch8t]. There were 44,000 page-views on the CMS public website, with the Higgs news article being by far the most popular item. CMS event displays from iSpy are fast becoming the iconic media images, featuring on numerous major news outlets (BBC, CNN, MSN...) as well as in the sci...
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
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.
Real symplectic formulation of local special geometry
Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar
2006-01-01
We consider a formulation of local special geometry in terms of Darboux special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the metric is obtained which is manifestly $\\mathbf{Sp}(2n,\\mathbb{R})$ covariant. Unlike the rigid case the metric is not given by the Hessian of the real function $S(P)$ which is the Legendre transform of the imaginary part of the holomorphic prepotential. Rather it is given by an expression that contains $S$, its Hessian and the conjugate momenta $S_I=\\frac{\\partial S}{\\partial P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional) metric proportional to the Hessian with an appropriate conformal factor.
Symplectic Structure of Intrinsic Time Gravity
Directory of Open Access Journals (Sweden)
Eyo Eyo Ita
2016-08-01
Full Text Available The Poisson structure of intrinsic time gravity is analysed. With the starting point comprising a unimodular three-metric with traceless momentum, a trace-induced anomaly results upon quantization. This leads to a revision of the choice of momentum variable to the (mixed index traceless momentric. This latter choice unitarily implements the fundamental commutation relations, which now take on the form of an affine algebra with SU(3 Lie algebra amongst the momentric variables. The resulting relations unitarily implement tracelessness upon quantization. The associated Poisson brackets and Hamiltonian dynamics are studied.
Deformations of polyhedra and polygons by the unitary group
Energy Technology Data Exchange (ETDEWEB)
Livine, Etera R. [Laboratoire de Physique, ENS Lyon, CNRS-UMR 5672, 46 Allée d' Italie, Lyon 69007, France and Perimeter Institute, 31 Caroline St N, Waterloo, Ontario N2L 2Y5 (Canada)
2013-12-15
We introduce the set of framed (convex) polyhedra with N faces as the symplectic quotient C{sup 2N}//SU(2). A framed polyhedron is then parametrized by N spinors living in C{sup 2} satisfying suitable closure constraints and defines a usual convex polyhedron plus extra U(1) phases attached to each face. We show that there is a natural action of the unitary group U(N) on this phase space, which changes the shape of faces and allows to map any (framed) polyhedron onto any other with the same total (boundary) area. This identifies the space of framed polyhedra to the Grassmannian space U(N)/ (SU(2)×U(N−2)). We show how to write averages of geometrical observables (polynomials in the faces' area and the angles between them) over the ensemble of polyhedra (distributed uniformly with respect to the Haar measure on U(N)) as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically. We also use the Itzykson-Zuber formula from matrix models as the generating function for these averages and correlations. In the quantum case, a canonical quantization of the framed polyhedron phase space leads to the Hilbert space of SU(2) intertwiners (or, in other words, SU(2)-invariant states in tensor products of irreducible representations). The total boundary area as well as the individual face areas are quantized as half-integers (spins), and the Hilbert spaces for fixed total area form irreducible representations of U(N). We define semi-classical coherent intertwiner states peaked on classical framed polyhedra and transforming consistently under U(N) transformations. And we show how the U(N) character formula for unitary transformations is to be considered as an extension of the Itzykson-Zuber to the quantum level and generates the traces of all polynomial observables over the Hilbert space of intertwiners. We finally apply the same formalism to two dimensions and show that classical (convex) polygons can be described in
Which finite simple groups are unit groups?
DEFF Research Database (Denmark)
Davis, Christopher James; Occhipinti, Tommy
2014-01-01
We prove that if G is a finite simple group which is the unit group of a ring, then G is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order 2^k −1 for some k; or (c) a projective special linear group PSLn(F2) for some n ≥ 3. Moreover, these groups do all occur a...
Group Cohesion in Experiential Growth Groups
Steen, Sam; Vasserman-Stokes, Elaina; Vannatta, Rachel
2014-01-01
This article explores the effect of web-based journaling on changes in group cohesion within experiential growth groups. Master's students were divided into 2 groups. Both used a web-based platform to journal after each session; however, only 1 of the groups was able to read each other's journals. Quantitative data collected before and…
Zimpfer, David G.
1992-01-01
Lists 21 new publications in group work, of which 9 are reviewed. Those discussed include publications on group counseling and psychotherapy, structured groups, support groups, psychodrama, and social group work. (Author/NB)
Indian Academy of Sciences (India)
Jyotishman Bhowmick
2015-11-07
Nov 7, 2015 ... Classical. Quantum. Background. Compact Hausdorff space. Unital C∗ algebra. Gelfand-Naimark. Compact Group. Compact Quantum Group. Woronowicz. Group Action. Coaction. Woronowicz. Riemannian manifold. Spectral triple. Connes. Isometry group. Quantum Isometry Group. To be discussed.
Group typicality, group loyalty and cognitive development.
Patterson, Meagan M
2014-09-01
Over the course of childhood, children's thinking about social groups changes in a variety of ways. Developmental Subjective Group Dynamics (DSGD) theory emphasizes children's understanding of the importance of conforming to group norms. Abrams et al.'s study, which uses DSGD theory as a framework, demonstrates the social cognitive skills underlying young elementary school children's thinking about group norms. Future research on children's thinking about groups and group norms should explore additional elements of this topic, including aspects of typicality beyond loyalty. © 2014 The British Psychological Society.
AREVA group overview; Presentation du groupe AREVA
Energy Technology Data Exchange (ETDEWEB)
NONE
2002-02-08
This document presents the Group Areva, a world nuclear industry leader, from a financial holding company to an industrial group, operating in two businesses: the nuclear energy and the components. The structure and the market of the group are discussed, as the financial assets. (A.L.B.)
Overgroups of root groups in classical groups
Aschbacher, Michael
2016-01-01
The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of c-root subgroups.
Interagency mechanical operations group numerical systems group
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-09-01
This report consists of the minutes of the May 20-21, 1971 meeting of the Interagency Mechanical Operations Group (IMOG) Numerical Systems Group. This group looks at issues related to numerical control in the machining industry. Items discussed related to the use of CAD and CAM, EIA standards, data links, and numerical control.
Chevalley, Claude
2018-01-01
The standard text on the subject for many years, this introductory treatment covers classical linear groups, topological groups, manifolds, analytic groups, differential calculus of Cartan, and compact Lie groups and their representations. 1946 edition.
Introduction to Sporadic Groups
Directory of Open Access Journals (Sweden)
Luis J. Boya
2011-01-01
Full Text Available This is an introduction to finite simple groups, in particular sporadic groups, intended for physicists. After a short review of group theory, we enumerate the 1+1+16=18 families of finite simple groups, as an introduction to the sporadic groups. These are described next, in three levels of increasing complexity, plus the six isolated ''pariah'' groups. The (old five Mathieu groups make up the first, smallest order level. The seven groups related to the Leech lattice, including the three Conway groups, constitute the second level. The third and highest level contains the Monster group M, plus seven other related groups. Next a brief mention is made of the remaining six pariah groups, thus completing the 5+7+8+6=26 sporadic groups. The review ends up with a brief discussion of a few of physical applications of finite groups in physics, including a couple of recent examples which use sporadic groups.
Group theoretical methods and wavelet theory: coorbit theory and applications
Feichtinger, Hans G.
2013-05-01
Before the invention of orthogonal wavelet systems by Yves Meyer1 in 1986 Gabor expansions (viewed as discretized inversion of the Short-Time Fourier Transform2 using the overlap and add OLA) and (what is now perceived as) wavelet expansions have been treated more or less at an equal footing. The famous paper on painless expansions by Daubechies, Grossman and Meyer3 is a good example for this situation. The description of atomic decompositions for functions in modulation spaces4 (including the classical Sobolev spaces) given by the author5 was directly modeled according to the corresponding atomic characterizations by Frazier and Jawerth,6, 7 more or less with the idea of replacing the dyadic partitions of unity of the Fourier transform side by uniform partitions of unity (so-called BUPU's, first named as such in the early work on Wiener-type spaces by the author in 19808). Watching the literature in the subsequent two decades one can observe that the interest in wavelets "took over", because it became possible to construct orthonormal wavelet systems with compact support and of any given degree of smoothness,9 while in contrast the Balian-Low theorem is prohibiting the existence of corresponding Gabor orthonormal bases, even in the multi-dimensional case and for general symplectic lattices.10 It is an interesting historical fact that* his construction of band-limited orthonormal wavelets (the Meyer wavelet, see11) grew out of an attempt to prove the impossibility of the existence of such systems, and the final insight was that it was not impossible to have such systems, and in fact quite a variety of orthonormal wavelet system can be constructed as we know by now. Meanwhile it is established wisdom that wavelet theory and time-frequency analysis are two different ways of decomposing signals in orthogonal resp. non-orthogonal ways. The unifying theory, covering both cases, distilling from these two situations the common group theoretical background lead to the
Special metrics and group actions in geometry
Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi
2017-01-01
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
Group Work: How to Use Groups Effectively
Burke, Alison
2011-01-01
Many students cringe and groan when told that they will need to work in a group. However, group work has been found to be good for students and good for teachers. Employers want college graduates to have developed teamwork skills. Additionally, students who participate in collaborative learning get better grades, are more satisfied with their…
Free Boolean Topological Groups
Directory of Open Access Journals (Sweden)
Ol’ga Sipacheva
2015-11-01
Full Text Available Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.
McGrath, Joseph E.
1978-01-01
Summarizes research on small group processes by giving a comprehensive account of the types of variables primarily studied in the laboratory. These include group structure, group composition, group size, and group relations. Considers effects of power, leadership, conformity to social norms, and role relationships. (Author/AV)
Druţu, Cornelia
2018-01-01
The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the f...
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
Group purchasing: an overview.
Wetrich, J G
1987-07-01
The various types and operational methods of purchasing groups are described, and evaluation of groups is discussed. Since group purchasing is increasing in popularity as a method of controlling drug costs, community and hospital pharmacy managers may need to evaluate various groups to determine the appropriateness of their services. Groups are categorized as independent, system based, or alliance or association based. Instead of "purchasing," some groups develop contracts for hospitals, which then purchase directly from the vendor. Aside from this basic difference between groups that purchase and groups that contract, comparisons among groups are difficult because of the wide variation in sizes and services. Competition developing from diversification among groups has led to "super groups," formed from local and regional groups. In evaluating groups, advantages and disadvantages germane to accomplishing the member's objectives must be considered. To ensure a group's success, members must be committed and support the group's philosophies; hospital pharmacists must help to establish a strong formulary system. To select vendors, groups should develop formal qualification and selection criteria and should not base a decision solely on price. The method of solicitation (bidding or negotiating), as well as the role of the prime vendor, should be studied. Legal implications of group purchasing, especially in the areas of administrative fees and drug diversion, must also be considered. The most advantageous group for each organization will include members with common missions and will be able to implement strategies for future success.
Ordered groups and infinite permutation groups
1996-01-01
The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that t...
ALIGNMENTS OF GROUP GALAXIES WITH NEIGHBORING GROUPS
International Nuclear Information System (INIS)
Wang Yougang; Chen Xuelei; Park, Changbom; Yang Xiaohu; Choi, Yun-Young
2009-01-01
Using a sample of galaxy groups found in the Sloan Digital Sky Survey Data Release 4, we measure the following four types of alignment signals: (1) the alignment between the distributions of the satellites of each group relative to the direction of the nearest neighbor group (NNG); (2) the alignment between the major axis direction of the central galaxy of the host group (HG) and the direction of the NNG; (3) the alignment between the major axes of the central galaxies of the HG and the NNG; and (4) the alignment between the major axes of the satellites of the HG and the direction of the NNG. We find strong signal of alignment between the satellite distribution and the orientation of central galaxy relative to the direction of the NNG, even when the NNG is located beyond 3r vir of the host group. The major axis of the central galaxy of the HG is aligned with the direction of the NNG. The alignment signals are more prominent for groups that are more massive and with early-type central galaxies. We also find that there is a preference for the two major axes of the central galaxies of the HG and NNG to be parallel for the system with both early central galaxies, however, not for the systems with both late-type central galaxies. For the orientation of satellite galaxies, we do not find any significant alignment signals relative to the direction of the NNG. From these four types of alignment measurements, we conclude that the large-scale environment traced by the nearby group affects primarily the shape of the host dark matter halo, and hence also affects the distribution of satellite galaxies and the orientation of central galaxies. In addition, the NNG directly affects the distribution of the satellite galaxies by inducing asymmetric alignment signals, and the NNG at very small separation may also contribute a second-order impact on the orientation of the central galaxy in the HG.
International Nuclear Information System (INIS)
Andritzky, W.
1978-01-01
For the first empirical study of citizens' action groups 331 such groups were consulted. Important information was collected on the following aspects of these groups: their self-image, areas and forms of activities, objectives and their extent, how long the group has existed, successes and failures and their forms of organisation. (orig.) [de
Communication in Organizational Groups
Monica RADU
2007-01-01
Organizational group can be defined as some persons between who exist interactive connections (functional, communication, affective, normative type). Classification of these groups can reflect the dimension, type of relationship or type of rules included. Organizational groups and their influence over the individual efficiency and the efficiency of the entire group are interconnected. Spontaneous roles in these groups sustain the structure of the relationship, and the personality of each indi...
[Social crisis, spontaneous groups and group order].
Edelman, Lucila; Kordon, Diana
2002-12-01
Argentina has gone through very difficult times during the last years and, in particularly, new kinds of social practices have emerged in order to cope with the crisis. This situation demands and urges a new type of reflection upon the double role of groups, as tools to transform reality and as a way to elaborate those processes regarding subjectivity. In this paper we analyse some topics regarding the groupal field (considering spontaneous groups as well as groupal devices that allow to elaborate the crisis). We consider social bond to be the condition of possibility for the existence of the psyche and of time continuity, and that it also makes possible personal and social elaboration of trauma, crisis and social catastrophe. We develop some aspects of an specific device (the reflection group), which we have already depicted in another moment, showing it's usefulness to cope with social crisis and to promote the subjective elaboration of crisis.
Introduction to topological groups
Husain, Taqdir
2018-01-01
Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.
... The Treatment Of MSUD The MSUD Family Support Group has provided funds to Buck Institute for its ... of the membership of the MSUD Family Support Group, research for improved treatments and potential cure was ...
Nilpotent -local finite groups
Cantarero, José; Scherer, Jérôme; Viruel, Antonio
2014-10-01
We provide characterizations of -nilpotency for fusion systems and -local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.
U.S. Department of Health & Human Services — The Group Unique Physician Identifier Number (UPIN) File is the business entity file that contains the group practice UPIN and descriptive information. It does NOT...
Group Decision Process Support
DEFF Research Database (Denmark)
Gøtze, John; Hijikata, Masao
1997-01-01
Introducing the notion of Group Decision Process Support Systems (GDPSS) to traditional decision-support theorists.......Introducing the notion of Group Decision Process Support Systems (GDPSS) to traditional decision-support theorists....
Harman, Robert L.; Franklin, Richard W.
1975-01-01
Gestalt therapy in groups is not limited to individual work in the presence of an audience. Describes several ways to involve gestalt groups interactionally. Interactions described focus on learning by doing and discovering, and are noninterpretive. (Author/EJT)
Group B streptococcus - pregnancy
... medlineplus.gov/ency/patientinstructions/000511.htm Group B streptococcus - pregnancy To use the sharing features on this page, please enable JavaScript. Group B streptococcus (GBS) is a type of bacteria that some ...
DEFF Research Database (Denmark)
Hansen, Annette Skovsted
2014-01-01
Motivation for the activity I use this strategy for forming groups to ensure diverse/multicultural groups that combine a variety of different strengths and resources based on student's academic, disciplinary, linguistic, national, personal and work backgrounds.......Motivation for the activity I use this strategy for forming groups to ensure diverse/multicultural groups that combine a variety of different strengths and resources based on student's academic, disciplinary, linguistic, national, personal and work backgrounds....
The Areva Group; Le groupe Areva
Energy Technology Data Exchange (ETDEWEB)
NONE
2004-08-01
This document provides information on the Areva Group, a world nuclear industry leader, offering solutions for nuclear power generation, electricity transmission and distribution and interconnect systems to the telecommunications, computer and automotive markets. It presents successively the front end division including the group business lines involved in producing nuclear fuel for electric power generation (uranium mining, concentration, conversion and enrichment and nuclear fuel fabrication); the reactors and services division which designs and builds PWR, BWR and research reactors; the back end division which encompasses the management of the fuel that has been used in nuclear power plants; the transmission and distribution division which provides products, systems and services to the medium and high voltage energy markets; the connectors division which designs and manufactures electrical, electronic and optical connectors, flexible micro circuitry and interconnection systems. Areva is implemented in Europe, north and south america, africa and asia-pacific. (A.L.B.)
Groups, combinatorics and geometry
Ivanov, A A; Saxl, J
2003-01-01
Over the past 20 years, the theory of groups in particular simplegroups, finite and algebraic has influenced a number of diverseareas of mathematics. Such areas include topics where groups have beentraditionally applied, such as algebraic combinatorics, finitegeometries, Galois theory and permutation groups, as well as severalmore recent developments.
Energy Technology Data Exchange (ETDEWEB)
Nagaitsev S.; Berg J.
2012-06-10
The primary subject of working group 7 at the 2012 Advanced Accelerator Concepts Workshop was muon accelerators for a muon collider or neutrino factory. Additionally, this working group included topics that did not fit well into other working groups. Two subjects were discussed by more than one speaker: lattices to create a perfectly integrable nonlinear lattice, and a Penning trap to create antihydrogen.
International Nuclear Information System (INIS)
2002-01-01
This document presents the Group Areva, a world nuclear industry leader, from a financial holding company to an industrial group, operating in two businesses: the nuclear energy and the components. The structure and the market of the group are discussed, as the financial assets. (A.L.B.)
Group Psychotherapy in Denmark.
Jørgensen, Lars Bo; Thygesen, Bente; Aagaard, Søren
2015-10-01
This is a short article on the history and training standards in the Institute of Group Analysis in Copenhagen (IGA-CPH). We describe theoretical orientations and influences in the long-term training program and new initiatives, like courses in mentalization-based group treatment and a dynamic short-term group therapy course, as well as research in group psychotherapy in Denmark. Some group analytic initiatives in relation to social issues and social welfare are presented, as well as initiatives concerning the school system and unemployment.
Milewski, Emil G
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Group Theory I includes sets and mapping, groupoids and semi-groups, groups, isomorphisms and homomorphisms, cyclic groups, the Sylow theorems, and finite p-groups.
Steinberg, Robert
2016-01-01
Robert Steinberg's Lectures on Chevalley Groups were delivered and written during the author's sabbatical visit to Yale University in the 1967-1968 academic year. The work presents the status of the theory of Chevalley groups as it was in the mid-1960s. Much of this material was instrumental in many areas of mathematics, in particular in the theory of algebraic groups and in the subsequent classification of finite groups. This posthumous edition incorporates additions and corrections prepared by the author during his retirement, including a new introductory chapter. A bibliography and editorial notes have also been added. This is a great unsurpassed introduction to the subject of Chevalley groups that influenced generations of mathematicians. I would recommend it to anybody whose interests include group theory. -Efim Zelmanov, University of California, San Diego Robert Steinberg's lectures on Chevalley groups were given at Yale University in 1967. The notes for the lectures contain a wonderful exposition of ...
HR Department
2012-01-01
There will be an e-groups training course on 16 March 2012 which will cover the main e-groups functionalities i.e.: creating and managing e-groups, difference between static and dynamic e-groups, configuring posting restrictions and archives, examples of where e-groups can be used in daily work. Even if you have already worked with e-groups, this may be a good opportunity to learn about the best practices and security related recommendations when using e-groups. You can find more details as well as enrolment form for the training (it’s free) here. The number of places is limited, so enrolling early is recommended. Technical Training Tel. 72844
Giannone, Francesca; Giordano, Cecilia; Di Blasi, Maria
2015-10-01
This article describes the history and the prevailing orientations of group psychotherapy in Italy (psychoanalytically oriented, psychodrama, CBT groups) and particularly group analysis. Provided free of charge by the Italian health system, group psychotherapy is growing, but its expansion is patchy. The main pathways of Italian training in the different group psychotherapy orientations are also presented. Clinical-theoretical elaboration on self development, psychopathology related to group experiences, and the methodological attention paid to objectives and methods in different clinical groups are issues related to group therapy in Italy. Difficulties in the relationship between research and clinical practice are discussed, as well as the empirical research network that tries to bridge the gap between research and clinical work in group psychotherapy. The economic crisis in Italy has led to massive cuts in health care and to an increasing demand for some forms of psychological treatment. For these reasons, and because of its positive cost-benefit ratio, group psychotherapy is now considered an important tool in the national health care system to expand the clinical response to different forms of psychological distress.
Bestvina, Mladen; Vogtmann, Karen
2014-01-01
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...
CLASSIFICATION OF CRIMINAL GROUPS
Natalia Romanova
2013-01-01
New types of criminal groups are emerging in modern society. These types have their special criminal subculture. The research objective is to develop new parameters of classification of modern criminal groups, create a new typology of criminal groups and identify some features of their subculture. Research methodology is based on the system approach that includes using the method of analysis of documentary sources (materials of a criminal case), method of conversations with themembers of the...
Nada Hribar
2001-01-01
The group included adolescents from secondary school and some students. The group had weekly sessions or twice on mounth. The adolescents had varied simptoms: depressive, anxiety, psychosomatic disorders, learning difficulties, cunduct problems. All of adolescents were common on many problems in social interactions. The goal of therapeutic work were: to increase assertiveness skills and to reduce the anxious in social situations. The adolescents in group raised a self-esteem and developed som...
Johnson, D L
1997-01-01
The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied. This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.
Li, Quan-Lin; Ma, Jing-Yu; Xie, Mingzhou; Xia, Li
2017-01-01
By analyzing energy-efficient management of data centers, this paper proposes and develops a class of interesting {\\it Group-Server Queues}, and establishes two representative group-server queues through loss networks and impatient customers, respectively. Furthermore, such two group-server queues are given model descriptions and necessary interpretation. Also, simple mathematical discussion is provided, and simulations are made to study the expected queue lengths, the expected sojourn times ...
Symmetries of noncommutative scalar field theory
International Nuclear Information System (INIS)
De Goursac, Axel; Wallet, Jean-Christophe
2011-01-01
We investigate symmetries of the scalar field theory with a harmonic term on the Moyal space with the Euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on the symplectic structure. We find that the invariance under the orthogonal group can also be restored at the quantum level by restricting the symplectic structures to a particular orbit.
Environmental groups in politics
International Nuclear Information System (INIS)
Lowe, P.; Goyder, J.
1983-01-01
The subject is covered in chapters, entitled: introduction; (Part I) the environmental movement (environmental groups and the attentive public; the episodic development of the environmental movement; the underlying values of environmentalism; the roots of environmental concern; the social limits to growth; elite manipulation of values); the organisation of environmental groups; environmental groups in national politics; environmental groups in local politics; (Part II) the Henley Society; Friends of the Earth; the National Trust; the Royal Society for Nature Conservation; the European Environmental Bureau. (U.K.)
International Nuclear Information System (INIS)
Drabant, B.; Schlieker, M.
1993-01-01
The complex quantum groups are constructed. They are q-deformations of the real Lie groups which are obtained as the complex groups corresponding to the Lie algebras of type A n-1 , B n , C n . Following the ideas of Faddeev, Reshetikhin and Takhtajan Hopf algebras of regular functionals U R for these complexified quantum groups are constructed. One has thus in particular found a construction scheme for the q-Lorentz algebra to be identified as U(sl q (2,C). (orig.)
Federal Laboratory Consortium — The Explosive Technology Group (ETG) provides diverse technical expertise and an agile, integrated approach to solve complex challenges for all classes of energetic...
DEFF Research Database (Denmark)
Hjorth, Poul G.
2007-01-01
Since 1998 European Study Groups have been held in Denmark, and Danish companies from LEGO and NOVO to very small high-tech firms have participated. I briefly describe the history, the organisation and the format of the Danish Study Groups, and highlight a few problem solutions.......Since 1998 European Study Groups have been held in Denmark, and Danish companies from LEGO and NOVO to very small high-tech firms have participated. I briefly describe the history, the organisation and the format of the Danish Study Groups, and highlight a few problem solutions....
Lipkin, Harry J
2002-01-01
According to the author of this concise, high-level study, physicists often shy away from group theory, perhaps because they are unsure which parts of the subject belong to the physicist and which belong to the mathematician. However, it is possible for physicists to understand and use many techniques which have a group theoretical basis without necessarily understanding all of group theory. This book is designed to familiarize physicists with those techniques. Specifically, the author aims to show how the well-known methods of angular momentum algebra can be extended to treat other Lie group
International Nuclear Information System (INIS)
Olmos, C.
1990-05-01
The restricted holonomy group of a Riemannian manifold is a compact Lie group and its representation on the tangent space is a product of irreducible representations and a trivial one. Each one of the non-trivial factors is either an orthogonal representation of a connected compact Lie group which acts transitively on the unit sphere or it is the isotropy representation of a single Riemannian symmetric space of rank ≥ 2. We prove that, all these properties are also true for the representation on the normal space of the restricted normal holonomy group of any submanifold of a space of constant curvature. 4 refs
Directory of Open Access Journals (Sweden)
Maike Buchin
2015-03-01
Full Text Available The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology. The trajectory grouping structure has three natural parameters that allow more global views of the data in group size, group duration, and entity inter-distance. We prove complexity bounds on the maximum number of maximal groups that can be present, and give algorithms to compute the grouping structure efficiently. We also study how the trajectory grouping structure can be made robust, that is, how brief interruptions of groups can be disregarded in the global structure, adding a notion of persistence to the structure. Furthermore, we showcase the results of experiments using data generated by the NetLogo flocking model and from the Starkey project. The Starkey data describe the movement of elk, deer, and cattle. Although there is no ground truth for the grouping structure in this data, the experiments show that the trajectory grouping structure is plausible and has the desired effects when changing the essential parameters. Our research provides the first complete study of trajectory group evolvement, including combinatorial,algorithmic, and experimental results.
Computational methods working group
International Nuclear Information System (INIS)
Gabriel, T.A.
1997-09-01
During the Cold Moderator Workshop several working groups were established including one to discuss calculational methods. The charge for this working group was to identify problems in theory, data, program execution, etc., and to suggest solutions considering both deterministic and stochastic methods including acceleration procedures.
DEFF Research Database (Denmark)
Bøgh, Kenneth Sejdenfaden; Skovsgaard, Anders; Jensen, Christian S.
2013-01-01
. Such groups are relevant to users who wish to conveniently explore several options before making a decision such as to purchase a specific product. Specifically, we demonstrate a practical proposal for finding top-k PoI groups in response to a query. We show how problem parameter settings can be mapped...
Toleration, Groups, and Multiculturalism
DEFF Research Database (Denmark)
Lægaard, Sune
2014-01-01
have the ability to interfere with the group’s activities, an object of dislike or disapproval, an agent enjoying non-interference or a moral patient. This means that 'toleration of groups' can mean quite different things depending on the exact meaning of 'group' in relation to each component...
... IV) to kill the germs. If you take antibiotics while you’re in labor, the chances are very good that your baby won’t get this infection. What if my baby has group B strep? If your baby gets group B strep, he or she will be treated with IV antibiotics to kill the bacteria. Your baby will stay ...
McLeod, John
1984-01-01
Suggests that drama, as well as training or therapy, may be employed as a useful research and practice paradigm in working with small groups. The implications of this view for group development as a whole, and for member and leader participation, are explored. (JAC)
Walker, Karen
2010-01-01
According to Johnson and Johnson, group work helps increase student retention and satisfaction, develops strong oral communication and social skills, as well as higher self-esteem (University of Minnesota, n.d.). Group work, when planned and implemented deliberately and thoughtfully helps students develop cognitive and leadership skills as well as…
Physically detached 'compact groups'
Hernquist, Lars; Katz, Neal; Weinberg, David H.
1995-01-01
A small fraction of galaxies appear to reside in dense compact groups, whose inferred crossing times are much shorter than a Hubble time. These short crossing times have led to considerable disagreement among researchers attempting to deduce the dynamical state of these systems. In this paper, we suggest that many of the observed groups are not physically bound but are chance projections of galaxies well separated along the line of sight. Unlike earlier similar proposals, ours does not require that the galaxies in the compact group be members of a more diffuse, but physically bound entity. The probability of physically separated galaxies projecting into an apparent compact group is nonnegligible if most galaxies are distributed in thin filaments. We illustrate this general point with a specific example: a simulation of a cold dark matter universe, in which hydrodynamic effects are included to identify galaxies. The simulated galaxy distribution is filamentary and end-on views of these filaments produce apparent galaxy associations that have sizes and velocity dispersions similar to those of observed compact groups. The frequency of such projections is sufficient, in principle, to explain the observed space density of groups in the Hickson catalog. We discuss the implications of our proposal for the formation and evolution of groups and elliptical galaxies. The proposal can be tested by using redshift-independent distance estimators to measure the line-of-sight spatial extent of nearby compact groups.
Introduction to quantum groups
International Nuclear Information System (INIS)
Sudbery, A.
1996-01-01
These pedagogical lectures contain some motivation for the study of quantum groups; a definition of ''quasi triangular Hopf algebra'' with explanations of all the concepts required to build it up; descriptions of quantised universal enveloping algebras and the quantum double; and an account of quantised function algebras and the action of quantum groups on quantum spaces. (author)
International Nuclear Information System (INIS)
Peggs, S.
1994-01-01
This paper summarizes the activities of the beam dynamics working group of the LHC Collective Effects Workshop that was held in Montreux in 1994. It reviews the presentations that were made to the group, the discussions that ensued, and the consensuses that evolved
Dinklocker, Christina
1992-01-01
After training in the Total Quality Management concept, a suburban Ohio school district created a Deming Users' Group to link agencies, individuals, and ideas. The group has facilitated ongoing school/business collaboration, networking among individuals from diverse school systems, mentoring and cooperative learning activities, and resource…
Asymmetry within social groups
DEFF Research Database (Denmark)
Barker, Jessie; Loope, Kevin J.; Reeve, H. Kern
2016-01-01
Social animals vary in their ability to compete with group members over shared resources and also vary in their cooperative efforts to produce these resources. Competition among groups can promote within-group cooperation, but many existing models of intergroup cooperation do not explicitly account...... of two roles, with relative competitive efficiency and the number of individuals varying between roles. Players in each role make simultaneous, coevolving decisions. The model predicts that although intergroup competition increases cooperative contributions to group resources by both roles, contributions...... are predominantly from individuals in the less competitively efficient role, whereas individuals in the more competitively efficient role generally gain the larger share of these resources. When asymmetry in relative competitive efficiency is greater, a group's per capita cooperation (averaged across both roles...
Supervision and group dynamics
DEFF Research Database (Denmark)
Hansen, Søren; Jensen, Lars Peter
2004-01-01
An important aspect of the problem based and project organized study at Aalborg University is the supervision of the project groups. At the basic education (first year) it is stated in the curriculum that part of the supervisors' job is to deal with group dynamics. This is due to the experience...... that many students are having difficulties with practical issues such as collaboration, communication, and project management. Most supervisors either ignore this demand, because they do not find it important or they find it frustrating, because they do not know, how to supervise group dynamics...... as well as at Aalborg University. The first visible result has been participating supervisors telling us that the course has inspired them to try supervising group dynamics in the future. This paper will explore some aspects of supervising group dynamics as well as, how to develop the Aalborg model...
International Nuclear Information System (INIS)
2009-01-01
A key aspect of the workshop was the interaction and exchange of ideas and information among the 40 participants. To facilitate this activity the workshop participants were divided into five discussions groups. These groups reviewed selected subjects and reported back to the main body with summaries of their considerations. Over the 3 days the 5 discussion groups were requested to focus on the following subjects: the characteristics and capabilities of 'good' organisations; how to ensure sufficient resources; how to ensure competence within the organisation; how to demonstrate organisational suitability; the regulatory oversight processes - including their strengths and weaknesses. A list of the related questions that were provided to the discussion groups can be found in Appendix 3. Also included in Appendix 3 are copies of the slides the groups prepared that summarised their considerations
Natural analogue working group
International Nuclear Information System (INIS)
Come, B.; Chapman, N.
1986-01-01
A Natural Analogue Working Group was established by the Commission of the European Communities in 1985. The purpose of this group is to bring together modellers with earth scientists and others, so that maximum benefit can be obtained from natural analogue studies with a view to safe geological disposal of radioactive waste. The first meeting of this group was held in Brussels from November 5 to 7, 1985. The discussions mainly concerned the identification of the modellers' needs and of the earth scientists' capacity to provide for them. Following the debates, a written statement was produced by the Group; this document forms the core of the present Report. Notes and outlines of many of the presentations made are grouped in four appendixes. The valuable contribution of all those involved in the meeting is gratefully acknowledged
Clay, Adam
2016-01-01
This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
Mazzoni, Sara E; Carter, Ebony B
2017-06-01
Patients participating in group prenatal care gather together with women of similar gestational ages and 2 providers who cofacilitate an educational session after a brief medical assessment. The model was first described in the 1990s by a midwife for low-risk patients and is now practiced by midwives and physicians for both low-risk patients and some high-risk patients, such as those with diabetes. The majority of literature on group prenatal care uses CenteringPregnancy, the most popular model. The first randomized controlled trial of CenteringPregnancy showed that it reduced the risk of preterm birth in low-risk women. However, recent meta-analyses have shown similar rates of preterm birth, low birthweight, and neonatal intensive care unit admission between women participating in group prenatal care and individual prenatal care. There may be subgroups, such as African Americans, who benefit from this type of prenatal care with significantly lower rates of preterm birth. Group prenatal care seems to result in increased patient satisfaction and knowledge and use of postpartum family planning as well as improved weight gain parameters. The literature is inconclusive regarding breast-feeding, stress, depression, and positive health behaviors, although it is theorized that group prenatal care positively affects these outcomes. It is unclear whether group prenatal care results in cost savings, although it may in large-volume practices if each group consists of approximately 8-10 women. Group prenatal care requires a significant paradigm shift. It can be difficult to implement and sustain. More randomized trials are needed to ascertain the true benefits of the model, best practices for implementation, and subgroups who may benefit most from this innovative way to provide prenatal care. In short, group prenatal care is an innovative and promising model with comparable pregnancy outcomes to individual prenatal care in the general population and improved outcomes in some
Critical groups - basic concepts
International Nuclear Information System (INIS)
Carter, M.W.
1992-01-01
The potential exposure pathways from the land application site to man are presented. It is emphasised that the critical group is not necessary the population group closest to the source. It could be the group impact by the most significant pathways(s). Only by assessing the importance of each of these pathways and then combining them can a proper choice of critical group be made. It would be wrong to select a critical group on the basis that it seems the most probable one, before the pathways have been properly assessed. A calculation in Carter (1983) suggested that for the operating mine site, the annual doses to an Aboriginal person, a service worker and a local housewife, were all about the same and were in the range 0.1 to 0.2 mSv per year. Thus it may be that for the land application area, the critical group turns out to be non-Aboriginal rather than the expected Aboriginal group. 6 refs., 3 figs
Groups - Modular Mathematics Series
Jordan, David
1994-01-01
This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic.
Introduction to quantum groups
Chaichian, Masud
1996-01-01
In the past decade there has been an extemely rapid growth in the interest and development of quantum group theory.This book provides students and researchers with a practical introduction to the principal ideas of quantum groups theory and its applications to quantum mechanical and modern field theory problems. It begins with a review of, and introduction to, the mathematical aspects of quantum deformation of classical groups, Lie algebras and related objects (algebras of functions on spaces, differential and integral calculi). In the subsequent chapters the richness of mathematical structure
Energy Technology Data Exchange (ETDEWEB)
Dunigan, T.; Cao, C.
1997-08-01
This report describes an architecture and implementation for doing group key management over a data communications network. The architecture describes a protocol for establishing a shared encryption key among an authenticated and authorized collection of network entities. Group access requires one or more authorization certificates. The implementation includes a simple public key and certificate infrastructure. Multicast is used for some of the key management messages. An application programming interface multiplexes key management and user application messages. An implementation using the new IP security protocols is postulated. The architecture is compared with other group key management proposals, and the performance and the limitations of the implementation are described.
Directory of Open Access Journals (Sweden)
Nada Hribar
2001-03-01
Full Text Available The group included adolescents from secondary school and some students. The group had weekly sessions or twice on mounth. The adolescents had varied simptoms: depressive, anxiety, psychosomatic disorders, learning difficulties, cunduct problems. All of adolescents were common on many problems in social interactions. The goal of therapeutic work were: to increase assertiveness skills and to reduce the anxious in social situations. The adolescents in group raised a self-esteem and developed some assertiveness skills: eye contact" and effective communication skills, persistence, refusing and requesting, giving and receiving critism, etc. The methods of work and techniques were based on principles of cognitive-behaviour therapy.
Matrix groups for undergraduates
Tapp, Kristopher
2005-01-01
Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.
UnitedHealth Group provides accessible and affordable services, improved quality of care, coordinated health care efforts, and a supportive environment for shared decision making between patients and their physicians.
Homogeneous group, research, institution
Directory of Open Access Journals (Sweden)
Francesca Natascia Vasta
2014-09-01
Full Text Available The work outlines the complex connection among empiric research, therapeutic programs and host institution. It is considered the current research state in Italy. Italian research field is analyzed and critic data are outlined: lack of results regarding both the therapeutic processes and the effectiveness of eating disorders group analytic treatment. The work investigates on an eating disorders homogeneous group, led into an eating disorder outpatient service. First we present the methodological steps the research is based on including the strong connection among theory and clinical tools. Secondly clinical tools are described and the results commented. Finally, our results suggest the necessity of validating some more specifical hypothesis: verifying the relationship between clinical improvement (sense of exclusion and painful emotions reduction and specific group therapeutic processes; verifying the relationship between depressive feelings, relapses and transition trough a more differentiated groupal field.Keywords: Homogeneous group; Eating disorders; Institutional field; Therapeutic outcome
Color transparency study group
International Nuclear Information System (INIS)
Appel, J.A.; Pordes, S.; Botts, J.; Bunce, G.; Farrar, G.
1990-01-01
The group studied the relatively new notion of color transparency, discussed present experimental evidence for the effect, and explored several ideas for future experiments. This write-up summarizes these discussions. 11 refs., 1 fig
International Nuclear Information System (INIS)
Leivo, H.P.
1992-01-01
The algebraic approach to quantum groups is generalized to include what may be called an anyonic symmetry, reflecting the appearance of phases more general than ±1 under transposition. (author). 6 refs
Directory of Open Access Journals (Sweden)
Coghetto Roland
2015-06-01
Full Text Available We translate the articles covering group theory already available in the Mizar Mathematical Library from multiplicative into additive notation. We adapt the works of Wojciech A. Trybulec [41, 42, 43] and Artur Korniłowicz [25].
Coghetto Roland
2015-01-01
We translate the articles covering group theory already available in the Mizar Mathematical Library from multiplicative into additive notation. We adapt the works of Wojciech A. Trybulec [41, 42, 43] and Artur Korniłowicz [25].
Creativity and group innovation
Nijstad, B.A.; de Dreu, C.K.W.
2002-01-01
Comments on M. West's article regarding the validity of an integrative model of creativity and innovation implementation in work groups. Variables affecting the level of team innovation; Relationship between predictors and team innovation; Promotion of constructive conflict.
Energy Technology Data Exchange (ETDEWEB)
Thomas, J. [Surface Mining Association for Research and Technology, AB (Canada)
2008-07-01
The Truck Shovel Users Group (TSUG) was developed as part of the Surface Mining Association for Research and Technology (SMART), an association of companies that meet to coordinate technology developments for the mining industry. The TSUG meet regularly to discuss equipment upgrades, maintenance planning systems, and repair techniques. The group strives to maximize the value of its assets through increased safety, equipment performance and productivity. This presentation provided administrative details about the TSUG including contact details and admission costs. It was concluded that members of the group must be employed by companies that use heavy mining equipment, and must also be willing to host meetings, make presentations, and support the common goals of the group. tabs., figs.
Hall, Marshall
2018-01-01
This 1959 text offers an unsurpassed resource for learning and reviewing the basics of a fundamental and ever-expanding area. "This remarkable book undoubtedly will become a standard text on group theory." - American Scientist.
2006-01-01
The Radioactive Waste Section of the Radiation Protection Group wishes to inform you that the Radioactive Waste Treatment Centre will be closed on the afternoon of Tuesday 19 December 2006. Thank-you for your understanding.
The Military Cooperation Group
National Research Council Canada - National Science Library
Renzi, Jr, Alfred E
2006-01-01
.... This thesis will describe a structure to assist with both those needs. The premise is that an expanded and improved network of US Military Groups is the weapon of choice for the war on terror, and beyond...
Directory of Open Access Journals (Sweden)
Canals B.
2012-03-01
Full Text Available This chapter is a concise mathematical introduction into the algebra of groups. It is build up in the way that definitions are followed by propositions and proofs. The concepts and the terminology introduced here will serve as a basis for the following chapters that deal with group theory in the stricter sense and its application to problems in physics. The mathematical prerequisites are at the bachelor level.1
Auslander, Maurice
2014-01-01
This classic monograph is geared toward advanced undergraduates and graduate students. The treatment presupposes some familiarity with sets, groups, rings, and vector spaces. The four-part approach begins with examinations of sets and maps, monoids and groups, categories, and rings. The second part explores unique factorization domains, general module theory, semisimple rings and modules, and Artinian rings. Part three's topics include localization and tensor products, principal ideal domains, and applications of fundamental theorem. The fourth and final part covers algebraic field extensions
2017-07-01
home for the arrival of school- aged children. TIP: Do not conduct focus groups in a command conference room in the command group area. Doing so...organizational effectiveness and equal opportunity/equal employment opportunity/fair treatment and sexual assault and response factors (which are listed on the... Sexual Harassment (C) Sex Harassment Retaliation (D) Discrimination - Sex (E) Discrimination - Race (F) Discrimination - Disability (G
Kfir Eliaz; Debraj Ray
2004-01-01
The phenomenon of "choice shifts" in group decision-making is fairly ubiquitous in the social psychology literature. Faced with a choice between a ``safe" and ``risky" decision, group members appear to move to one extreme or the other, relative to the choices each member might have made on her own. Both risky and cautious shifts have been identified in different situations. This paper demonstrates that from an individual decision-making perspective, choice shifts may be viewed as a systematic...
Olejarski, Michael; Appleton, Amy; Deltorchio, Stephen
2009-01-01
The Group Capability Model (GCM) is a software tool that allows an organization, from first line management to senior executive, to monitor and track the health (capability) of various groups in performing their contractual obligations. GCM calculates a Group Capability Index (GCI) by comparing actual head counts, certifications, and/or skills within a group. The model can also be used to simulate the effects of employee usage, training, and attrition on the GCI. A universal tool and common method was required due to the high risk of losing skills necessary to complete the Space Shuttle Program and meet the needs of the Constellation Program. During this transition from one space vehicle to another, the uncertainty among the critical skilled workforce is high and attrition has the potential to be unmanageable. GCM allows managers to establish requirements for their group in the form of head counts, certification requirements, or skills requirements. GCM then calculates a Group Capability Index (GCI), where a score of 1 indicates that the group is at the appropriate level; anything less than 1 indicates a potential for improvement. This shows the health of a group, both currently and over time. GCM accepts as input head count, certification needs, critical needs, competency needs, and competency critical needs. In addition, team members are categorized by years of experience, percentage of contribution, ex-members and their skills, availability, function, and in-work requirements. Outputs are several reports, including actual vs. required head count, actual vs. required certificates, CGI change over time (by month), and more. The program stores historical data for summary and historical reporting, which is done via an Excel spreadsheet that is color-coded to show health statistics at a glance. GCM has provided the Shuttle Ground Processing team with a quantifiable, repeatable approach to assessing and managing the skills in their organization. They now have a common
Parton Distributions Working Group
International Nuclear Information System (INIS)
Barbaro, L. de; Keller, S. A.; Kuhlmann, S.; Schellman, H.; Tung, W.-K.
2000-01-01
This report summarizes the activities of the Parton Distributions Working Group of the QCD and Weak Boson Physics workshop held in preparation for Run II at the Fermilab Tevatron. The main focus of this working group was to investigate the different issues associated with the development of quantitative tools to estimate parton distribution functions uncertainties. In the conclusion, the authors introduce a Manifesto that describes an optimal method for reporting data
International Nuclear Information System (INIS)
Stephens, C. R.
2006-01-01
In this article I give a brief account of the development of research in the Renormalization Group in Mexico, paying particular attention to novel conceptual and technical developments associated with the tool itself, rather than applications of standard Renormalization Group techniques. Some highlights include the development of new methods for understanding and analysing two extreme regimes of great interest in quantum field theory -- the ''high temperature'' regime and the Regge regime
Independents' group posts loss
International Nuclear Information System (INIS)
Sanders, V.; Price, R.B.
1992-01-01
Low oil gas prices and special charges caused the group of 50 U.S. independent producers Oil and Gas Journal tracks to post a combined loss in first half 1992. The group logged a net loss of $53 million in the first half compared with net earnings of $354 million in first half 1991, when higher oil prices during the Persian Gulf crisis buoyed earnings in spite of crude oil and natural gas production declines. The combined loss in the first half follows a 45% drop in the group's earnings in 1991 and compares with the OGJ group of integrated oil companies whose first half 1992 income fell 47% from the prior year. Special charges, generally related to asset writedowns, accounted for most of the almost $560 million in losses posted by about the third of the group. Nerco Oil and Gas Inc., Vancouver, Wash., alone accounted for almost half that total with charges related to an asset writedown of $238 million in the first quarter. Despite the poor first half performance, the outlook is bright for sharply improved group earnings in the second half, assuming reasonably healthy oil and gas prices and increased production resulting from acquisitions and in response to those prices
Assessment of Group Preferences and Group Uncertainty for Decision Making
1976-06-01
the individ- uals. decision making , group judgments should be preferred to individual judgments if obtaining group judgments costs more. -26- -YI IV... decision making group . IV. A. 3. Aggregation using conjugate distribution. Arvther procedure for combining indivi(jai probability judgments into a group...statisticized group group decision making group judgment subjective probability Delphi method expected utility nominal group 20. ABSTRACT (Continue on
Cyclic Soft Groups and Their Applications on Groups
Directory of Open Access Journals (Sweden)
Hacı Aktaş
2014-01-01
Full Text Available In crisp environment the notions of order of group and cyclic group are well known due to many applications. In this paper, we introduce order of the soft groups, power of the soft sets, power of the soft groups, and cyclic soft group on a group. We also investigate the relationship between cyclic soft groups and classical groups.
International Nuclear Information System (INIS)
1994-01-01
In December 1992, western governors and four federal agencies established a Federal Advisory Committee to Develop On-site Innovative Technologies for Environmental Restoration and Waste Management (the DOIT Committee). The purpose of the Committee is to advise the federal government on ways to improve waste cleanup technology development and the cleanup of federal sites in the West. The Committee directed in January 1993 that information be collected from a wide range of potential stakeholders and that innovative technology candidate projects be identified, organized, set in motion, and evaluated to test new partnerships, regulatory approaches, and technologies which will lead to improve site cleanup. Five working groups were organized, one to develop broad project selection and evaluation criteria and four to focus on specific contaminant problems. A Coordinating Group comprised of working group spokesmen and federal and state representatives, was set up to plan and organize the routine functioning of these working groups. The working groups were charged with defining particular contaminant problems; identifying shortcomings in technology development, stakeholder involvement, regulatory review, and commercialization which impede the resolution of these problems; and identifying candidate sites or technologies which could serve as regional innovative demonstration projects to test new approaches to overcome the shortcomings. This report from the Coordinating Group to the DOIT Committee highlights the key findings and opportunities uncovered by these fact-finding working groups. It provides a basis from which recommendations from the DOIT Committee to the federal government can be made. It also includes observations from two public roundtables, one on commercialization and another on regulatory and institutional barriers impeding technology development and cleanup
Springer, T A
1998-01-01
"[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text." –Mathematical Reviews (Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of t...
Summary report: injection group
International Nuclear Information System (INIS)
Simpson, J.; Ankenbrandt, C.; Brown, B.
1984-01-01
The injector group attempted to define and address several problem areas related to the SSC injector as defined in the Reference Design Study (RDS). It also considered the topic of machine utilization, particularly the question of test beam requirements. Details of the work are given in individually contributed papers, but the general concerns and consensus of the group are presented within this note. The group recognized that the injector as outlined in the RDS was developed primarily for costing estimates. As such, it was not necessarily well optimized from the standpoint of insuring the required beam properties for the SSC. On the other hand, considering the extraordinary short time in which the RDS was prepared, it is an impressive document and a good basis from which to work. Because the documented SSC performance goals are ambitious, the group sought an injector solution which would more likely guarantee that SSC performance not be limited by its injectors. As will be seen, this leads to a somewhat different solution than that described in the RDS. Furthermore, it is the consensus of the group that the new, conservative approach represents only a modest cost increase of the overall project well worth the confidence gained and the risks avoided
Matrix groups for undergraduates
Tapp, Kristopher
2016-01-01
Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots. This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups. From reviews of the First Edition: This book could be used as an excellent textbook for a one semester course at university and it will prepare students for a graduate course on Lie groups, Lie algebras, etc. … The book combines an intuitive style of writing w...
Pérez-Zepeda, M U; Ávila-Funes, J A; Gutiérrez-Robledo, L M; García-Peña, C
2016-01-01
The implementation of an aging biomarker into clinical practice is under debate. The Frailty Index is a model of deficit accumulation and has shown to accurately capture frailty in older adults, thus bridging biological with clinical practice. To describe the association of socio-demographic characteristics and the Frailty Index in different age groups (from 20 to over one hundred years) in a representative sample of Mexican subjects. Cross-sectional analysis. Nationwide and population-representative survey. Adults 20-years and older interviewed during the last Mexican National Health and Nutrition Survey (2012). A 30-item Frailty Index following standard construction was developed. Multi-level regression models were performed to test the associations of the Frailty Index with multiple socio-demographic characteristics across age groups. A total of 29,504 subjects was analyzed. The 30-item Frailty Index showed the highest scores in the older age groups, especially in women. No sociodemographic variable was associated with the Frailty Index in all the studied age groups. However, employment, economic income, and smoking status were more consistently found across age groups. To our knowledge, this is the first report describing the Frailty Index in a representative large sample of a Latin American country. Increasing age and gender were closely associated with a higher score.
Energy Technology Data Exchange (ETDEWEB)
David G. Loomis
2012-05-28
The Illinois Wind Working Group (IWWG) was founded in 2006 with about 15 members. It has grown to over 200 members today representing all aspects of the wind industry across the State of Illinois. In 2008, the IWWG developed a strategic plan to give direction to the group and its activities. The strategic plan identifies ways to address critical market barriers to the further penetration of wind. The key to addressing these market barriers is public education and outreach. Since Illinois has a restructured electricity market, utilities no longer have a strong control over the addition of new capacity within the state. Instead, market acceptance depends on willing landowners to lease land and willing county officials to site wind farms. Many times these groups are uninformed about the benefits of wind energy and unfamiliar with the process. Therefore, many of the project objectives focus on conferences, forum, databases and research that will allow these stakeholders to make well-educated decisions.
Hennink, Monique M
2014-01-01
The Understanding Research series focuses on the process of writing up social research. The series is broken down into three categories: Understanding Statistics, Understanding Measurement, and Understanding Qualitative Research. The books provide researchers with guides to understanding, writing, and evaluating social research. Each volume demonstrates how research should be represented, including how to write up the methodology as well as the research findings. Each volume also reviews how to appropriately evaluate published research. Focus Group Discussions addresses the challenges associated with conducting and writing focus group research. It provides detailed guidance on the practical and theoretical considerations in conducting focus group discussions including: designing the discussion guide, recruiting participants, training a field team, moderating techniques and ethical considerations. Monique Hennink describes how a methodology section is read and evaluated by others, such as journal reviewers or ...
International Nuclear Information System (INIS)
Solomon, A. I.
2010-01-01
The 'Bell' of the title refers to bipartite Bell states, and their extensions to, for example, tripartite systems. The 'Group' of the title is the Braid Group in its various representations; while 'Tangle' refers to the property of entanglement which is present in both of these scenarios. The objective of this note is to explore the relation between Quantum Entanglement and Topological Links, and to show that the use of the language of entanglement in both cases is more than one of linguistic analogy.
Majid, Shahn
2002-05-01
Here is a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes for the Part III pure mathematics course at Cambridge University, the book is suitable as a primary text for graduate courses in quantum groups or supplementary reading for modern courses in advanced algebra. The material assumes knowledge of basic and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The volume is a primer for mathematicians but it will also be useful for mathematical physicists.
Introduction to quantum groups
International Nuclear Information System (INIS)
Monteiro, Marco A.R.
1994-01-01
An elementary introduction to quantum groups is presented. The example of Universal Enveloping Algebra of deformed SU(2) is analysed in detail. It is also discussed systems made up of bosonic q-oscillators at finite temperature within the formalism of Thermo-Field Dynamics. (author). 39 refs
Hsiang, Wu-Yi
2017-01-01
This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive 'tour of revisiting' the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semi-simple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartans' theory on Lie groups and symmetric spaces.With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we develop the above theory via a route quite different from the original methods engaged by most other books.We begin our revisiting with the compact theory which is much simpler than that of the general semi-simple Lie theory; mainly due to the well fittings between the Frobenius-Schur character theory and the maximal tori theorem of É Cartan together with Weyl's reduction (cf. Lectures 1-4). It is a wonderful reality of the Lie t...
... Intolerance Group (GIG), the industry leader in the certification of gluten-free products and food services, announced today that a wide ... of gluten-free products. One of the top certification programs in the world, GFCO inspects products and manufacturing facilities for gluten, in an effort ...
CERN PhotoLab
1980-01-01
The Radiobiology Group carries out experiments to study the effect of radiation on living cells. The photo shows the apparatus for growing broad beans which have been irradiated by 250 GeV protons. The roots are immersed in a tank of running water (CERN Weekly Bulletin 26 January 1981 and Annual Report 1980 p. 160). Karen Panman, Marilena Streit-Bianchi, Roger Paris.
Energy Technology Data Exchange (ETDEWEB)
Umeda, Yasukazu; Hikita, Shiro; Tuji, Sintaro (Mitsubishi Electric Corp., Tokyo (Japan))
1988-09-05
Items to be evaluated in the group control of elevators, and a typical control system are described. A new system in which the fuzzy rule base is employed is introduced together with the configuration. The items to be evaluated are waiting time, riding time, accuracy of forecasting, energy saving, and ease of usage. The everage waiting time of less than 20 seconds with less than 3% waiting rate of more than 60 seconds is accepted as a satisfactory service condition. There are many conflicting matters in group-controlling, and the study for the controlling must deal with the optimization of multi-purpose problems. The standards for group-control evaluation differ according to building structures and the tastes of users, and an important problem is where to give emphasis of the evaluation. The TRAFFIC PATTERN LEARNING METHOD has been applied in the system for careful control to accommodate the traffic. No specific function is provided for the evaluation, but the call allocation is made by fuzzy rule-base. The configuration of a new group-control system is introduced. 7 references, 7 figures, 1 table.
Smith, Walter T., Jr.; Patterson, John M.
1984-01-01
Literature on analytical methods related to the functional groups of 17 chemical compounds is reviewed. These compounds include acids, acid azides, alcohols, aldehydes, ketones, amino acids, aromatic hydrocarbons, carbodiimides, carbohydrates, ethers, nitro compounds, nitrosamines, organometallic compounds, peroxides, phenols, silicon compounds,…
Moral motivation within groups
Lee, Romy van der
2013-01-01
Morality is of particular importance to people: People want to be considered moral and want to belong to moral groups. Consequently, morality judgments have the potential to motivate individuals to behave in ways that are considered to be ‘good’. In the current dissertation, I examined the impact of
the Universe About Cosmology Planck Satellite Launched Cosmology Videos Professor George Smoot's group conducts research on the early universe (cosmology) using the Cosmic Microwave Background radiation (CMB science goals regarding cosmology. George Smoot named Director of Korean Cosmology Institute The GRB
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 10. Groups and Symmetry: A Guide to Discovering Mathematics. Geetha Venkataraman. Book Review Volume 4 Issue 10 October 1999 pp 91-92. Fulltext. Click here to view fulltext PDF. Permanent link:
Public interest group involvement
International Nuclear Information System (INIS)
Shelley, P.
1986-01-01
Including public interest groups in the siting process for nuclear waste disposal facilities is of great importance. Controversial sitings often result in litigation, but involving public interest groups early in the process will lessen the change of this. They act as surrogates for the general public and should be considered as members of the team. It is important to remember though, that all public interest groups are different. In choosing public panels such as public advisory committees, members should not be chosen on the basis of some quota. Opposition groups should not be excluded. Also, it is important to put the right person in charge of the committee. The goal of public involvement is to identify the conflicts. This must be done during the decision process, because conflicts must be known before they can be eliminated. Regarding litigation, it is important to ease through and around legal battles. If the siting process has integrity and a good faith effort has been shown, the court should uphold the effort. In addition, it is important to be negotiable and to eliminate shortcuts
The leukosis/sarcoma (L/S) group of diseases designates a variety of transmissible benign and malignant neoplasms of chickens caused by members that belong to the family Retroviridae. Because the expansion of the literature on this disease, it is no longer feasible to cite all relevant publications ...
Working Group Report: Neutrinos
Energy Technology Data Exchange (ETDEWEB)
de Gouvea, A.; Pitts, K.; Scholberg, K.; Zeller, G. P. [et al.
2013-10-16
This document represents the response of the Intensity Frontier Neutrino Working Group to the Snowmass charge. We summarize the current status of neutrino physics and identify many exciting future opportunities for studying the properties of neutrinos and for addressing important physics and astrophysics questions with neutrinos.
International Nuclear Information System (INIS)
Caldas, L.V.E.
1990-01-01
The main activities of the radiation dosimetry group is described, including the calibration of instruments, sources and radioactive solutions and the determination of neutron flux; development, production and market dosimetric materials; development radiation sensor make the control of radiation dose received by IPEN workers; development new techniques for monitoring, etc. (C.G.C.)
R.W. Hamilton (Rebecca); S. Puntoni (Stefano); N.T. Tavassoli (Nader)
2006-01-01
textabstractCategorization is a core psychological process central to consumer and managerial decision-making. While a substantial amount of research has been conducted to examine individual categorization behaviors, relatively little is known about the group categorization process. In two
Indian Academy of Sciences (India)
The purpose of the meeting was to form a group of people who ... able by looking at the energy deposited at the face of the final dipole, 4.5 m from ... A F Zarnecki has made a good start on background studies, V Telnov has proposed.
Cornwell, J F
1989-01-01
Recent devopments, particularly in high-energy physics, have projected group theory and symmetry consideration into a central position in theoretical physics. These developments have taken physicists increasingly deeper into the fascinating world of pure mathematics. This work presents important mathematical developments of the last fifteen years in a form that is easy to comprehend and appreciate.
African Journals Online (AJOL)
Ehab
Age groups vulnerable to serious attacks of anaphylaxis include infants, teenagers, pregnant women, and the elderly. Concomitant diseases, such as severe or uncontrolled asthma, cardiovascular disease, mastocytosis or clonal mast cell disorders and the concurrent use of some medications such as beta adrenergic ...
Degi, Bruce J.
1999-01-01
Offers a reflection on the shootings at Columbine High School in Littleton, Colorado, on April 20, 1999. Notes how every special-interest group has used the tragedy to support its own point of view, and concludes that teachers have become bystanders in the education of America's children. (SR)
Ignalina Safety Analysis Group
International Nuclear Information System (INIS)
Ushpuras, E.
1995-01-01
The article describes the fields of activities of Ignalina NPP Safety Analysis Group (ISAG) in the Lithuanian Energy Institute and overview the main achievements gained since the group establishment in 1992. The group is working under the following guidelines: in-depth analysis of the fundamental physical processes of RBMK-1500 reactors; collection, systematization and verification of the design and operational data; simulation and analysis of potential accident consequences; analysis of thermohydraulic and neutronic characteristics of the plant; provision of technical and scientific consultations to VATESI, Governmental authorities, and also international institutions, participating in various projects aiming at Ignalina NPP safety enhancement. The ISAG is performing broad scientific co-operation programs with both Eastern and Western scientific groups, supplying engineering assistance for Ignalina NPP. ISAG is also participating in the joint Lithuanian - Swedish - Russian project - Barselina, the first Probabilistic Safety Assessment (PSA) study of Ignalina NPP. The work is underway together with Maryland University (USA) for assessment of the accident confinement system for a range of breaks in the primary circuit. At present the ISAG personnel is also involved in the project under the grant from the Nuclear Safety Account, administered by the European Bank for reconstruction and development for the preparation and review of an in-depth safety assessment of the Ignalina plant
Gartner Group. Stamford, CT
Gartner Group is the one of the leading independent providers of research and analysis material for IT professionals. Their reports provide in-depth analysis of dominant trends, companies and products. CERN has obtained a licence making these reports available online to anyone within CERN. The database contains not only current reports, updated monthly, but also some going back over a year.
International Nuclear Information System (INIS)
Lisboa, P.; Michael, C.
1982-01-01
We address the question of designing optimum discrete sets of points to represent numerically a continuous group manifold. We consider subsets which are extensions of the regular discrete subgroups. Applications to Monte Carlo simulation of SU(2) and SU(3) gauge theory are discussed. (orig.)
Nelson, Jonathan E.
1980-01-01
Numerous ideas for teaching badminton to large groups are presented. The focus is on drills and techniques for off the court instructional stations. Instead of having students waiting their turn to play, more students can participate actively as they rotate from one station to another. (JN)
Group leaders optimization algorithm
Daskin, Anmer; Kais, Sabre
2011-03-01
We present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique which is designed into a group architecture. To demonstrate the efficiency of the method, a standard suite of single and multi-dimensional optimization functions along with the energies and the geometric structures of Lennard-Jones clusters are given as well as the application of the algorithm on quantum circuit design problems. We show that as an improvement over previous methods, the algorithm scales as N 2.5 for the Lennard-Jones clusters of N-particles. In addition, an efficient circuit design is shown for a two-qubit Grover search algorithm which is a quantum algorithm providing quadratic speedup over the classical counterpart.
TS Department
2008-01-01
Please note that owing the preparations for the Open Days, the FM Group will not able to handle specific requests for waste collection from 2nd to 6th of April, nor removal or PC transport requests between the 31 March and 11 April. We kindly ask you to plan the collection of all types of waste and any urgent transport of office furniture or PCs before 31 March. Waste collection requests must be made by contacting FM Support on 77777 or at the e-mail address mailto:Fm.Support@cern.ch; removal of office furniture or PC transport requests must be made using the EDH ‘Transport request’ form (select "Removals" or "PC transport" from the drop-down menu). For any question concerning the sorting of waste, please consult the following web site: http://dechets-waste.web.cern.ch/dechets-waste/ Thank you for your understanding and collaboration. TS/FM Group
Mindfulness for group facilitation
DEFF Research Database (Denmark)
Adriansen, Hanne Kirstine; Krohn, Simon
2014-01-01
In this paper, we argue that mindfulness techniques can be used for enhancing the outcome of group performance. The word mindfulness has different connotations in the academic literature. Broadly speaking there is ‘mindfulness without meditation’ or ‘Western’ mindfulness which involves active...... thinking and ‘Eastern’ mindfulness which refers to an open, accepting state of mind, as intended with Buddhist-inspired techniques such as meditation. In this paper, we are interested in the latter type of mindfulness and demonstrate how Eastern mindfulness techniques can be used as a tool for facilitation....... A brief introduction to the physiology and philosophy of Eastern mindfulness constitutes the basis for the arguments of the effect of mindfulness techniques. The use of mindfulness techniques for group facilitation is novel as it changes the focus from individuals’ mindfulness practice...
International Nuclear Information System (INIS)
Anon.
1993-01-01
A working group at a Canada/USA symposium on climate change and the Arctic identified major concerns and issues related to terrestrial resources. The group examined the need for, and the means of, involving resource managers and users at local and territorial levels in the process of identifying and examining the impacts and consequences of climatic change. Climatic change will be important to the Arctic because of the magnitude of the change projected for northern latitudes; the apparent sensitivity of its terrestrial ecosystems, natural resources, and human support systems; and the dependence of the social, cultural, and economic welfare of Arctic communities, businesses, and industries on the health and quality of their environment. Impacts of climatic change on the physical, biological, and associated socio-economic environment are outlined. Gaps in knowledge needed to quantify these impacts are listed along with their relationships with resource management. Finally, potential actions for response and adaptation are presented
International Nuclear Information System (INIS)
Alvarez-Gaume, L.; Gomez, C.; Sierra, G.
1990-01-01
We show that the duality properties of Rational Conformal Field Theories follow from the defining relations and the representation theory of quantum groups. The fusion and braiding matrices are q-analogues of the 6j-symbols and the modular transformation matrices are obtained from the properties of the co-multiplication. We study in detail the Wess-Zumino-Witten models and the rational gaussian models as examples, but carry out the arguments in general. We point out the connections with the Chern-Simons approach. We give general arguments of why the general solution to the polynomial equations of Moore and Seiberg describing the duality properties of Rational Conformal Field Theories defines a Quantum Group acting on the space of conformal blocks. A direct connection between Rational Theories and knot invariants is also presented along the lines of Jones' original work. (orig.)
International Nuclear Information System (INIS)
2004-08-01
This document provides information on the Areva Group, a world nuclear industry leader, offering solutions for nuclear power generation, electricity transmission and distribution and interconnect systems to the telecommunications, computer and automotive markets. It presents successively the front end division including the group business lines involved in producing nuclear fuel for electric power generation (uranium mining, concentration, conversion and enrichment and nuclear fuel fabrication); the reactors and services division which designs and builds PWR, BWR and research reactors; the back end division which encompasses the management of the fuel that has been used in nuclear power plants; the transmission and distribution division which provides products, systems and services to the medium and high voltage energy markets; the connectors division which designs and manufactures electrical, electronic and optical connectors, flexible micro circuitry and interconnection systems. Areva is implemented in Europe, north and south america, africa and asia-pacific. (A.L.B.)
The Ombudperson Initiative Group
Laura Stewart
Following many discussions that took place at some of the ATLAS Women's Network lunch gatherings, a few ATLAS women joined forces with similarly concerned CERN staff women to form a small group last Fall to discuss the need for a CERN-wide Ombudsperson. This has since evolved into the Ombudsperson Initiative Group (OIG) currently composed of the following members: Barbro Asman, Stockholm University; Pierre Charrue, CERN AB; Anna Cook, CERN IT; Catherine Delamare, CERN and IT Ombudsperson; Paula Eerola, Lund University; Pauline Gagnon, Indiana University; Eugenia Hatziangeli, CERN AB; Doreen Klem, CERN IT; Bertrand Nicquevert, CERN TS and Laura Stewart, CERN AT. On June 12, members of the OIG met with representatives of Human Resources (HR) and the Equal Opportunity Advisory Panel (EOAP) to discuss the proposal drafted by the OIG. The meeting was very positive. Everybody agreed that the current procedures at CERN applicable in the event of conflict required a thorough review, and that a professionnally trai...
Metrically universal abelian groups
Czech Academy of Sciences Publication Activity Database
Doucha, Michal
2017-01-01
Roč. 369, č. 8 (2017), s. 5981-5998 ISSN 0002-9947 R&D Projects: GA AV ČR IAA100190902 Institutional support: RVO:67985840 Keywords : Abelian group Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.426, year: 2016 http://www.ams.org/journals/tran/2017-369-08/S0002-9947-2017-07059-8/
International Nuclear Information System (INIS)
King, N.M.
1980-01-01
The Storage Ring Group set out to identify and pursue salient problems in accelerator physics for heavy ion fusion, divorced from any particular reference design concept. However, it became apparent that some basic parameter framework was required to correlate the different study topics. As the Workshop progressed, ring parameters were modified and updated. Consequently, the accompanying papers on individual topics will be found to refer to slightly varied parameters, according to the stage at which the different problems were tackled
International Nuclear Information System (INIS)
Warren, G.; Ludeking, L.; McDonald, J.; Nguyen, K.; Goplen, B.
1990-01-01
The MAGIC User's Group has been established to facilitate the use of electromagnetic particle-in-cell software by universities, government agencies, and industrial firms. The software consists of a series of independent executables that are capable of inter-communication. MAGIC, SOS, μ SOS are used to perform electromagnetic simulations while POSTER is used to provide post-processing capabilities. Each is described in the paper. Use of the codes for Klystrode simulation is discussed
Energy Technology Data Exchange (ETDEWEB)
NONE
2001-07-01
The goal of this working group was to foment discussions about the use and limitations of multi-bunch, representatives from most operating or in-project synchrotron radiation sources (ALS, SPEAR, BESSY-2, SPRING-8, ANKA, DELTA, PEP-2, DIAMOND, ESRF...) have presented their experience. The discussions have been led around 3 topics: 1) resistive wall instabilities and ion instabilities, 2) higher harmonic cavities, and 3) multibunch feedback systems.
International Nuclear Information System (INIS)
McCauley, V.S.; Keiser, J.R.
1992-01-01
This paper summarizes the findings of the Containment Working Group which met at the Workshop on Radioactive, Hazardous, and/or Mixed Waste Sludge Management. The Containment Working Group (CWG) examined the problems associated with providing adequate containment of waste forms from both short- and long-term storage. By its nature, containment encompasses a wide variety of waste forms, storage conditions, container types, containment schemes, and handling activities. A containment system can be anything from a 55-gal drum to a 100-ft-long underground vault. Because of the diverse nature of containment systems, the CWG chose to focus its limited time on broad issues that are applicable to the design of any containment system, rather than attempting to address problems specific to a particular containment system or waste-form type. Four major issues were identified by the CWG. They relate to: (1) service conditions and required system performance; (2) ultimate disposition; (3) cost and schedule; and (4) acceptance criteria, including quality assurance/quality control (QA/QC) concerns. All of the issues raised by the group are similar in that they all help to define containment system requirements
International Nuclear Information System (INIS)
Tsujikura, Y.
2000-01-01
The workshop of 26-27 june 2000, on nuclear power Plant LIfe Management (PLIM), also included working groups in which major issues facing PLIM activities for nuclear power plants were identified and discussed. The first group was on Technology. Utilities should consider required provisions capacity by properly maintaining and preserving the existing power plants to the extent practicable and taking into account growing demand, limits of energy conservation, and difficulties in finding new power plant sites. Generally, the extension of the life of nuclear power plant (e.g. from 40 years to 60 years) is an attractive option for utilities, as the marginal cost of most existing nuclear power plants is lower than that of almost all other power sources. It is also an attractive option for environmental protection. Consequently, PLIM has become an important issue in the context of the regulatory reform of the electricity markets. Therefore, the three main objectives of the Technology working group are: 1) Documenting how the safety of nuclear power plants being operated for the long-term has been confirmed, and suggesting ways of sharing this information. 2) Addressing development of advanced maintenance technologies necessary over the plant lifetime, and clarifying their technical challenges. 3) Suggesting potential areas of research and development that might, be necessary. Some potential examples of such research include: - improving the effectiveness of maintenance methods to assure detection of incipient faults; - providing cost effective preventive maintenance programmes; - furnishing systematic, cost-effective refurbishment programmes framed to be consistent with efforts to extend the time between re-fuelling; - developing a methodology that moves routine maintenance on-line without compromising safety. (author)
International Nuclear Information System (INIS)
Pressley, A.; Chari, V.; Tata Inst. of Fundamental Research, Bombay
1990-01-01
The authors presents an introduction to quantum groups defined as a deformation of the universal enveloping algebra of a Lie algebra. After the description of Hopf algebras with some examples the approach of Drinfel'd and Jimbo is described, where the quantization of a Lie algebra represents a Hopf algebra, defined over the algebra of formal power series in an indetermined h. The authors show that this approach arises from a r-matrix, which satisfies the classical Yang-Baxter equation. As example quantum sl 2 is considered. Furthermore the approaches of Manin and Woroniwicz and the R-matrix approach are described. (HSI)
Unilever Group : equity valuation
Pires, Susana Sofia Castelo
2014-01-01
The following dissertation has the purpose to value the Unilever Group, but more specifically Unilever N.V. being publicly traded in the Amsterdam Exchange Index. Unilever is seen as a global player and one of most successful and competitive fast-moving consumer goods companies. In order to valuate Unilever’s equity, a Discounted Cash Flow (DCF) approach is first carried out, since it is believed to be the most reliable methodology. The value estimated was €36.39, advising one to buy its s...
Liao, Tim Futing
2011-01-01
An incomparably useful examination of statistical methods for comparisonThe nature of doing science, be it natural or social, inevitably calls for comparison. Statistical methods are at the heart of such comparison, for they not only help us gain understanding of the world around us but often define how our research is to be carried out. The need to compare between groups is best exemplified by experiments, which have clearly defined statistical methods. However, true experiments are not always possible. What complicates the matter more is a great deal of diversity in factors that are not inde
Renormalization Group Functional Equations
Curtright, Thomas L
2011-01-01
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories. With minimal assumptions, the methods produce continuous flows from step-scaling {\\sigma} functions, and lead to exact functional relations for the local flow {\\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.
DEFF Research Database (Denmark)
Dove, Graham; Abildgaard, Sille Julie Jøhnk; Biskjær, Michael Mose
, both individually and when grouped, and their role in categorisation in semantic long-term memory. To do this, we adopt a multimodal analytical approach focusing on interaction between humans, and between humans and artefacts, alongside language. We discuss in detail examples of four different...... externalisation functions served by Post-ItTM notes, and show how these functions are present in complex overlapping combinations rather than being discrete. We then show how the temporal development of Post-ItTM note interactions supports categorisation qualities of semantic long-term memory....
DEFF Research Database (Denmark)
Dove, Graham; Abildgaard, Sille Julie; Biskjær, Michael Mose
2017-01-01
, both individually and when grouped, and their role in categorisation in semantic long-term memory. To do this, we adopt a multimodal analytical approach focusing on interaction between humans, and between humans and artefacts, alongside language. We discuss in detail examples of four different...... externalisation functions served by Post-ItTM notes, and show how these functions are present in complex overlapping combinations rather than being discrete. We then show how the temporal development of Post-ItTM note interactions supports categorisation qualities of semantic long-term memory....
Farmer, David W
1995-01-01
In most mathematics textbooks, the most exciting part of mathematics-the process of invention and discovery-is completely hidden from the reader. The aim of Groups and Symmetry is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: Its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequ
Holman, Gordon D.
1989-01-01
The primary purpose of the Theory and Modeling Group meeting was to identify scientists engaged or interested in theoretical work pertinent to the Max '91 program, and to encourage theorists to pursue modeling which is directly relevant to data which can be expected to result from the program. A list of participants and their institutions is presented. Two solar flare paradigms were discussed during the meeting -- the importance of magnetic reconnection in flares and the applicability of numerical simulation results to solar flare studies.
DEFF Research Database (Denmark)
Terslev, Lene; Iagnocco, Annamaria; Bruyn, George A W
2017-01-01
OBJECTIVE: To provide an update from the Outcome Measures in Rheumatology (OMERACT) Ultrasound Working Group on the progress for defining ultrasound (US) minimal disease activity threshold at joint level in rheumatoid arthritis (RA) and for standardization of US application in juvenile idiopathic......) and power Doppler (PD). Synovial effusion (SE) was scored a binary variable. For JIA, a Delphi approach and subsequent validation in static images and patient-based exercises were used to developed preliminary definitions for synovitis and a scoring system. RESULTS: For minimal disease activity, 7% HC had...
Thomson, John, 1837-1921, photographer
2003-01-01
158 x 111 mm. Woodburytype. A view showing a group of villagers seated in a paved courtyard in front of a stonewalled house (the principal house in the village). The village is near the town of Paphos. The photograph appears in Thomson's 'Through Cyprus with the camera, in the autumn of 1878' (vol.2, London: Sampson Low, Marston, Searle, and Rivington, 1879). Thomson states that the purpose of the gathering was twofold: to welcome strangers to the village and to discuss a point of law c...
Bevalac computer support group
International Nuclear Information System (INIS)
McParland, C.; Bronson, M.
1985-01-01
During the past year, a group was created and placed under the leadership of Charles McParland. This is an expansion of previous Bevalac software efforts and has responsibilities in three major hardware and software areas. The first area is the support of the existing data acquisition/analysis VAX 11/780s at the Bevalac. The second area is the continued support of present data acquisition programs. The third principal area of effort is the development of new data acquisition systems to meet the increasing needs of the Bevalac experimental program
Social group utility maximization
Gong, Xiaowen; Yang, Lei; Zhang, Junshan
2014-01-01
This SpringerBrief explains how to leverage mobile users' social relationships to improve the interactions of mobile devices in mobile networks. It develops a social group utility maximization (SGUM) framework that captures diverse social ties of mobile users and diverse physical coupling of mobile devices. Key topics include random access control, power control, spectrum access, and location privacy.This brief also investigates SGUM-based power control game and random access control game, for which it establishes the socially-aware Nash equilibrium (SNE). It then examines the critical SGUM-b
Even and odd symplectic and Kaehlerian structures on projective superspaces
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Nersessyan, A.P.
1992-01-01
Supergeneralization of CP(N) provided by even and odd Kaehlerian structures from Hamiltonian reduction are construct. Operator Δ which used in Batalin - Vilkovsky quantization formalism and mechanics which are bi-Hamiltonian under corresponding even and odd Poisson brackets are considered. 21 refs
Galilean Duffin-Kemmer-Petiau algebra and symplectic structure
Fernandes, M C B; Vianna, J D M
2003-01-01
We develop the Duffin-Kemmer-Petiau (DKP) approach in the phase-space picture of quantum mechanics by considering DKP algebras in a Galilean covariant context. Specifically, we develop an algebraic calculus based on a tensor algebra defined on a five-dimensional space which plays the role of spacetime background of the non-relativistic DKP equation. The Liouville operator is determined and the Liouville-von Neumann equation is written in two situations: the free particle and a particle in an external electromagnetic field. A comparison between the non-relativistic and the relativistic cases is commented.
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.
Symplectic evolution of Wigner functions in Markovian open systems.
Brodier, O; Almeida, A M Ozorio de
2004-01-01
The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.
Symplectic symmetry of the neutrino mass for many neutrino flavors
International Nuclear Information System (INIS)
Oeztuerk, N.; Ankara Univ.
2001-01-01
The algebraic structure of the neutrino mass Hamiltonian is presented for two neutrino flavors considering both Dirac and Majorana mass terms. It is shown that the algebra is Sp(8) and also discussed how the algebraic structure generalizes for the case of more than two neutrino flavors. (orig.)
Statistical equilibrium and symplectic geometry in general relativity
International Nuclear Information System (INIS)
Iglesias, P.
1981-09-01
A geometrical construction is given of the statistical equilibrium states of a system of particles in the gravitational field in general relativity. By a method of localization variables, the expression of thermodynamic values is given and the compatibility of this description is shown with a macroscopic model of a relativistic continuous medium for a given value of the free-energy function [fr
Internal deformation of Lie algebroids and symplectic realizations
Energy Technology Data Exchange (ETDEWEB)
Carinena, Jose F [Departamento de Fisica Teorica, Universidad de Zara-goza, 50009 Zaragoza (Spain); Costa, Joana M Nunes da [Departamento de Matematica, Universidade de Coimbra, 3001-454 Coimbra (Portugal); Santos, PatrIcia [Departamento de Fisica e Matematica, Instituto Superior de Engenharia de Coimbra, 3030-199 Coimbra (Portugal)
2006-06-02
Given a Lie algebroid and a bundle over its base which is endowed with a localizable Poisson structure and a flat connection, we construct an extended bundle whose dual is endowed with an almost-Poisson structure that is a quadratic Poisson structure when a certain compatibility property is satisfied. This new formalism on Lie algebroids describes systems with internal degrees of freedom.
Nondeterministic noiseless amplification via non-symplectic phase space transformations
International Nuclear Information System (INIS)
Walk, Nathan; Lund, Austin P; Ralph, Timothy C
2013-01-01
We analyse the action of an ideal noiseless linear amplifier operator, g a-hat † a-hat, using the Wigner function phase space representation. In this setting we are able to clarify the gain g for which a physical output is produced when this operator is acted upon inputs other than coherent states. We derive compact closed form expressions for the action of N local amplifiers, with potentially different gains, on arbitrary N-mode Gaussian states and provide several examples of the utility of this formalism for determining important quantities including amplification and the strength and purity of the distilled entanglement, and for optimizing the use of the amplification in quantum information protocols. (paper)
Internal deformation of Lie algebroids and symplectic realizations
International Nuclear Information System (INIS)
Carinena, Jose F; Costa, Joana M Nunes da; Santos, PatrIcia
2006-01-01
Given a Lie algebroid and a bundle over its base which is endowed with a localizable Poisson structure and a flat connection, we construct an extended bundle whose dual is endowed with an almost-Poisson structure that is a quadratic Poisson structure when a certain compatibility property is satisfied. This new formalism on Lie algebroids describes systems with internal degrees of freedom
ATLAS Detector Interface Group
Mapelli, L
Originally organised as a sub-system in the DAQ/EF-1 Prototype Project, the Detector Interface Group (DIG) was an information exchange channel between the Detector systems and the Data Acquisition to provide critical detector information for prototype design and detector integration. After the reorganisation of the Trigger/DAQ Project and of Technical Coordination, the necessity to provide an adequate context for integration of detectors with the Trigger and DAQ lead to organisation of the DIG as one of the activities of Technical Coordination. Such an organisation emphasises the ATLAS wide coordination of the Trigger and DAQ exploitation aspects, which go beyond the domain of the Trigger/DAQ project itself. As part of Technical Coordination, the DIG provides the natural environment for the common work of Trigger/DAQ and detector experts. A DIG forum for a wide discussion of all the detector and Trigger/DAQ integration issues. A more restricted DIG group for the practical organisation and implementation o...
TS Department
2008-01-01
In order to prepare the organization of the Open Days, please note that FM Group will not able to take into account either specific requests for waste collection from 2nd to 6th of April, either removal or PC transport requests between the 31st and the 11th of March. We kindly ask you to plan the collection of any type of waste and the urgent transport of office furniture or PC before the 31st of March. Waste collection requests shall be formulated contacting FM Support at 77777 or at the email address mailto:Fm.Support@cern.ch; removal of office furniture or PC transport requests must be made using the EDH ‘Transport request’ form selecting the "Removals" or the "PC transport" category from the drop-down menu. For any question concerning the waste sorting, please consult the following web address: http://dechets-waste.web.cern.ch/dechets-waste/. Thank you for your understanding and collaboration. TS/FM Group
Directory of Open Access Journals (Sweden)
Baltezarević Vesna
2009-01-01
Full Text Available Our reality, having been subject to the numerous social crises during the last decades of the 20th century, is characterized by frequent incidences of powerlessness and alienation. The man is more frequently a subject to loneliness and overcomes the feeling of worthlessness, no matter whether he considers himself an individual or a part of a whole larger social. Such an environment leads to development of aggression in all fields of ones life. This paper has as an objective the pointing out of the mental harassment that is manifested in the working environment. There is a prevalence of mobbing cases, as a mode of pathological communication. The result of this is that a person, subjected to this kind of abuse, is soon faced with social isolation. This research also aspires to initiate the need for social groups self-organization of which victims are part of. The reaction modality of a social group directly conditions the outcome of the deliberate social drama, one is subjected to it as a result of mobbing.
Meningococcal group B vaccines.
Findlow, Jamie
2013-06-01
Meningococcal disease remains a devastating and feared infection with a significant morbidity and mortality profile. The successful impact of meningococcal capsular group C glyconconjugate vaccines introduced into the UK infant immunization schedule in 1999, has resulted in >80% of disease now being attributable to meningococcal capsular group B (MenB). MenB glyconconjugate vaccines are not immunogenic and hence, vaccine design has focused on sub-capsular antigens. Recently, a four component vaccine to combat MenB disease (4CMenB) has progressed through clinical development and was approved by the European Medicines Agency at the end of 2012. This vaccine has proven safe and immunogenic and has been predicted to provide protection against ~73% of the MenB disease from England and Wales. Recommendation/implementation of the vaccine into the UK infant schedule is currently being evaluated. 4CMenB has the potential to provide protection against a significant proportion of MenB disease in the UK which is currently unpreventable.
International Nuclear Information System (INIS)
Doroshuk, B.W.
2000-01-01
The workshop of 26-27 june 2000, on nuclear power Plant LIfe Management (PLIM), also included working groups in which major issues facing PLIM activities for nuclear power plants were identified and discussed. The third group was on Business. The discussion concerned the following points: There are concerns about retaining experienced/trained personnel, and maintaining a good working relationship among them, as well as about the closure of research facilities, the reduction in staff numbers under increasing economic pressure and the lack of new nuclear power plant constructions. The marginal cost of producing electricity is lower for most existing nuclear power plants than for almost all other energy sources. Refurbishment costs are usually relatively small compared with new investments. The ongoing regulatory reform of the electricity market will bring increasing competition. Although PLIM has been carried out in many countries with favourable results, there are still uncertainties which affect business decisions regarding financial and market risks in PLIM activities. Recommendations were made. (author)
2013-01-01
The CERN Administration would like to remind you that staff members and fellows have the possibility to take out a life insurance contract on favourable terms through a Group Life Insurance. This insurance is provided by the company Helvetia and is available to you on a voluntary basis. The premium, which varies depending on the age and gender of the person insured, is calculated on the basis of the amount of the death benefit chosen by the staff member/fellow and can be purchased in slices of 10,000 CHF. The contract normally ends at the retirement age (65/67 years) or when the staff member/fellow leaves the Organization. The premium is deducted monthly from the payroll. Upon retirement, the staff member can opt to maintain his membership under certain conditions. More information about Group Life Insurance can be found at: Regulations (in French) Table of premiums The Pension Fund Benefit Service &...
International Nuclear Information System (INIS)
Tankeev, Sergei G
2000-01-01
For an arithmetic model X of a Fermat surface or a hyperkahler variety with Betti number b 2 (V otimes k-bar)>3 over a purely imaginary number field k, we prove the finiteness of the l-components of Br'(X) for all primes l>>0. This yields a variant of a conjecture of M. Artin. If V is a smooth projective irregular surface over a number field k and V(k)≠ nothing, then the l-primary component of Br(V)/Br(k) is an infinite group for every prime l. Let A 1 →M 1 be the universal family of elliptic curves with a Jacobian structure of level N>=3 over a number field k supset of Q(e 2πi/N ). Assume that M 1 (k) ≠ nothing. If V is a smooth projective compactification of the surface A 1 , then the l-primary component of Br(V)/Br(M-bar 1 ) is a finite group for each sufficiently large prime l
International Nuclear Information System (INIS)
Anon.
1981-01-01
The accomplishments of the task group studies over the past year are reviewed. The purposes of biological investigations, in the context of subseabed disposal, are: an evaluation of the dose to man; an estimation of effects on the ecosystem; and an estimation of the influence of organisms on and as barriers to radionuclide migration. To accomplish these ends, the task group adopted the following research goals: (1) acquire more data on biological accumulation of specific radionuclides, such as those of Tc, Np, Ra, and Sr; (2) acquire more data on transfer coefficients from sediment to organism; (3) Calculate mass transfer rates, construct simple models using them, and estimate collective dose commitment; (4) Identify specific pathways or transfer routes, determine the rates of transfer, and make dose limit calculations with simple models; (5) Calculate dose rates to and estimate irradiation effects on the biota as a result of waste emplacement, by reference to background irradiation calculations. (6) Examine the effect of the biota on altering sediment/water radionuclide exchange; (7) Consider the biological data required to address different accident scenarios; (8) Continue to provide the basic biological information for all of the above, and ensure that the system analysis model is based on the most realistic and up-to-date concepts of marine biologists; and (9) Ensure by way of free exchange of information that the data used in any model are the best currently available
DEFF Research Database (Denmark)
Lindegaard, Laura Bang
2014-01-01
Scholars of ethnomethodologically informed discourse studies are often sceptical of the use of interview data such as focus group data. Some scholars quite simply reject interview data with reference to a general preference for so-called naturally occurring data. Other scholars acknowledge...... that interview data can be of some use if the distinction between natural and contrived data is given up and replaced with a distinction between interview data as topic or as resource. In greater detail, such scholars argue that interview data are perfectly adequate if the researcher wants to study the topic...... of interview interaction, but inadequate as data for studying phenomena that go beyond the phenomenon of interview interaction. Neither of these more and less sceptical positions are, on the face of it, surprising due to the ethnomethodological commitment to study social order as accomplished in situ...
2013-01-01
The CERN Administration wishes to inform staff members and fellows having taken out optional life insurance under the group contract signed by CERN that the following changes to the rules and regulations entered into force on 1 January 2013: The maximum age for an active member has been extended from 65 to 67 years. The beneficiary clause now allows insured persons to designate one or more persons of their choice to be their beneficiary(-ies), either at the time of taking out the insurance or at a later date, in which case the membership/modification form must be updated accordingly. Beneficiaries must be clearly identified (name, first name, date of birth, address). The membership/modification form is available on the FP website: http://fp.web.cern.ch/helvetia-life-insurance For further information, please contact: Valentina Clavel (Tel. 73904) Peggy Pithioud (Tel. 72736)
DEFF Research Database (Denmark)
Jahnsen, Rasmus O; Sandberg-Schaal, Anne; Frimodt-Møller, Niels
2015-01-01
Increased incidence of infections with multidrug-resistant bacterial strains warrants an intensive search for novel potential antimicrobial agents. Here, an antimicrobial peptide analogue with a cationic/hydrophobic alternating design displaying only moderate activity against Gram-positive pathog......Increased incidence of infections with multidrug-resistant bacterial strains warrants an intensive search for novel potential antimicrobial agents. Here, an antimicrobial peptide analogue with a cationic/hydrophobic alternating design displaying only moderate activity against Gram......, the most favorable hydrophobic activity-inducing moieties were found to be cyclohexylacetyl and pentafluorophenylacetyl groups, while the presence of a short PEG-like chain had no significant effect on activity. Introduction of cationic moieties conferred no effect or merely a moderate activity...
Optimised Renormalisation Group Flows
Litim, Daniel F
2001-01-01
Exact renormalisation group (ERG) flows interpolate between a microscopic or classical theory and the corresponding macroscopic or quantum effective theory. For most problems of physical interest, the efficiency of the ERG is constrained due to unavoidable approximations. Approximate solutions of ERG flows depend spuriously on the regularisation scheme which is determined by a regulator function. This is similar to the spurious dependence on the ultraviolet regularisation known from perturbative QCD. Providing a good control over approximated ERG flows is at the root for reliable physical predictions. We explain why the convergence of approximate solutions towards the physical theory is optimised by appropriate choices of the regulator. We study specific optimised regulators for bosonic and fermionic fields and compare the optimised ERG flows with generic ones. This is done up to second order in the derivative expansion at both vanishing and non-vanishing temperature. An optimised flow for a ``proper-time ren...
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Quantum Secure Group Communication.
Li, Zheng-Hong; Zubairy, M Suhail; Al-Amri, M
2018-03-01
We propose a quantum secure group communication protocol for the purpose of sharing the same message among multiple authorized users. Our protocol can remove the need for key management that is needed for the quantum network built on quantum key distribution. Comparing with the secure quantum network based on BB84, we show our protocol is more efficient and securer. Particularly, in the security analysis, we introduce a new way of attack, i.e., the counterfactual quantum attack, which can steal information by "invisible" photons. This invisible photon can reveal a single-photon detector in the photon path without triggering the detector. Moreover, the photon can identify phase operations applied to itself, thereby stealing information. To defeat this counterfactual quantum attack, we propose a quantum multi-user authorization system. It allows us to precisely control the communication time so that the attack can not be completed in time.
Energy Technology Data Exchange (ETDEWEB)
Artuso, M.; et al.,
2013-10-18
Sensors play a key role in detecting both charged particles and photons for all three frontiers in Particle Physics. The signals from an individual sensor that can be used include ionization deposited, phonons created, or light emitted from excitations of the material. The individual sensors are then typically arrayed for detection of individual particles or groups of particles. Mounting of new, ever higher performance experiments, often depend on advances in sensors in a range of performance characteristics. These performance metrics can include position resolution for passing particles, time resolution on particles impacting the sensor, and overall rate capabilities. In addition the feasible detector area and cost frequently provides a limit to what can be built and therefore is often another area where improvements are important. Finally, radiation tolerance is becoming a requirement in a broad array of devices. We present a status report on a broad category of sensors, including challenges for the future and work in progress to solve those challenges.
Representation Theory of Algebraic Groups and Quantum Groups
Gyoja, A; Shinoda, K-I; Shoji, T; Tanisaki, Toshiyuki
2010-01-01
Invited articles by top notch expertsFocus is on topics in representation theory of algebraic groups and quantum groupsOf interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics
International Nuclear Information System (INIS)
Von Maravic, H.
1993-01-01
Natural analogue studies have been carried out for several years in the framework of the European Community's R and D programme on radioactive waste; and within its recent fourth five-year programme on 'Management and storage of radioactive waste (1990-94)' the Community is participating in the Oklo study, natural analogue for transfer processes in a geological repository. The Oklo project is coordinated by CEA-IPSN (F) and involves laboratories from several CEA directorates (IPSN, DTA and DCC) which collaborate with other institutions from France: CREGU, Nancy; CNRS, Strasbourg and ENSMD, Fontainebleau. Moreover, institutes from non-EC member States are also taking part in the Oklo study. The second joint CEC-CEA progress meeting of the Oklo Working Group was held in April 1992 in Brussels and gave the possibility of reviewing and discussing progress made since its first meeting in February 1991 at CEA in Fontenay-aux-Roses. About 40 participants from 15 laboratories and organizations coming from France, Canada, Gabon, Japan, Sweden and the USA underline the great interest in the ongoing research activities. The meeting focused on the different tasks within the CEC-CEA Oklo project concerning (i) field survey and sampling, (ii) characterization of the source term, (iii) studies of the petrographical and geochemical system, and (iv) studies of the hydrogeological system and hydrodynamic modelling. (author) 17 papers are presented
The Liabilities Management Group
International Nuclear Information System (INIS)
Whitehead, A.W.
1998-01-01
The Liabilities Management Group (LMG) was initiated by DTI. It is a cooperative forum which was set up in 1995. The current participants are DTI, UKAEA, NLM (for BNFL), MOD and Magnox Electric. The LMG was initiated to produce closer cooperation between public sector liability management organizations, achieve more cost-effective management of UK nuclear liabilities and enhance development of the UK nuclear decommissioning and waste management strategy. The objectives are to compare practices between liabilities management organizations discuss the scope for collaboration identify priority areas for possible collaboration agree action plans for exploring and undertaking such collaboration.Four task forces have been formed to look at specific areas (R and D, safety, contracts, and project management) and each reports separately to the LMG. The LMG has achieved its original aim of bringing together those with public sector liability management responsibilities. All participants feel that the LMG has been useful and that it should continue. Looking to the future, there is a continuing need for the LMG to facilitate removal of barriers to the achievement of best value for money. The LMG might also consider addressing the 'business process' elements that a liability management organization must be good at in order to define best practice in these. (author)
CORRELATION BETWEEN GROUP LOCAL DENSITY AND GROUP LUMINOSITY
Energy Technology Data Exchange (ETDEWEB)
Deng Xinfa [School of Science, Nanchang University, Jiangxi 330031 (China); Yu Guisheng [Department of Natural Science, Nanchang Teachers College, Jiangxi 330103 (China)
2012-11-10
In this study, we investigate the correlation between group local number density and total luminosity of groups. In four volume-limited group catalogs, we can conclude that groups with high luminosity exist preferentially in high-density regions, while groups with low luminosity are located preferentially in low-density regions, and that in a volume-limited group sample with absolute magnitude limit M{sub r} = -18, the correlation between group local number density and total luminosity of groups is the weakest. These results basically are consistent with the environmental dependence of galaxy luminosity.
Group Counseling in the Schools
Perusse, Rachelle; Goodnough, Gary E.; Lee, Vivian V.
2009-01-01
Group counseling is an effective intervention when working in a school setting. In this article, the authors discuss the different kinds of groups offered in schools, types of group interventions, strategies to use in forming groups, and how to collaborate with others in the school. Because leading groups in schools is a specialized skill, the…
Naive Theories of Social Groups
Rhodes, Marjorie
2012-01-01
Four studies examined children's (ages 3-10, Total N = 235) naive theories of social groups, in particular, their expectations about how group memberships constrain social interactions. After introduction to novel groups of people, preschoolers (ages 3-5) reliably expected agents from one group to harm members of the other group (rather than…
Making Cooperative Learning Groups Work.
Hawley, James; De Jong, Cherie
1995-01-01
Discusses the use of cooperative-learning groups with middle school students. Describes cooperative-learning techniques, including group roles, peer evaluation, and observation and monitoring. Considers grouping options, including group size and configuration, dyads, the think-pair-share lecture, student teams achievement divisions, jigsaw groups,…
Fermilab Steering Group Report
Energy Technology Data Exchange (ETDEWEB)
Beier, Eugene; /Pennsylvania U.; Butler, Joel; /Fermilab; Dawson, Sally; /Brookhaven; Edwards, Helen; /Fermilab; Himel, Thomas; /SLAC; Holmes, Stephen; /Fermilab; Kim, Young-Kee; /Fermilab /Chicago U.; Lankford, Andrew; /UC, Irvine; McGinnis, David; /Fermilab; Nagaitsev, Sergei; /Fermilab; Raubenheimer, Tor; /SLAC /Fermilab
2007-01-01
The Fermilab Steering Group has developed a plan to keep U.S. accelerator-based particle physics on the pathway to discovery, both at the Terascale with the LHC and the ILC and in the domain of neutrinos and precision physics with a high-intensity accelerator. The plan puts discovering Terascale physics with the LHC and the ILC as Fermilab's highest priority. While supporting ILC development, the plan creates opportunities for exciting science at the intensity frontier. If the ILC remains near the Global Design Effort's technically driven timeline, Fermilab would continue neutrino science with the NOVA experiment, using the NuMI (Neutrinos at the Main Injector) proton plan, scheduled to begin operating in 2011. If ILC construction must wait somewhat longer, Fermilab's plan proposes SNuMI, an upgrade of NuMI to create a more powerful neutrino beam. If the ILC start is postponed significantly, a central feature of the proposed Fermilab plan calls for building an intense proton facility, Project X, consisting of a linear accelerator with the currently planned characteristics of the ILC combined with Fermilab's existing Recycler Ring and the Main Injector accelerator. The major component of Project X is the linac. Cryomodules, radio-frequency distribution, cryogenics and instrumentation for the linac are the same as or similar to those used in the ILC at a scale of about one percent of a full ILC linac. Project X's intense proton beams would open a path to discovery in neutrino science and in precision physics with charged leptons and quarks. World-leading experiments would allow physicists to address key questions of the Quantum Universe: How did the universe come to be? Are there undiscovered principles of nature: new symmetries, new physical laws? Do all the particles and forces become one? What happened to the antimatter? Building Project X's ILC-like linac would offer substantial support for ILC development by accelerating the
Linear deformations of discrete groups and constructions of multivalued groups
International Nuclear Information System (INIS)
Yagodovskii, Petr V
2000-01-01
We construct deformations of discrete multivalued groups described as special deformations of their group algebras in the class of finite-dimensional associative algebras. We show that the deformations of ordinary groups producing multivalued groups are defined by cocycles with coefficients in the group algebra of the original group and obtain classification theorems on these deformations. We indicate a connection between the linear deformations of discrete groups introduced in this paper and the well-known constructions of multivalued groups. We describe the manifold of three-dimensional associative commutative algebras with identity element, fixed basis, and a constant number of values. The group algebras of n-valued groups of order three (three-dimensional n-group algebras) form a discrete set in this manifold
Group B Streptococcus and Pregnancy
... B Strep and Pregnancy • What is group B streptococcus (GBS)? • What does it mean to be colonized ... planned cesarean birth? •Glossary What is group B streptococcus (GBS)? Group B streptococcus is one of the ...
Harmonic Analysis and Group Representation
Figa-Talamanca, Alessandro
2011-01-01
This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.
Topological K-Kolmogorov groups
International Nuclear Information System (INIS)
Abd El-Sattar, A. Dabbour.
1987-07-01
The idea of the K-groups was used to define K-Kolmogorov homology and cohomology (over pairs of coefficient groups) which are descriptions of certain modifications of the Kolmogorov groups. The present work is devoted to the study of the topological properties of the K-Kolmogorov groups which lie at the root of the group duality based essentially upon Pontrjagin's concept of group multiplication. 14 refs
Post-Disaster Social Justice Group Work and Group Supervision
Bemak, Fred; Chung, Rita Chi-Ying
2011-01-01
This article discusses post-disaster group counseling and group supervision using a social justice orientation for working with post-disaster survivors from underserved populations. The Disaster Cross-Cultural Counseling model is a culturally responsive group counseling model that infuses social justice into post-disaster group counseling and…
Group Leader Development: Effects of Personal Growth and Psychoeducational Groups
Ohrt, Jonathan H.; Robinson, E. H., III; Hagedorn, W. Bryce
2013-01-01
The purpose of this quasi-experimental study was to compare the effects of personal growth groups and psychoeducational groups on counselor education students' (n = 74) empathy and group leader self-efficacy. Additionally, we compared the degree to which participants in each group valued: (a) cohesion, (b) catharsis, and (c) insight. There were no…
Feminist Principles in Survivor's Groups: Out-of-Group Contact.
Rittenhouse, JoAn
1997-01-01
Illustrates the value of theoretical concepts from Feminist Therapy in the group treatment of women survivors. Theoretical underpinnings are supported using data taken from clinical experience and by examining group themes and out-of-group contact developed from the case sample. Principles regarding feminist groups are proposed. (RJM)
Zientek, Michael L.; Loferski, Patricia J.; Parks, Heather L.; Schulte, Ruth F.; Seal, Robert R.; Schulz, Klaus J.; DeYoung,, John H.; Seal, Robert R.; Bradley, Dwight C.
2017-12-19
The platinum-group elements (PGEs)—platinum, palladium, rhodium, ruthenium, iridium, and osmium—are metals that have similar physical and chemical properties and tend to occur together in nature. PGEs are indispensable to many industrial applications but are mined in only a few places. The availability and accessibility of PGEs could be disrupted by economic, environmental, political, and social events. The United States net import reliance as a percentage of apparent consumption is about 90 percent.PGEs have many industrial applications. They are used in catalytic converters to reduce carbon monoxide, hydrocarbon, and nitrous oxide emissions in automobile exhaust. The chemical industry requires platinum or platinum-rhodium alloys to manufacture nitric oxide, which is the raw material used to manufacture explosives, fertilizers, and nitric acid. In the petrochemical industry, platinum-supported catalysts are needed to refine crude oil and to produce aromatic compounds and high-octane gasoline. Alloys of PGEs are exceptionally hard and durable, making them the best known coating for industrial crucibles used in the manufacture of chemicals and synthetic materials. PGEs are used by the glass manufacturing industry in the production of fiberglass and flat-panel and liquid crystal displays. In the electronics industry, PGEs are used in computer hard disks, hybridized integrated circuits, and multilayer ceramic capacitors.Aside from their industrial applications, PGEs are used in such other fields as health, consumer goods, and finance. Platinum, for example, is used in medical implants, such as pacemakers, and PGEs are used in cancer-fighting drugs. Platinum alloys are an ideal choice for jewelry because of their white color, strength, and resistance to tarnish. Platinum, palladium, and rhodium in the form of coins and bars are also used as investment commodities, and various financial instruments based on the value of these PGEs are traded on major exchanges
Emotional collectives: How groups shape emotions and emotions shape groups.
van Kleef, Gerben A; Fischer, Agneta H
2016-01-01
Group settings are epicentres of emotional activity. Yet, the role of emotions in groups is poorly understood. How do group-level phenomena shape group members' emotional experience and expression? How are emotional expressions recognised, interpreted and shared in group settings? And how do such expressions influence the emotions, cognitions and behaviours of fellow group members and outside observers? To answer these and other questions, we draw on relevant theoretical perspectives (e.g., intergroup emotions theory, social appraisal theory and emotions as social information theory) and recent empirical findings regarding the role of emotions in groups. We organise our review according to two overarching themes: how groups shape emotions and how emotions shape groups. We show how novel empirical approaches break important new ground in uncovering the role of emotions in groups. Research on emotional collectives is thriving and constitutes a key to understanding the social nature of emotions.
Group performance and group learning at dynamic system control tasks
International Nuclear Information System (INIS)
Drewes, Sylvana
2013-01-01
Proper management of dynamic systems (e.g. cooling systems of nuclear power plants or production and warehousing) is important to ensure public safety and economic success. So far, research has provided broad evidence for systematic shortcomings in individuals' control performance of dynamic systems. This research aims to investigate whether groups manifest synergy (Larson, 2010) and outperform individuals and if so, what processes lead to these performance advantages. In three experiments - including simulations of a nuclear power plant and a business setting - I compare the control performance of three-person-groups to the average individual performance and to nominal groups (N = 105 groups per experiment). The nominal group condition captures the statistical advantage of aggregated group judgements not due to social interaction. First, results show a superior performance of groups compared to individuals. Second, a meta-analysis across all three experiments shows interaction-based process gains in dynamic control tasks: Interacting groups outperform the average individual performance as well as the nominal group performance. Third, group interaction leads to stable individual improvements of group members that exceed practice effects. In sum, these results provide the first unequivocal evidence for interaction-based performance gains of groups in dynamic control tasks and imply that employers should rely on groups to provide opportunities for individual learning and to foster dynamic system control at its best.
Does group efficacy increase group identification? Resolving their paradoxical relationship
van Zomeren, Martijn; Leach, Colin Wayne; Spears, Russell
2010-01-01
Although group identification and group efficacy are both important predictors of collective action against collective disadvantage, there is mixed evidence for their (causal) relationship. Meta-analytic and correlational evidence suggests an overall positive relationship that has been interpreted
Secure Group Communications for Large Dynamic Multicast Group
Institute of Scientific and Technical Information of China (English)
Liu Jing; Zhou Mingtian
2003-01-01
As the major problem in multicast security, the group key management has been the focus of research But few results are satisfactory. In this paper, the problems of group key management and access control for large dynamic multicast group have been researched and a solution based on SubGroup Secure Controllers (SGSCs) is presented, which solves many problems in IOLUS system and WGL scheme.
How to conduct focus groups: researching group priorities through discussion.
1992-01-01
Focus groups serve to uncover priorities and beliefs of a target group, but health project designers do not always take the time to seek this information beforehand. Focus groups also allow various local subgroups to communicate their concerns before the project starts. Focus groups can also breed ideas and dialogue that individual interviews cannot and they provide baseline information so managers can determine if attitudes or priorities have resulted from the project. Diverse people have different beliefs, e.g., women who have young children view oral rehydration therapy differently from women with no children. Project designers can use these basic differences to arrive at some conclusions about general attitudes. Focus group facilitators should have a discussion outline to help keep the group on the topic of concern. They should limit sessions to 60-90 minutes. Each focus groups should include 8-10 people. It is important to have members of various community subgroups in each group. Yet group designers should be careful not to include within the same group, those who may intimidate other people in the group, e.g., in situations where farmers depend on middlemen, farmers may not be open if middlemen are also in the focus group. Facilitators should launch each session with an attempt to encourage the members to be open and to feel comfortable. For example, in Malawi, a facilitator leads her focus group discussions with songs. Stories are another icebreaker. It is important that all focus groups centering around a certain project discuss the same topics. Facilitators need to stress to the group that all discussions are to be kept confidential. The designers should also carefully word the questions so that facilitators will not impart their bias. Facilitators should not direct the group to certain conclusions, but instead keep the discussions focused.
Group covariance and metrical theory
International Nuclear Information System (INIS)
Halpern, L.
1983-01-01
The a priori introduction of a Lie group of transformations into a physical theory has often proved to be useful; it usually serves to describe special simplified conditions before a general theory can be worked out. Newton's assumptions of absolute space and time are examples where the Euclidian group and translation group have been introduced. These groups were extended to the Galilei group and modified in the special theory of relativity to the Poincare group to describe physics under the given conditions covariantly in the simplest way. The criticism of the a priori character leads to the formulation of the general theory of relativity. The general metric theory does not really give preference to a particular invariance group - even the principle of equivalence can be adapted to a whole family of groups. The physical laws covariantly inserted into the metric space are however adapted to the Poincare group. 8 references
Defining and Classifying Interest Groups
DEFF Research Database (Denmark)
Baroni, Laura; Carroll, Brendan; Chalmers, Adam
2014-01-01
The interest group concept is defined in many different ways in the existing literature and a range of different classification schemes are employed. This complicates comparisons between different studies and their findings. One of the important tasks faced by interest group scholars engaged...... in large-N studies is therefore to define the concept of an interest group and to determine which classification scheme to use for different group types. After reviewing the existing literature, this article sets out to compare different approaches to defining and classifying interest groups with a sample...... in the organizational attributes of specific interest group types. As expected, our comparison of coding schemes reveals a closer link between group attributes and group type in narrower classification schemes based on group organizational characteristics than those based on a behavioral definition of lobbying....
What Is a Group? Young Children's Perceptions of Different Types of Groups and Group Entitativity.
Directory of Open Access Journals (Sweden)
Maria Plötner
Full Text Available To date, developmental research on groups has focused mainly on in-group biases and intergroup relations. However, little is known about children's general understanding of social groups and their perceptions of different forms of group. In this study, 5- to 6-year-old children were asked to evaluate prototypes of four key types of groups: an intimacy group (friends, a task group (people who are collaborating, a social category (people who look alike, and a loose association (people who coincidently meet at a tram stop. In line with previous work with adults, the vast majority of children perceived the intimacy group, task group, and social category, but not the loose association, to possess entitativity, that is, to be a 'real group.' In addition, children evaluated group member properties, social relations, and social obligations differently in each type of group, demonstrating that young children are able to distinguish between different types of in-group relations. The origins of the general group typology used by adults thus appear early in development. These findings contribute to our knowledge about children's intuitive understanding of groups and group members' behavior.
Effectiveness of Group Supervision versus Combined Group and Individual Supervision.
Ray, Dee; Altekruse, Michael
2000-01-01
Investigates the effectiveness of different types of supervision (large group, small group, combined group, individual supervision) with counseling students (N=64). Analyses revealed that all supervision formats resulted in similar progress in counselor effectiveness and counselor development. Participants voiced a preference for individual…
Group Insight Versus Group Desensitization in Treating Speech Anxiety
Meichenbaum, Donald H.; And Others
1971-01-01
Results of this study indicated that the insight group was as effective as the desensitization group in significantly reducing speech anxiety over control group levels as assessed by behavioral, cognitive, and self-report measures given immediately after posttreatment and later at a three-month follow-up. (Author)
Re-Examining Group Development in Adventure Therapy Groups.
DeGraaf, Don; Ashby, Jeff
1998-01-01
Small-group development is an important aspect of adventure therapy. Supplementing knowledge of sequential stages of group development with knowledge concerning within-stage nonsequential development yields a richer understanding of groups. Integrating elements of the individual counseling relationship (working alliance, transference, and real…
Saving Face and Group Identity
DEFF Research Database (Denmark)
Eriksson, Tor; Mao, Lei; Villeval, Marie-Claire
2015-01-01
their self- but also other group members' image. This behavior is frequent even in the absence of group identity. When group identity is more salient, individuals help regardless of whether the least performer is an in-group or an out-group. This suggests that saving others' face is a strong social norm.......Are people willing to sacrifice resources to save one's and others' face? In a laboratory experiment, we study whether individuals forego resources to avoid the public exposure of the least performer in their group. We show that a majority of individuals are willing to pay to preserve not only...
Enhancing Social Communication Between Groups
T. Stevens; P. Hughes (Peter); D. Williams; I. Craigie; I. Kegel; P.S. Cesar Garcia (Pablo Santiago); A.J. Jansen (Jack); M.F. Usrsu; M. Frantzis; N. Farber; M. Lutzky; S. Vogel
2010-01-01
htmlabstractThis paper describes a prototype software platform that supports advanced communications services, specifically services enabling effective group-to-group communications with a social purpose, between remote homes. The architecture, the individual components, their interfaces, and the
Coordinated Control of Vehicle Groups
National Research Council Canada - National Science Library
Kumar, Vijay
2004-01-01
.... There are three main objectives: (1) to develop a theoretical paradigm for formalizing the concepts of a group, a team, and control of groups, with specified tasks such as exploring, mapping, searching, and transporting objects; (2...
Criminal groups and criminal subculture
Romanova N.M.
2013-01-01
The paper provides a classification of criminal groups, structured by the following parameters: a) operation mode (secret/open), b) law-enforcement and administrative support (presence/absence). We describe four types of criminal groups: a) legitimized criminal organization, b) secret criminal organization engaged in illegal business, c) secret general crime group, and d) general crime group operating openly. The four types differ in the content of criminal subculture. Modern criminal subcult...
Group Cooperation in Outdoor Education
Matthews, Bruce E.
1978-01-01
Utilizing the Beatles' Yellow Submarine fantasy (e.g., the Blue Meanies), this outdoor education program is designed for sixth graders and special education students. Activities developed at the Cortland Resident Outdoor Education Camp include a series of group stress/challenge activities to be accomplished by everyone in the group, as a group.…
Reinterpreting between-group inequality
Elbers, C.T.M.; Lanjouw, P.F.; Mistiaen, J.; Özler, B
2008-01-01
We evaluate observed inequality between population groups against a benchmark of the maximum between-group inequality attainable given the number and relative sizes of those groups under examination. Because our measure is normalized by these parameters, drawing comparisons across different settings
Ability Grouping in Social Studies.
Social Education, 1992
1992-01-01
Presents a position statement of the National Council for the Social Studies (NCSS). Reports that the NCSS objects to ability grouping in social studies. Argues that ability grouping disadvantages minority, handicapped, and low ability students. Suggests that ability grouping undermines the democratic ideals that should be the basis of the social…