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.
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 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)
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.)
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.
Symplectic invariants of some families of Lagrangian T3-fibrations
International Nuclear Information System (INIS)
Castano Bernard, R.
2003-12-01
We construct families of Lagrangian 3-torus fibrations resembling the topology of some of the singularities in Topological Mirror Symmetry. We perform a detailed analysis of the affine structure on the base of these fibrations near their discriminant loci. This permits us to classify the aforementioned families up to fibre preserving symplectomorphism. The kind of degenerations we investigate give rise to a large number of symplectic invariants. (author)
Fast symplectic 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
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)
Conformal invariance and pion wave functions of nonleading twist
International Nuclear Information System (INIS)
Braun, V.M.; Filyanov, I.E.
1989-01-01
The restrictions are studied for the general structure of pion wave functions of twist 3 and twist 4 imposed by the conformal symmetry and the equations of motion. A systematic expansion of wave functions in the conformal spin is built and the first order corrections to asymptotic formulae are calculated by the QCD sum rule method. In particular, we have found a multiplicatively renormalizable contribution into the two-particle wave function of twist 4 which cannot be expanded in a finite set of Gegenbauer polynomials. 19 refs.; 5 figs
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....
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
Twisted Poincare invariance, noncommutative gauge theories and UV-IR mixing
Energy Technology Data Exchange (ETDEWEB)
Balachandran, A.P. [Department of Physics, Syracuse University, Syracuse NY, 13244-1130 (United States)], E-mail: bal@physics.syr.edu; Pinzul, A. [Insituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, SP (Brazil)], E-mail: apinzul@fma.if.usp.br; Queiroz, A.R. [Centro Internacional de Fisica da Materia Condensada, Universidade de Brasilia, C.P. 04667, Brasilia, DF (Brazil); Universidade Federal de Goias, Campus Avancado de Catalao, Departamento de Fisica, St. Universitario - 75700-000, Catalao-GO (Brazil)], E-mail: amilcarq@gmail.com
2008-10-09
In the absence of gauge fields, quantum field theories on the Groenewold-Moyal (GM) plane are invariant under a twisted action of the Poincare group if they are formulated following [M. Chaichian, P.P. Kulish, K. Nishijima, A. Tureanu, Phys. Lett. B 604 (2004) 98, (hep-th/0408069); P. Aschieri, C. Blohmann, M. Dimitrijevic, F. Meyer, P. Schupp, J. Wess, Class. Quantum Grav. 22 (2005) 3511, (hep-th/0504183); A.P. Balachandran, A. Pinzul, B.A. Qureshi, S. Vaidya, (hep-th/0608138); A.P. Balachandran, A. Pinzul, B.A. Qureshi, S. Vaidya, (arXiv: 0708.0069 [hep-th]); A.P. Balachandran, A. Pinzul, B.A. Qureshi, S. Vaidya, (arXiv: 0708.1379 [hep-th]); A.P. Balachandran, A. Pinzul, B.A. Qureshi, (arXiv: 0708.1779 [hep-th])]. In that formulation, such theories also have no UV-IR mixing [A.P. Balachandran, A. Pinzul, B.A. Qureshi, Phys. Lett. B 634 (2006) 434, (hep-th/0508151)]. Here we investigate UV-IR mixing in gauge theories with matter following the approach of [A.P. Balachandran, A. Pinzul, B. A. Qureshi, S. Vaidya, (hep-th/0608138); A.P. Balachandran, A. Pinzul, B.A. Qureshi, S. Vaidya, (arXiv: 0708.0069 [hep-th])]. We prove that there is UV-IR mixing in the one-loop diagram of the S-matrix involving a coupling between gauge and matter fields on the GM plane, the gauge field being non-Abelian. There is no UV-IR mixing if it is Abelian.
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
Obstructions for twist star products
Bieliavsky, Pierre; Esposito, Chiara; Waldmann, Stefan; Weber, Thomas
2018-05-01
In this short note, we point out that not every star product is induced by a Drinfel'd twist by showing that not every Poisson structure is induced by a classical r-matrix. Examples include the higher genus symplectic Pretzel surfaces and the symplectic sphere S^2.
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...
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
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.
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...
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...
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.)
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
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.
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)
Generalised twisted partition functions
Petkova, V B
2001-01-01
We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D Conformal Field Theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT.
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.
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
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.
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.
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.)
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
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...
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.
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
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...
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.
DEFF Research Database (Denmark)
Randrup, Thomas; Røgen, Peter
1997-01-01
is an invariant of ambient isotopy measuring the topological twist of the closed strip. We classify closed strips in euclidean 3-space by their knots and their twisting number. We prove that this classification exactly divides closed strips into isotopy classes. Using this classification we point out how some...
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.
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)].
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
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.
CSIR Research Space (South Africa)
Forbes, A
2010-12-01
Full Text Available Research at the Mathematical Optics Group uses "twisted" light to study new quatum-based information security systems. In order to understand the structure of "twisted" light, it is useful to start with an ordinary light beam with zero twist, namely...
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.
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...
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)
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.
Noncommutative geometry and twisted conformal symmetry
International Nuclear Information System (INIS)
Matlock, Peter
2005-01-01
The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted coproduct. This allows for the definition of conformal symmetry in a noncommutative background geometry. The twisted coproduct is reviewed for the Poincare algebra and the construction is then extended to the full conformal algebra. The case of Moyal-type noncommutativity of the coordinates is considered. It is demonstrated that conformal invariance need not be viewed as incompatible with noncommutative geometry; the noncommutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincare algebra
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
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-12-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
International Nuclear Information System (INIS)
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-01-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
Energy Technology Data Exchange (ETDEWEB)
Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)
2012-12-15
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
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)
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
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
DVCS amplitude with kinematical twist-3 terms
International Nuclear Information System (INIS)
Radyushkin, A.V.; Weiss, C.
2000-01-01
The authors compute the amplitude of deeply virtual Compton scattering (DVCS) using the calculus of QCD string operators in coordinate representation. To restore the electromagnetic gauge invariance (transversality) of the twist-2 amplitude they include the operators of twist-3 which appear as total derivatives of twist-2 operators. The results are equivalent to a Wandzura-Wilczek approximation for twist-3 skewed parton distributions. They find that this approximation gives a finite result for the amplitude of a longitudinally polarized virtual photon, while the amplitude for transverse polarization is divergent, i.e., factorization breaks down in this term
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...
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.
Larocque, Hugo; Kaminer, Ido; Grillo, Vincenzo; Leuchs, Gerd; Padgett, Miles J.; Boyd, Robert W.; Segev, Mordechai; Karimi, Ebrahim
2018-04-01
Electrons have played a significant role in the development of many fields of physics during the last century. The interest surrounding them mostly involved their wave-like features prescribed by the quantum theory. In particular, these features correctly predict the behaviour of electrons in various physical systems including atoms, molecules, solid-state materials, and even in free space. Ten years ago, new breakthroughs were made, arising from the new ability to bestow orbital angular momentum (OAM) to the wave function of electrons. This quantity, in conjunction with the electron's charge, results in an additional magnetic property. Owing to these features, OAM-carrying, or twisted, electrons can effectively interact with magnetic fields in unprecedented ways and have motivated materials scientists to find new methods for generating twisted electrons and measuring their OAM content. Here, we provide an overview of such techniques along with an introduction to the exciting dynamics of twisted electrons.
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.
Dickens, Charles
2005-01-01
Oliver Twist is one of Dickens's most popular novels, with many famous film, television and musical adaptations. It is a classic story of good against evil, packed with humour and pathos, drama and suspense, in which the orphaned Oliver is brought up in a harsh workhouse, and then taken in and
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
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
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)
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
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)
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.
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
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
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)
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
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...
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.
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
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.
Twisted supersymmetry: Twisted symmetry versus renormalizability
International Nuclear Information System (INIS)
Dimitrijevic, Marija; Nikolic, Biljana; Radovanovic, Voja
2011-01-01
We discuss a deformation of superspace based on a Hermitian twist. The twist implies a *-product that is noncommutative, Hermitian and finite when expanded in a power series of the deformation parameter. The Leibniz rule for the twisted supersymmetry transformations is deformed. A minimal deformation of the Wess-Zumino action is proposed and its renormalizability properties are discussed. There is no tadpole contribution, but the two-point function diverges. We speculate that the deformed Leibniz rule, or more generally the twisted symmetry, interferes with renormalizability properties of the model. We discuss different possibilities to render a renormalizable model.
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.
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
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 ...
Casali, Eduardo; Tourkine, Piotr
2018-03-01
Twistor string models have been known for more than a decade now but have come back under the spotlight recently with the advent of the scattering equation formalism which has greatly generalized the scope of these models. A striking ubiquitous feature of these models has always been that, contrary to usual string theory, they do not admit vibrational modes and thus describe only conventional field theory. In this paper we report on the surprising discovery of a whole new sector of one of these theories which we call "twisted strings," when spacetime has compact directions. We find that the spectrum is enhanced from a finite number of states to an infinite number of interacting higher spin massive states. We describe both bosonic and world sheet supersymmetric models, their spectra and scattering amplitudes. These models have distinctive features of both string and field theory, for example they are invariant under stringy T-duality but have the high energy behavior typical of field theory. Therefore they describe a new kind of field theories in target space, sitting on their own halfway between string and field theory.
Hitchin's connection, Toeplitz operators, and symmetry invariant deformation quantization
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard
2012-01-01
We introduce the notion of a rigid family of Kähler structures on a symplectic manifold. We then prove that a Hitchin connection exists for any rigid holomorphic family of Kähler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints...... a mapping class group invariant formal quantization of the smooth symplectic leaves of the moduli space of flat SU(n)-connections on any compact surface....... quantization. Finally, these results are applied to the moduli space situation in which Hitchin originally constructed his connection. First we get a proof that the Hitchin connection in this case is the same as the connection constructed by Axelrod, Della Pietra, and Witten. Second we obtain in this way...
Radjavi, Heydar
2003-01-01
This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces,
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...
Leibniz algebroids, twistings and exceptional generalized geometry
Baraglia, David
2011-01-01
We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a construction starting from graded Lie algebras. In this case the Leibniz bracket is a derived bracket and there are higher derived brackets resulting in an $L_\\infty$-structure. The algebroids can be twisted by a non-abelian cohomology class and we prove that the twis...
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.
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....
Twisted network programming essentials
Fettig, Abe
2005-01-01
Twisted Network Programming Essentials from O'Reilly is a task-oriented look at this new open source, Python-based technology. The book begins with recommendations for various plug-ins and add-ons to enhance the basic package as installed. It then details Twisted's collection simple network protocols, and helper utilities. The book also includes projects that let you try out the Twisted framework for yourself. For example, you'll find examples of using Twisted to build web services applications using the REST architecture, using XML-RPC, and using SOAP. Written for developers who want to s
Twisted entire cyclic cohomology, J-L-O cocycles and equivariant spectral triples
International Nuclear Information System (INIS)
Goswami, D.
2002-07-01
We study the 'quantized calculus' corresponding to the algebraic ideas related to 'twisted cyclic cohomology'. With very similar definitions and techniques, we define and study 'twisted entire cyclic cohomology' and the 'twisted Chern character' associated with an appropriate operator theoretic data called 'twisted spectral data', which consists of a spectral triple in the conventional sense of noncommutative geometry and an additional positive operator having some specified properties. Furthermore, it is shown that given a spectral triple (in the conventional sense) which is equivariant under the action of a compact matrix pseudogroup, it is possible to obtain a canonical twisted spectral data and hence the corresponding (twisted) Chern character, which will be invariant under the action of the pseudogroup, in contrast to the fact that the Chern character coming from the conventional noncommutative geometry need not be invariant under the above action. (author)
Invariant subspaces in some function spaces on symmetric spaces. II
International Nuclear Information System (INIS)
Platonov, S S
1998-01-01
Let G be a semisimple connected Lie group with finite centre, K a maximal compact subgroup of G, and M=G/K a Riemannian symmetric space of non-compact type. We study the problem of describing the structure of closed linear subspaces in various function spaces on M that are invariant under the quasiregular representation of the group G. We consider the case when M is a symplectic symmetric space of rank 1
Exterior difference systems and invariance properties of discrete mechanics
International Nuclear Information System (INIS)
Xie Zheng; Xie Duanqiang; Li Hongbo
2008-01-01
Invariance properties describe the fundamental physical laws in discrete mechanics. Can those properties be described in a geometric way? We investigate an exterior difference system called the discrete Euler-Lagrange system, whose solution has one-to-one correspondence with solutions of discrete Euler-Lagrange equations, and use it to define the first integrals. The preservation of the discrete symplectic form along the discrete Hamilton phase flows and the discrete Noether's theorem is also described in the language of difference forms
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".
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.
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.
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.
International Nuclear Information System (INIS)
Mackrodt, C.; Reeh, H.
1997-01-01
General summational invariants, i.e., conservation laws acting additively on asymptotic particle states, are investigated within a classical framework for point particles with nontrivial scattering. copyright 1997 American Institute of Physics
Twisted classical Poincare algebras
International Nuclear Information System (INIS)
Lukierski, J.; Ruegg, H.; Tolstoy, V.N.; Nowicki, A.
1993-11-01
We consider the twisting of Hopf structure for classical enveloping algebra U(g), where g is the inhomogeneous rotations algebra, with explicite formulae given for D=4 Poincare algebra (g=P 4 ). The comultiplications of twisted U F (P 4 ) are obtained by conjugating primitive classical coproducts by F element of U(c)xU(c), where c denotes any Abelian subalgebra of P 4 , and the universal R-matrices for U F (P 4 ) are triangular. As an example we show that the quantum deformation of Poincare algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincare algebra. The interpretation of twisted Poincare algebra as describing relativistic symmetries with clustered 2-particle states is proposed. (orig.)
Leibniz algebroids, twistings and exceptional generalized geometry
Baraglia, D.
2012-05-01
We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a construction starting from graded Lie algebras. In this case the Leibniz bracket is a derived bracket and there are higher derived brackets resulting in an L∞-structure. The algebroids can be twisted by a non-abelian cohomology class and we prove that the twisting class is described by a Maurer-Cartan equation. For compact manifolds we construct a Kuranishi moduli space of this equation which is shown to be affine algebraic. We explain how these results are related to exceptional generalized geometry.
Energy Technology Data Exchange (ETDEWEB)
Villalobos Baillie, Orlando
1988-12-15
In the quantum chromodynamics (QCD) candidate theory of interquark forces, calculations involve summing the effects from many different possible quark/gluon interactions. In addition to the 'leading term' frequently used as the basis for QCD calculations, additional contributions — so-called 'higher twists' — are modulated by powers of kinematical factors. An illuminating international workshop to discuss higher twist QCD was held at the College de France, Paris, from 21-23 September.
Twisted boundary states in c=1 coset conformal field theories
International Nuclear Information System (INIS)
Ishikawa, Hiroshi; Yamaguchi, Atsushi
2003-01-01
We study the mutual consistency of twisted boundary conditions in the coset conformal field theory G/H. We calculate the overlap of the twisted boundary states of G/H with the untwisted ones, and show that the twisted boundary states are consistently defined in the charge-conjugation modular invariant. The overlap of the twisted boundary states is expressed by the branching functions of a twisted affine Lie algebra. As a check of our argument, we study the diagonal coset theory so(2n) 1 +so(2n) 1 /so(2n) 2 , which is equivalent to the orbifold S 1 /Z 2 at a particular radius. We construct the boundary states twisted by the automorphisms of the unextended Dynkin diagram of so(2n), and show their mutual consistency by identifying their counterpart in the orbifold. For the triality of so(8), the twisted states of the coset theory correspond to neither the Neumann nor the Dirichlet boundary states of the orbifold and yield conformal boundary states that preserve only the Virasoro algebra. (author)
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.
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.
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.
SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry
Baulieu, Laurent
2011-01-01
The N=1,d=10 superYang-Mills action is constructed in a twisted form, using SU(5)-invariant decomposition of spinors in 10 dimensions. The action and its off-shell closed twisted scalar supersymmetry operator Q derive from a Chern-Simons term. The action can be decomposed as the sum of a term in the cohomology of Q and of a term that is Q-exact. The first term is a fermionic Chern-Simons term for a twisted component of the Majorana-Weyl gluino and it is related to the second one by a twisted vector supersymmetry with 5 parameters. The cohomology of Q and some topological observables are defined from descent equations. In this SU(5)
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.
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.)
A Transformation Called "Twist"
Hwang, Daniel
2010-01-01
The transformations found in secondary mathematics curriculum are typically limited to stretches and translations (e.g., ACARA, 2010). Advanced students may find the transformation, twist, to be of further interest. As most available resources are written for professional-level readers, this article is intended to be an introduction accessible to…
DEFF Research Database (Denmark)
Yiu, Man Lung; Jensen, Christian Søndergaard; Xuegang, Huang
2008-01-01
-based matching generally fall short in offering practical query accuracy guarantees. Our proposed framework, called SpaceTwist, rectifies these shortcomings for k nearest neighbor (kNN) queries. Starting with a location different from the user's actual location, nearest neighbors are retrieved incrementally...
Arutyunov, G.E.; de Leeuw, M.; van Tongeren, S.J.
2010-01-01
We study finite-size corrections to the magnon dispersion relation in three models which differ from string theory on AdS5 x S5 in their boundary conditions. Asymptotically, this is accomplished by twisting the transfer matrix in a way which manifestly preserves integrability. In model I all
Perturbative string theory in BRST invariant formalism
International Nuclear Information System (INIS)
Di Vecchia, P.; Hornfeck, K.; Frau, M.; Lerda, A.
1988-01-01
In this talk we present a constructive and very explicit way of calculating multiloop amplitudes in string theories. The main ingredients are the BRST invariant N String Vertex and the BRST invariant twisted propagator. This approach naturally leads to the Schottky parametrization of moduli space in terms of multipliers and fixed points of the g projective transformations which characterize a Riemann surface of genus g. The complete expression (including measure) of the multiloop corrections to the N String Vertex for the bosonic string is exhibited. (orig.)
Link invariant and $G_2$ web space
Sakamoto, Takuro; Yonezawa, Yasuyoshi
2017-01-01
In this paper, we reconstruct Kuperberg’s $G_2$ web space [5, 6]. We introduce a new web diagram (a trivalent graph with only double edges) and new relations between Kuperberg’s web diagrams and the new web diagram. Using the web diagrams, we give crossing formulas for the $R$-matrices associated to some irreducible representations of $U_q(G_2)$ and calculate $G_2$ quantum link invariants for generalized twist links.
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 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.
Iterative methods for overlap and twisted mass fermions
International Nuclear Information System (INIS)
Chiarappa, T.; Jansen, K.; Shindler, A.; Wetzorke, I.; Scorzato, L.; Urbach, C.; Wenger, U.
2006-09-01
We present a comparison of a number of iterative solvers of linear systems of equations for obtaining the fermion propagator in lattice QCD. In particular, we consider chirally invariant overlap and chirally improved Wilson (maximally) twisted mass fermions. The comparison of both formulations of lattice QCD is performed at four fixed values of the pion mass between 230 MeV and 720 MeV. For overlap fermions we address adaptive precision and low mode preconditioning while for twisted mass fermions we discuss even/odd preconditioning. Taking the best available algorithms in each case we find that calculations with the overlap operator are by a factor of 30-120 more expensive than with the twisted mass operator. (orig.)
Iterative methods for overlap and twisted mass fermions
Energy Technology Data Exchange (ETDEWEB)
Chiarappa, T. [Univ. di Milano Bicocca (Italy); Jansen, K.; Shindler, A.; Wetzorke, I. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Nagai, K.I. [Wuppertal Univ. (Gesamthochschule) (Germany). Fachbereich Physik; Papinutto, M. [INFN Sezione di Roma Tre, Rome (Italy); Scorzato, L. [European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), Villazzano (Italy); Urbach, C. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Wenger, U. [ETH Zuerich (Switzerland). Inst. fuer Theoretische Physik
2006-09-15
We present a comparison of a number of iterative solvers of linear systems of equations for obtaining the fermion propagator in lattice QCD. In particular, we consider chirally invariant overlap and chirally improved Wilson (maximally) twisted mass fermions. The comparison of both formulations of lattice QCD is performed at four fixed values of the pion mass between 230 MeV and 720 MeV. For overlap fermions we address adaptive precision and low mode preconditioning while for twisted mass fermions we discuss even/odd preconditioning. Taking the best available algorithms in each case we find that calculations with the overlap operator are by a factor of 30-120 more expensive than with the twisted mass operator. (orig.)
Directory of Open Access Journals (Sweden)
Daijiro Fukuda
2004-01-01
Full Text Available Using diagrammatic pictures of tensor contractions, we consider a Hopf algebra (Aop⊗ℛλA** twisted by an element ℛλ∈A*⊗Aop corresponding to a Hopf algebra morphism λ:A→A. We show that this Hopf algebra is quasitriangular with the universal R-matrix coming from ℛλ when λ2=idA, generalizing the quantum double construction which corresponds to the case λ=idA.
One-dimensional structures behind twisted and untwisted superYang-Mills theory
Baulieu, Laurent
2011-01-01
We give a one-dimensional interpretation of the four-dimensional twisted N=1 superYang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N=1 superYang-Mills theory.
On the description of exclusive processes beyond the leading twist approximation
International Nuclear Information System (INIS)
Anikin, I.V.; Ivanov, D.Yu.; Pire, B.; Szymanowski, L.; Wallon, S.
2010-01-01
We describe hard exclusive processes beyond the leading twist approximation in a framework based on the Taylor expansion of the amplitude around the dominant light-cone directions. This naturally introduces an appropriate set of non-perturbative correlators whose number is minimalized after taking into account QCD equations of motion and the invariance under rotation on the light-cone. We exemplify this method at the twist 3 level and show that the coordinate and momentum space descriptions are fully equivalent.
On the description of exclusive processes beyond the leading twist approximation
Energy Technology Data Exchange (ETDEWEB)
Anikin, I.V. [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation); Ivanov, D.Yu. [Institute of Mathematics, 630090 Novosibirsk (Russian Federation); Pire, B., E-mail: pire@cpht.polytechnique.f [CPhT, Ecole Polytechnique, CNRS, F-91128 Palaiseau (France); Szymanowski, L. [Soltan Institute for Nuclear Studies, Hoza 69, 00-681 Warsaw (Poland); Wallon, S. [LPT, Universite d' Orsay, CNRS, 91404 Orsay (France); UPMC Univ. Paris 6, Faculte de Physique, 4 place Jussieu, 75252 Paris Cedex 05 (France)
2010-01-04
We describe hard exclusive processes beyond the leading twist approximation in a framework based on the Taylor expansion of the amplitude around the dominant light-cone directions. This naturally introduces an appropriate set of non-perturbative correlators whose number is minimalized after taking into account QCD equations of motion and the invariance under rotation on the light-cone. We exemplify this method at the twist 3 level and show that the coordinate and momentum space descriptions are fully equivalent.
One-dimensional structures behind twisted and untwisted super Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Baulieu, Laurent [CERN, Geneve (Switzerland). Theoretical Div.; Toppan, Francesco, E-mail: baulieu@lpthe.jussieu.f, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
2010-07-01
We give a one-dimensional interpretation of the four-dimensional twisted N = 1 super Yang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N = 1 super Yang-Mills theory. (author)
One-dimensional structures behind twisted and untwisted super Yang-Mills theory
International Nuclear Information System (INIS)
Baulieu, Laurent
2010-01-01
We give a one-dimensional interpretation of the four-dimensional twisted N = 1 super Yang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N = 1 super Yang-Mills theory. (author)
Directory of Open Access Journals (Sweden)
Yuji Koike
2016-08-01
Full Text Available We compute the contribution from the longitudinally polarized proton to the twist-3 double-spin asymmetry ALT in inclusive (light hadron production from proton–proton collisions, i.e., p↑p→→hX. We show that using the relevant QCD equation-of-motion relation and Lorentz invariance relation allows one to eliminate the twist-3 quark-gluon correlator (associated with the longitudinally polarized proton in favor of one-variable twist-3 quark distributions and the (twist-2 transversity parton density. Including this result with the twist-3 pieces associated with the transversely polarized proton and unpolarized final-state hadron (which have already been calculated in the literature, we now have the complete leading-order cross section for this process.
The Twist Tensor Nuclear Norm for Video Completion.
Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui
2017-12-01
In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.
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.
International Nuclear Information System (INIS)
Shindler, A.
2007-07-01
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Shindler, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2007-07-15
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
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.
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)
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
Twist limits for late twisting double somersaults on trampoline.
Yeadon, M R; Hiley, M J
2017-06-14
An angle-driven computer simulation model of aerial movement was used to determine the maximum amount of twist that could be produced in the second somersault of a double somersault on trampoline using asymmetrical movements of the arms and hips. Lower bounds were placed on the durations of arm and hip angle changes based on performances of a world trampoline champion whose inertia parameters were used in the simulations. The limiting movements were identified as the largest possible odd number of half twists for forward somersaulting takeoffs and even number of half twists for backward takeoffs. Simulations of these two limiting movements were found using simulated annealing optimisation to produce the required amounts of somersault, tilt and twist at landing after a flight time of 2.0s. Additional optimisations were then run to seek solutions with the arms less adducted during the twisting phase. It was found that 3½ twists could be produced in the second somersault of a forward piked double somersault with arms abducted 8° from full adduction during the twisting phase and that three twists could be produced in the second somersault of a backward straight double somersault with arms fully adducted to the body. These two movements are at the limits of performance for elite trampolinists. Copyright © 2017 Elsevier Ltd. All rights reserved.
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.
TEK twisted gradient flow running coupling
Pérez, Margarita García; Keegan, Liam; Okawa, Masanori
2014-01-01
We measure the running of the twisted gradient flow coupling in the Twisted Eguchi-Kawai (TEK) model, the SU(N) gauge theory on a single site lattice with twisted boundary conditions in the large N limit.
Teaching Spatial Awareness for Better Twisting Somersaults.
Hennessy, Jeff T.
1985-01-01
The barani (front somersault with one-half twist) and the back somersault with one twist are basic foundation skills necessary for more advanced twisting maneuvers. Descriptions of these movements on a trampoline surface are offered. (DF)
Twisting perturbed parafermions
Directory of Open Access Journals (Sweden)
A.V. Belitsky
2017-07-01
Full Text Available The near-collinear expansion of scattering amplitudes in maximally supersymmetric Yang–Mills theory at strong coupling is governed by the dynamics of stings propagating on the five sphere. The pentagon transitions in the operator product expansion which systematize the series get reformulated in terms of matrix elements of branch-point twist operators in the two-dimensional O(6 nonlinear sigma model. The facts that the latter is an asymptotically free field theory and that there exists no local realization of twist fields prevents one from explicit calculation of their scaling dimensions and operator product expansion coefficients. This complication is bypassed making use of the equivalence of the sigma model to the infinite-level limit of WZNW models perturbed by current–current interactions, such that one can use conformal symmetry and conformal perturbation theory for systematic calculations. Presently, to set up the formalism, we consider the O(3 sigma model which is reformulated as perturbed parafermions.
Twisted boundary states and representation of generalized fusion algebra
International Nuclear Information System (INIS)
Ishikawa, Hiroshi; Tani, Taro
2006-01-01
The mutual consistency of boundary conditions twisted by an automorphism group G of the chiral algebra is studied for general modular invariants of rational conformal field theories. We show that a consistent set of twisted boundary states associated with any modular invariant realizes a non-negative integer matrix representation (NIM-rep) of the generalized fusion algebra, an extension of the fusion algebra by representations of the twisted chiral algebra associated with the automorphism group G. We check this result for several concrete cases. In particular, we find that two NIM-reps of the fusion algebra for su(3) k (k=3,5) are organized into a NIM-rep of the generalized fusion algebra for the charge-conjugation automorphism of su(3) k . We point out that the generalized fusion algebra is non-commutative if G is non-Abelian and provide some examples for G-bar S 3 . Finally, we give an argument that the graph fusion algebra associated with simple current extensions coincides with the generalized fusion algebra for the extended chiral algebra, and thereby explain that the graph fusion algebra contains the fusion algebra of the extended theory as a subalgebra
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.
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.
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)
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
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
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,...
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
Partial twisting for scalar mesons
International Nuclear Information System (INIS)
Agadjanov, Dimitri; Meißner, Ulf-G.; Rusetsky, Akaki
2014-01-01
The possibility of imposing partially twisted boundary conditions is investigated for the scalar sector of lattice QCD. According to the commonly shared belief, the presence of quark-antiquark annihilation diagrams in the intermediate state generally hinders the use of the partial twisting. Using effective field theory techniques in a finite volume, and studying the scalar sector of QCD with total isospin I=1, we however demonstrate that partial twisting can still be performed, despite the fact that annihilation diagrams are present. The reason for this are delicate cancellations, which emerge due to the graded symmetry in partially quenched QCD with valence, sea and ghost quarks. The modified Lüscher equation in case of partial twisting is given
Thathia, Shabnam H.; Ferguson, Stuart; Gautrey, Hannah E.; van Otterdijk, Sanne D.; Hili, Michela; Rand, Vikki; Moorman, Anthony V.; Meyer, Stefan; Brown, Robert; Strathdee, Gordon
2012-01-01
Background Altered regulation of many transcription factors has been shown to be important in the development of leukemia. TWIST2 modulates the activity of a number of important transcription factors and is known to be a regulator of hematopoietic differentiation. Here, we investigated the significance of epigenetic regulation of TWIST2 in the control of cell growth and survival and in response to cytotoxic agents in acute lymphoblastic leukemia. Design and Methods TWIST2 promoter methylation status was assessed quantitatively, by combined bisulfite and restriction analysis (COBRA) and pyrosequencing assays, in multiple types of leukemia and TWIST2 expression was determined by quantitative reverse transcriptase polymerase chain reaction analysis. The functional role of TWIST2 in cell proliferation, survival and response to chemotherapy was assessed in transient and stable expression systems. Results We found that TWIST2 was inactivated in more than 50% of cases of childhood and adult acute lymphoblastic leukemia through promoter hypermethylation and that this epigenetic regulation was especially prevalent in RUNX1-ETV6-driven cases. Re-expression of TWIST2 in cell lines resulted in a dramatic reduction in cell growth and induction of apoptosis in the Reh cell line. Furthermore, re-expression of TWIST2 resulted in increased sensitivity to the chemotherapeutic agents etoposide, daunorubicin and dexamethasone and TWIST2 hypermethylation was almost invariably found in relapsed adult acute lymphoblastic leukemia (91% of samples hypermethylated). Conclusions This study suggests a dual role for epigenetic inactivation of TWIST2 in acute lymphoblastic leukemia, initially through altering cell growth and survival properties and subsequently by increasing resistance to chemotherapy. PMID:22058208
Photophysics of internal twisting
International Nuclear Information System (INIS)
Heisel, F.; Miehe, J.A.; Lippert, E.; Rettig, W.; Bonacic-Koutecky, V.
1987-01-01
The formation and characteristics of the ''twisted intermolecular charge transfer'' is studied. Basic concepts on dual fluorescence, steady-state fluorescence, kinetic investigations and cage effects are discussed. The theoretical treatment on the electronic structure of the bonded π - donor - π acceptor pairs is outlined. The two-electron, two-orbital model, the ab initio CI models of simple double, charged and dative π - bonds as well as complex dative π - bonds and the origin of the dual fluorescence of 9.9'-Bianthryl are shown. Concerning the stochastic description of chemical reactions, Master equation, Markov, Birth-Death and Diffusion processes, Kramers-Moyal expansion, Langevin equation, Kramers' approach to steady-state rates of reaction and its extension to non-Markovian processes, and also unimolecular reactions in the absence of potential barrier are considered. Experimental results and interpretation on dynamics of DMABN in the excited state, kinetics of other dialkylanilines, extended donor-acceptor systems with anomalous fluorescence and donor-acceptor systems without anomalous fluorescence are given
Energy Technology Data Exchange (ETDEWEB)
Szymanowski, Lech [Soltan Institute for Nuclear Studies, Hoza 69, 00691, Warsaw (Poland); Anikin, Igor V. [Joint Institute for Nuclear Research - JINR, Joliot-Curie st., 6, Moskovskaya obl., 141980, Dubna (Russian Federation); Ivanov, Dmitry Yu [Sobolev Institute of Mathematics, Acad. Koptyug pr., 4, 630090 Novosibirsk (Russian Federation); Pire, Bernard [Centre de Physique Theorique - CPHT, UMR 7644, Ecole Polytechnique, Bat. 6, RDC, F91128 Palaiseau Cedex (France); Wallon, Samuel [Laboratoire de Physique Theorique d' Orsay - LPT, Bat. 210, Univ. Paris-Sud 11, 91405 Orsay Cedex (France)
2010-07-01
We describe a consistent approach to factorization of scattering amplitudes for exclusive processes beyond the leading twist approximation. The method is based on the Taylor expansion of the scattering amplitude in the momentum space around the dominant light-cone direction and thus naturally introduces an appropriate set of non-perturbative correlators which encode effects not only of the lowest but also of the higher Fock states of the produced particle. The reduction of original set of correlators to a set of independent ones is achieved with the help of equations of motion and invariance of the scattering amplitude under rotation on the light-cone. As a concrete application, we compute the expressions of the impact factor for the transition of virtual photon to transversally polarised {rho}-meson up to the twist 3 accuracy. (Phys.Lett.B682:413-418,2010 and Nucl.Phys.B828:1-68,2010.). (authors)
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.
Energy Technology Data Exchange (ETDEWEB)
Olver, Peter J [School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (United States)], E-mail: olver@math.umn.edu
2008-08-29
Given a Lie group acting on a manifold, our aim is to analyze the evolution of differential invariants under invariant submanifold flows. The constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex. Applications to integrable soliton dynamics, and to the evolution of differential invariant signatures, used in equivalence problems and object recognition and symmetry detection in images, are discussed.
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.
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)
Rotationally invariant correlation filtering
International Nuclear Information System (INIS)
Schils, G.F.; Sweeney, D.W.
1985-01-01
A method is presented for analyzing and designing optical correlation filters that have tailored rotational invariance properties. The concept of a correlation of an image with a rotation of itself is introduced. A unified theory of rotation-invariant filtering is then formulated. The unified approach describes matched filters (with no rotation invariance) and circular-harmonic filters (with full rotation invariance) as special cases. The continuum of intermediate cases is described in terms of a cyclic convolution operation over angle. The angular filtering approach allows an exact choice for the continuous trade-off between loss of the correlation energy (or specificity regarding the image) and the amount of rotational invariance desired
Computational invariant theory
Derksen, Harm
2015-01-01
This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...
International Nuclear Information System (INIS)
Ketov, S.V.; Lechtenfeld, O.; Parkes, A.J.
1993-12-01
The most general homogeneous monodromy conditions in N= 2 string theory are classified in terms of the conjugacy classes of the global symmetry group U(1, 1) x Z 2 . For classes which generate a discrete subgroup Γ, the corresponding target space backgrounds C 1,1 /Γ include half spaces, complex orbifolds and tori. We propose a generalization of the intercept formula to matrix-valued twists, and find massless physical states in a number of twisted cases. In particular, the sixteen Z 2 -twisted sectors of the N = 2 string are investigated, and the corresponding ground states are identified via bosonization and BRST cohomology. We find enough room for an extended multiplet of 'spacetime' supersymmetry, with the number of supersymmetries being dependent on global 'spacetime' topology. Unfortunately, world-sheet locality for the chiral vertex operators does not permit interactions for the massless 'spacetime' fermions; however possibly, an asymmetric GSO projection could evade this problem. (orig.)
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
Introduction to twisted conformal fields
International Nuclear Information System (INIS)
Kazama, Y.
1988-01-01
A pedagogical account is given of the recent developments in the theory of twisted conformal fields. Among other things, the main part of the lecture concerns the construction of the twist-emission vertex operator, which is a generalization of the fermion emission vertex in the superstring theory. Several different forms of the vertex are derived and their mutural relationships are clarified. In this paper, the authors include a brief survey of the history of the fermion emission vertex, as it offers a good perspective in which to appreciate the logical development
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.
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.
Waveguides with asymptotically diverging twisting
Czech Academy of Sciences Publication Activity Database
Krejčiřík, David
2015-01-01
Roč. 46, AUG (2015), s. 7-10 ISSN 0893-9659 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : quantum waveguide * exploding twisting * Quasi-bounded * Quasi-cylindrical * discrete spectrum Subject RIV: BE - Theoretical Physics Impact factor: 1.659, year: 2015
Rotation Invariance Neural Network
Li, Shiyuan
2017-01-01
Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol recognition. We can also get the position and orientation of the 2-D symbol by the network to achieve detection purpose for multiple non-overlap target. Last but not least, this architecture can achieve one-shot learning in some cases using thos...
Twist deformations of the supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Castro, P.G.; Chakraborty, B.; Toppan, F., E-mail: pgcastro@cbpf.b, E-mail: biswajit@bose.res.i, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Kuznetsova, Z., E-mail: zhanna.kuznetsova@ufabc.edu.b [Universidade Federal do ABC (UFABC), Santo Andre, SP (Brazil)
2009-07-01
The N-extended supersymmetric quantum mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its universal enveloping superalgebra. Two constructions are possible. For even N one can identify the 1D N-extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed. (author)
Lorentz invariance with an invariant energy scale.
Magueijo, João; Smolin, Lee
2002-05-13
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.
How many invariant polynomials are needed to decide local unitary equivalence of qubit states?
International Nuclear Information System (INIS)
Maciążek, Tomasz; Oszmaniec, Michał; Sawicki, Adam
2013-01-01
Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e., by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure
Renormalization constants for 2-twist operators in twisted mass QCD
International Nuclear Information System (INIS)
Alexandrou, C.; Constantinou, M.; Panagopoulos, H.; Stylianou, F.; Korzec, T.
2011-01-01
Perturbative and nonperturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the nonperturbative evaluation of the one-derivative twist-2 vector and axial-vector operators. Nonperturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing a corresponding to β=3.9, 4.05, 4.20. Subtraction of O(a 2 ) terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to O(a 2 ). The renormalization conditions are defined in the RI ' -MOM scheme, for both perturbative and nonperturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to MS at 2 GeV using 3-loop perturbative results for the conversion factors.
On the restoration of supersymmetry in twisted two-dimensional lattice Yang-Mills theory
International Nuclear Information System (INIS)
Catterall, Simon
2007-01-01
We study a discretization of N = 2 super Yang-Mills theory which possesses a single exact supersymmetry at non-zero lattice spacing. This supersymmetry arises after a reformulation of the theory in terms of twisted fields. In this paper we derive the action of the other twisted supersymmetries on the component fields and study, using Monte Carlo simulation, a series of corresponding Ward identities. Our results for SU(2) and SU(3) support a restoration of these additional supersymmetries without fine tuning in the infinite volume continuum limit. Additionally we present evidence supporting a restoration of (twisted) rotational invariance in the same limit. Finally we have examined the distribution of scalar field eigenvalues and find evidence for power law tails extending out to large eigenvalue. We argue that these tails indicate that the classical moduli space does not survive in the quantum theory
International Nuclear Information System (INIS)
Moriyasu, K.
1978-01-01
A pedagogical approach to gauge invariance is presented which is based on the analogy between gauge transformations and relativity. By using the concept of an internal space, purely geometrical arguments are used to teach the physical ideas behind gauge invariance. Many of the results are applicable to general gauge theories
Manifold-splitting regularization, self-linking, twisting, writhing numbers of space-time ribbons
International Nuclear Information System (INIS)
Tze, C.H.
1988-01-01
The authors present an alternative formulation of Polyakov's regularization of Gauss' integral formula for a single closed Feynman path. A key element in his proof of the D = 3 fermi-bose transmutations induced by topological gauge fields, this regularization is linked here with the existence and properties of a nontrivial topological invariant for a closed space ribbon. This self-linking coefficient, an integer, is the sum of two differential characteristics of the ribbon, its twisting and writhing numbers. These invariants form the basis for a physical interpretation of our regularization. Their connection to Polyakov's spinorization is discussed. The authors further generalize their construction to the self-linking, twisting and writhing of higher dimensional d = eta(odd) submanifolds in D = (2eta + 1) space-time
Measurement invariance versus selection invariance: Is fair selection possible?
Borsboom, D.; Romeijn, J.W.; Wicherts, J.M.
2008-01-01
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement
Measurement invariance versus selection invariance : Is fair selection possible?
Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement
Effective potentials for twisted fields
International Nuclear Information System (INIS)
Banach, R.
1981-01-01
Minus the density of the effective action, evaluated at the lowest eigenfunction of the (space-time) derivative part of the second (functional) derivative of the classical action, is proposed as a generalised definition of the effective potential, applicable to twisted as well as untwisted sectors of a field theory. The proposal is corroborated by several specific calculations in the twisted sector, namely phi 4 theory (real and complex) and wrong-sign-Gordon theory, in an Einstein cylinder, where the exact integrability of the static solutions confirms the effective potential predictions. Both models exhibit a phase transition, which the effective potential locates, and the one-loop quantum shift in the critical radius is computed for the real phi 4 model, being a universal result. Topological mass generation at the classical level is pointed out, and the exactness of the classical effective potential approximation for complex phi 4 is discussed. (author)
Twisting formula of epsilon factors
Indian Academy of Sciences (India)
Sazzad Ali Biswas
2017-08-07
Aug 7, 2017 ... In this article, we give a generalized twisting formula for ϵ(χ1χ2,ψ), when both χ1 and χ2 are ramified via the following local Jacobi sums. Let UF be the group of units in OF (ring of integers of F). For characters χ1, χ2 of F. × and a positive integer n, we define the local Jacobi sum. Jt(χ1,χ2, n) = ∑ x∈UF. Un.
Invariance Signatures: Characterizing contours by their departures from invariance
Squire, David; Caelli, Terry M.
1997-01-01
In this paper, a new invariant feature of two-dimensional contours is reported: the Invariance Signature. The Invariance Signature is a measure of the degree to which a contour is invariant under a variety of transformations, derived from the theory of Lie transformation groups. It is shown that the Invariance Signature is itself invariant under shift, rotation and scaling of the contour. Since it is derived from local properties of the contour, it is well-suited to a neural network implement...
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.
New twist on artificial muscles.
Haines, Carter S; Li, Na; Spinks, Geoffrey M; Aliev, Ali E; Di, Jiangtao; Baughman, Ray H
2016-10-18
Lightweight artificial muscle fibers that can match the large tensile stroke of natural muscles have been elusive. In particular, low stroke, limited cycle life, and inefficient energy conversion have combined with high cost and hysteretic performance to restrict practical use. In recent years, a new class of artificial muscles, based on highly twisted fibers, has emerged that can deliver more than 2,000 J/kg of specific work during muscle contraction, compared with just 40 J/kg for natural muscle. Thermally actuated muscles made from ordinary polymer fibers can deliver long-life, hysteresis-free tensile strokes of more than 30% and torsional actuation capable of spinning a paddle at speeds of more than 100,000 rpm. In this perspective, we explore the mechanisms and potential applications of present twisted fiber muscles and the future opportunities and challenges for developing twisted muscles having improved cycle rates, efficiencies, and functionality. We also demonstrate artificial muscle sewing threads and textiles and coiled structures that exhibit nearly unlimited actuation strokes. In addition to robotics and prosthetics, future applications include smart textiles that change breathability in response to temperature and moisture and window shutters that automatically open and close to conserve energy.
γ*→ρT impact factor with twist three accuracy
International Nuclear Information System (INIS)
Anikin, I. V.; Ivanov, D. Yu.; Pire, B.; Szymanowski, L.; Wallon, S.
2009-01-01
We evaluate the impact factor of the transition γ*→ρ T taking into account the twist 3 contributions. We show that a gauge invariant expression is obtained with the help of QCD equations of motion. Our results are free of end-point singularities. This opens the way to a consistent treatment of factorization for exclusive processes with a transversally polarized vector meson.
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.
Morozov, Albert D; Dragunov, Timothy N; Malysheva, Olga V
1999-01-01
This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book.The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical
Modeling and control of active twist aircraft
Cramer, Nicholas Bryan
The Wright Brothers marked the beginning of powered flight in 1903 using an active twist mechanism as their means of controlling roll. As time passed due to advances in other technologies that transformed aviation the active twist mechanism was no longer used. With the recent advances in material science and manufacturability, the possibility of the practical use of active twist technologies has emerged. In this dissertation, the advantages and disadvantages of active twist techniques are investigated through the development of an aeroelastic modeling method intended for informing the designs of such technologies and wind tunnel testing to confirm the capabilities of the active twist technologies and validate the model. Control principles for the enabling structural technologies are also proposed while the potential gains of dynamic, active twist are analyzed.
International Nuclear Information System (INIS)
Zhou, Jinyuan; Xie, Erqing; Sun, Gengzhi; Zhan, Zhaoyao; Zheng, Lianxi
2014-01-01
The dependences of twisting parameters on the electric and mechanical properties of twisted CNT fibers were systematically studied. Results from electric and mechanical measurements showed that twisting intensity is very effective to improve the electric and mechanical properties of CNT fibers. Further calculations combined with Raman results indicate that the twisting treatments, to a certain extent, can greatly enhance the strain transfer factors of the samples, which dominates the mechanical properties of CNT fibers. In addition, studies on the effect of twisting speeds suggested that lower twisting speed can lead to higher uniformity but lower performances in the electric and mechanical properties, higher twisting speed to higher Young’s modulus and higher conductance but lower uniformities. Ultra-strong uniform CNT fibers need to be prepared with a suitable twisting speed. (paper)
Cosmological disformal invariance
Energy Technology Data Exchange (ETDEWEB)
Domènech, Guillem; Sasaki, Misao [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Naruko, Atsushi, E-mail: guillem.domenech@yukawa.kyoto-u.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2015-10-01
The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.
Algorithms in invariant theory
Sturmfels, Bernd
2008-01-01
J. Kung and G.-C. Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics". The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.
Coordinate-invariant regularization
International Nuclear Information System (INIS)
Halpern, M.B.
1987-01-01
A general phase-space framework for coordinate-invariant regularization is given. The development is geometric, with all regularization contained in regularized DeWitt Superstructures on field deformations. Parallel development of invariant coordinate-space regularization is obtained by regularized functional integration of the momenta. As representative examples of the general formulation, the regularized general non-linear sigma model and regularized quantum gravity are discussed. copyright 1987 Academic Press, Inc
Integral Twist Actuation of Helicopter Rotor Blades for Vibration Reduction
Shin, SangJoon; Cesnik, Carlos E. S.
2001-01-01
Active integral twist control for vibration reduction of helicopter rotors during forward flight is investigated. The twist deformation is obtained using embedded anisotropic piezocomposite actuators. An analytical framework is developed to examine integrally-twisted blades and their aeroelastic response during different flight conditions: frequency domain analysis for hover, and time domain analysis for forward flight. Both stem from the same three-dimensional electroelastic beam formulation with geometrical-exactness, and axe coupled with a finite-state dynamic inflow aerodynamics model. A prototype Active Twist Rotor blade was designed with this framework using Active Fiber Composites as the actuator. The ATR prototype blade was successfully tested under non-rotating conditions. Hover testing was conducted to evaluate structural integrity and dynamic response. In both conditions, a very good correlation was obtained against the analysis. Finally, a four-bladed ATR system is built and tested to demonstrate its concept in forward flight. This experiment was conducted at NASA Langley Tansonic Dynamics Tunnel and represents the first-of-a-kind Mach-scaled fully-active-twist rotor system to undergo forward flight test. In parallel, the impact upon the fixed- and rotating-system loads is estimated by the analysis. While discrepancies are found in the amplitude of the loads under actuation, the predicted trend of load variation with respect to its control phase correlates well. It was also shown, both experimentally and numerically, that the ATR blade design has the potential for hub vibratory load reduction of up to 90% using individual blade control actuation. Using the numerical framework, system identification is performed to estimate the harmonic transfer functions. The linear time-periodic system can be represented by a linear time-invariant system under the three modes of blade actuation: collective, longitudinal cyclic, and lateral cyclic. A vibration
Remarks on twisted noncommutative quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Zahn, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2006-04-15
We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature. (Orig.)
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)
S-duality invariant perturbation theory improved by holography
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, Abhishek [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India); Honda, Masazumi [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 7610001 (Israel); Thakur, Somyadip [Tata Institute of Fundamental Research,Mumbai 400005 (India)
2017-04-26
We study anomalous dimensions of unprotected low twist operators in the four-dimensional SU (N)N=4 supersymmetric Yang-Mills theory. We construct a class of interpolating functions to approximate the dimensions of the leading twist operators for arbitrary gauge coupling τ. The interpolating functions are consistent with previous results on the perturbation theory, holographic computation and full S-duality. We use our interpolating functions to test a recent conjecture by the N=4 superconformal bootstrap that upper bounds on the dimensions are saturated at one of the duality-invariant points τ=i and τ=e{sup iπ/3}. It turns out that our interpolating functions have maximum at τ=e{sup iπ/3}, which are close to the conjectural values by the conformal bootstrap. In terms of the interpolating functions, we draw the image of conformal manifold in the space of the dimensions. We find that the image is almost a line despite the conformal manifold is two-dimensional. We also construct interpolating functions for the subleading twist operator and study level crossing phenomenon between the leading and subleading twist operators. Finally we study the dimension of the Konishi operator in the planar limit. We find that our interpolating functions match with numerical result obtained by Thermodynamic Bethe Ansatz very well. It turns out that analytic properties of the interpolating functions reflect an expectation on a radius of convergence of the perturbation theory.
Device for measuring well twistings
Energy Technology Data Exchange (ETDEWEB)
Kostin, Yu S; Golubin, S V; Keller, V F; Merzheyevskiy, A B; Zdorov, V P
1982-01-01
The device for measuring the well twistings with the use of fluids (poured into a vessel and which leave an imprint on the walls), containing a housing and adapter, is distinguished by the fact that in order to improve the accuracy of measurement by obtaining a clear imprint, it is equipped with cylinder that is spring-loaded in relation to the adapter, forming a vessel for fluid with the adapter. The adapter is made of two parts, one of which is made of neutral metal in relation to the fluid, and the other, from active in relation to the same fluid.
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
Beyond the relativistic point particle: A reciprocally invariant system and its generalisation
International Nuclear Information System (INIS)
Pavsic, Matej
2009-01-01
We investigate a reciprocally invariant system proposed by Low and Govaerts et al., whose action contains both the orthogonal and the symplectic forms and is invariant under global O(2,4) intersection Sp(2,4) transformations. We find that the general solution to the classical equations of motion has no linear term in the evolution parameter, τ, but only the oscillatory terms, and therefore cannot represent a particle propagating in spacetime. As a remedy, we consider a generalisation of the action by adopting a procedure similar to that of Bars et al., who introduced the concept of a τ derivative that is covariant under local Sp(2) transformations between the phase space variables x μ (τ) and p μ (τ). This system, in particular, is similar to a rigid particle whose action contains the extrinsic curvature of the world line, which turns out to be helical in spacetime. Another possible generalisation is the introduction of a symplectic potential proposed by Montesinos. We show how the latter approach is related to Kaluza-Klein theories and to the concept of Clifford space, a manifold whose tangent space at any point is Clifford algebra Cl(8), a promising framework for the unification of particles and forces.
Twist-stretch profiles of DNA chains
Zoli, Marco
2017-06-01
Helical molecules change their twist number under the effect of a mechanical load. We study the twist-stretch relation for a set of short DNA molecules modeled by a mesoscopic Hamiltonian. Finite temperature path integral techniques are applied to generate a large ensemble of possible configurations for the base pairs of the sequence. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. Simulating a broad range of twisting conformation, we compute the helix structural parameters by averaging over the ensemble of base pairs configurations. The method selects, for any applied force, the average twist angle which minimizes the molecule’s free energy. It is found that the chains generally over-twist under an applied stretching and the over-twisting is physically associated to the contraction of the average helix diameter, i.e. to the damping of the base pair fluctuations. Instead, assuming that the maximum amplitude of the bending fluctuations may decrease against the external load, the DNA molecule first over-twists for weak applied forces and then untwists above a characteristic force value. Our results are discussed in relation to available experimental information albeit for kilo-base long molecules.
Energy Technology Data Exchange (ETDEWEB)
Moller-Nielsen, Thomas [University of Oxford (United Kingdom)
2014-07-01
Physicists and philosophers have long claimed that the symmetries of our physical theories - roughly speaking, those transformations which map solutions of the theory into solutions - can provide us with genuine insight into what the world is really like. According to this 'Invariance Principle', only those quantities which are invariant under a theory's symmetries should be taken to be physically real, while those quantities which vary under its symmetries should not. Physicists and philosophers, however, are generally divided (or, indeed, silent) when it comes to explaining how such a principle is to be justified. In this paper, I spell out some of the problems inherent in other theorists' attempts to justify this principle, and sketch my own proposed general schema for explaining how - and when - the Invariance Principle can indeed be used as a legitimate tool of metaphysical inference.
World-line quantization of a reciprocally invariant system
International Nuclear Information System (INIS)
Govaerts, Jan; Jarvis, Peter D; Morgan, Stuart O; Low, Stephen G
2007-01-01
We present the world-line quantization of a system invariant under the symmetries of reciprocal relativity (pseudo-unitary transformations on 'phase-space coordinates' (x μ (τ), p μ (τ)) which preserve the Minkowski metric and the symplectic form, and global shifts in these coordinates, together with coordinate-dependent transformations of an additional compact phase coordinate, θ(τ)). The action is that of free motion over the corresponding Weyl-Heisenberg group. Imposition of the first class constraint, the generator of local time reparametrizations, on physical states enforces identification of the world-line cosmological constant with a fixed value of the quadratic Casimir of the quaplectic symmetry group Q(D-1,1)≅U(D-1,1)xH(D), the semi-direct product of the pseudo-unitary group with the Weyl-Heisenberg group (the central extension of the global translation group, with central extension associated with the phase variable θ(τ)). The spacetime spectrum of physical states is identified. Even though for an appropriate range of values the restriction enforced by the cosmological constant projects out negative norm states from the physical gauge invariant spectrum, leaving over spin zero states only, in this purely bosonic setting the mass-squared spectrum is continuous over the entire real line and thus includes a tachyonic branch as well
International Nuclear Information System (INIS)
Anikin, I.V.; Ivanov, D.Yu.; Pire, B.; Szymanowski, L.; Wallon, S.
2010-01-01
We describe a consistent approach to factorization of scattering amplitudes for exclusive processes beyond the leading twist approximation. The method involves the Taylor expansion of the scattering amplitude in the momentum space around the dominant light-cone direction and thus naturally introduces an appropriate set of non-perturbative correlators which encode effects not only of the lowest but also of the higher Fock states of the produced particle. The reduction of original set of correlators to a set of independent ones is achieved with the help of equations of motion and invariance of the scattering amplitude under rotation on the light cone. We compare the proposed method with the covariant method formulated in the coordinate space, based on the operator product expansion. We prove the equivalence of two proposed parametrizations of the ρ T distribution amplitudes. As a concrete application, we compute the expressions of the impact factor for the transition of virtual photon to transversally polarised ρ-meson up to the twist 3 accuracy within these two quite different methods and show that they are identical.
Energy Technology Data Exchange (ETDEWEB)
Perez-Nadal, Guillem [Universidad de Buenos Aires, Buenos Aires (Argentina)
2017-07-15
We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates ''scaling like time'' is generically greater than one. We propose the Cartesian product of two curved spaces, the metric of each space being parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry. (orig.)
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.
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
Quantisation of monotonic twist maps
International Nuclear Information System (INIS)
Boasman, P.A.; Smilansky, U.
1993-08-01
Using an approach suggested by Moser, classical Hamiltonians are generated that provide an interpolating flow to the stroboscopic motion of maps with a monotonic twist condition. The quantum properties of these Hamiltonians are then studied in analogy with recent work on the semiclassical quantization of systems based on Poincare surfaces of section. For the generalized standard map, the correspondence with the usual classical and quantum results is shown, and the advantages of the quantum Moser Hamiltonian demonstrated. The same approach is then applied to the free motion of a particle on a 2-torus, and to the circle billiard. A natural quantization condition based on the eigenphases of the unitary time--development operator is applied, leaving the exact eigenvalues of the torus, but only the semiclassical eigenvalues for the billiard; an explanation for this failure is proposed. It is also seen how iterating the classical map commutes with the quantization. (authors)
Hermiticity and gauge invariance
International Nuclear Information System (INIS)
Treder, H.J.
1987-01-01
In the Theory of Hermitian Relativity (HRT) the postulates of hermiticity and gauge invariance are formulated in different ways, due to a different understanding of the idea of hermiticity. However all hermitian systems of equations have to satisfy Einstein's weak system of equations being equivalent to Einstein-Schroedinger equations. (author)
International Nuclear Information System (INIS)
Pokhozhaev, Stanislav I
2011-01-01
The notion of Riemann quasi-invariants is introduced and their applications to several conservation laws are considered. The case of nonisentropic flow of an ideal polytropic gas is analysed in detail. Sufficient conditions for gradient catastrophes are obtained. Bibliography: 16 titles.
Invariant differential operators
Dobrev, Vladimir K
2016-01-01
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory.
Invariant differential operators
Dobrev, Vladimir K
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory.
International Nuclear Information System (INIS)
Bramson, B.D.
1978-01-01
An isolated system in general relativity makes a transition between stationary states. It is shown that the spin vectors of the system, long before and long after the emission of radiation, are supertranslation invariant and, hence, independent of the choice of Minkowski observation space. (author)
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
Invariants of generalized Lie algebras
International Nuclear Information System (INIS)
Agrawala, V.K.
1981-01-01
Invariants and invariant multilinear forms are defined for generalized Lie algebras with arbitrary grading and commutation factor. Explicit constructions of invariants and vector operators are given by contracting invariant forms with basic elements of the generalized Lie algebra. The use of the matrix of a linear map between graded vector spaces is emphasized. With the help of this matrix, the concept of graded trace of a linear operator is introduced, which is a rich source of multilinear forms of degree zero. To illustrate the use of invariants, a characteristic identity similar to that of Green is derived and a few Racah coefficients are evaluated in terms of invariants
Properties of invariant modelling and invariant glueing of vector fields
International Nuclear Information System (INIS)
Petukhov, V.R.
1987-01-01
Invariant modelling and invariant glueing of both continuous (rates and accelerations) and descrete vector fields, gradient and divergence cases are considered. The following appendices are discussed: vector fields in crystals, crystal disclinations, topological charges and their fields
Four-point functions with a twist
Energy Technology Data Exchange (ETDEWEB)
Bargheer, Till [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2017-01-15
We study the OPE of correlation functions of local operators in planar N=4 super Yang-Mills theory. The considered operators have an explicit spacetime dependence that is defined by twisting the translation generators with certain R-symmetry generators. We restrict to operators that carry a small number of excitations above the twisted BMN vacuum. The OPE limit of the four-point correlator is dominated by internal states with few magnons on top of the vacuum. The twisting directly couples all spacetime dependence of the correlator to these magnons. We analyze the OPE in detail, and single out the extremal states that have to cancel all double-trace contributions.
Euclidean supersymmetry, twisting and topological sigma models
International Nuclear Information System (INIS)
Hull, C.M.; Lindstroem, U.; Santos, L. Melo dos; Zabzine, M.; Unge, R. von
2008-01-01
We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N = 2, the R-symmetry is SO(2) x SO(1, 1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N = 2 models with H-flux so that the target geometry is generalised Kahler, it is necessary to work with a complexification of the sigma models. These issues are related to the obstructions to the existence of non-trivial twisted chiral superfields in Euclidean superspace.
Globally conformal invariant gauge field theory with rational correlation functions
Nikolov, N M; Todorov, I T; CERN. Geneva; Todorov, Ivan T.
2003-01-01
Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields $V_{\\kappa} (x_1, x_2)$ of dimension $(\\kappa, \\kappa)$. For a {\\it globally conformal invariant} (GCI) theory we write down the OPE of $V_{\\kappa}$ into a series of {\\it twist} (dimension minus rank) $2\\kappa$ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field. We argue that the theory of a GCI hermitian scalar field ${\\cal L} (x)$ of dimension 4 in $D = 4$ Minkowski space such that the 3-point functions of a pair of ${\\cal L}$'s and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density ${\\cal L} (x)$.
Status of time reversal invariance
International Nuclear Information System (INIS)
Henley, E.M.
1989-01-01
Time Reversal Invariance is introduced, and theories for its violation are reviewed. The present experimental and theoretical status of Time Reversal Invariance and tests thereof will be presented. Possible future tests will be discussed. 30 refs., 2 figs., 1 tab
Analytic invariants of boundary links
Garoufalidis, Stavros; Levine, Jerome
2001-01-01
Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally defined by M. Farber.
Moment invariants for particle beams
International Nuclear Information System (INIS)
Lysenko, W.P.; Overley, M.S.
1988-01-01
The rms emittance is a certain function of second moments in 2-D phase space. It is preserved for linear uncoupled (1-D) motion. In this paper, the authors present new functions of moments that are invariants for coupled motion. These invariants were computed symbolically using a computer algebra system. Possible applications for these invariants are discussed. Also, approximate moment invariants for nonlinear motion are presented
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.
On the twist-2 and twist-3 contributions to the spin-dependent electroweak structure functions
International Nuclear Information System (INIS)
Bluemlein, J.; Kochelev, N.
1997-01-01
The twist-2 and twist-3 contributions of the polarized deep-inelastic structure functions are calculated both for neutral and charged current interactions using the operator product expansion in lowest order in QCD. The relations between the different structure functions are determined. New integral relations are derived between the twist-2 contributions of the structure functions g 3 (x,Q 2 ) and g 5 (x,Q 2 ) and between combinations of the twist-3 contributions to the structure functions g 2 (x,Q 2 ) and g 3 (x,Q 2 ). The sum rules for polarized deep-inelastic scattering are discussed in detail. (orig.)
Twisted Vector Bundles on Pointed Nodal Curves
Indian Academy of Sciences (India)
Abstract. Motivated by the quest for a good compactification of the moduli space of -bundles on a nodal curve we establish a striking relationship between Abramovich's and Vistoli's twisted bundles and Gieseker vector bundles.
Reducing Lookups for Invariant Checking
DEFF Research Database (Denmark)
Thomsen, Jakob Grauenkjær; Clausen, Christian; Andersen, Kristoffer Just
2013-01-01
This paper helps reduce the cost of invariant checking in cases where access to data is expensive. Assume that a set of variables satisfy a given invariant and a request is received to update a subset of them. We reduce the set of variables to inspect, in order to verify that the invariant is still...
Conformal invariance in supergravity
International Nuclear Information System (INIS)
Bergshoeff, E.A.
1983-01-01
In this thesis the author explains the role of conformal invariance in supergravity. He presents the complete structure of extended conformal supergravity for N <= 4. The outline of this work is as follows. In chapter 2 he briefly summarizes the essential properties of supersymmetry and supergravity and indicates the use of conformal invariance in supergravity. The idea that the introduction of additional symmetry transformations can make clear the structure of a field theory is not reserved to supergravity only. By means of some simple examples it is shown in chapter 3 how one can always introduce additional gauge transformations in a theory of massive vector fields. Moreover it is shown how the gauge invariant formulation sometimes explains the quantum mechanical properties of the theory. In chapter 4 the author defines the conformal transformations and summarizes their main properties. He explains how these conformal transformations can be used to analyse the structure of gravity. The supersymmetric extension of these results is discussed in chapter 5. Here he describes as an example how N=1 supergravity can be reformulated in a conformally-invariant way. He also shows that beyond N=1 the gauge fields of the superconformal symmetries do not constitute an off-shell field representation of extended conformal supergravity. Therefore, in chapter 6, a systematic method to construct the off-shell formulation of all extended conformal supergravity theories with N <= 4 is developed. As an example he uses this method to construct N=1 conformal supergravity. Finally, in chapter 7 N=4 conformal supergravity is discussed. (Auth.)
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Kautský, J.; Šroubek, Filip
2010-01-01
Roč. 86, č. 1 (2010), s. 72-86 ISSN 0920-5691 R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/1593 Institutional research plan: CEZ:AV0Z10750506 Keywords : Implicit invariants * Orthogonal polynomials * Polynomial image deformation Subject RIV: BD - Theory of Information Impact factor: 4.930, year: 2010 http://library.utia.cas.cz/separaty/2009/ZOI/flusser-0329394.pdf
Czech Academy of Sciences Publication Activity Database
Suk, Tomáš; Flusser, Jan
2004-01-01
Roč. 26, č. 10 (2004), s. 1364-1367 ISSN 0162-8828 R&D Projects: GA ČR GA201/03/0675 Institutional research plan: CEZ:AV0Z1075907 Keywords : projective transform * moment invariants * object recognition Subject RIV: JD - Computer Applications, Robotics Impact factor: 4.352, year: 2004 http://library.utia.cas.cz/prace/20040112.pdf
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
Some relations between twisted K-theory and E8 gauge theory
International Nuclear Information System (INIS)
Mathai, Varghese; Sati, Hisham
2004-01-01
Recently, Diaconescu, Moore and Witten provided a nontrivial link between K-theory and M-theory, by deriving the partition function of the Ramond-Ramond fields of Type IIA string theory from an E8 gauge theory in eleven dimensions. We give some relations between twisted K-theory and M-theory by adapting the method of Diaconescu-Moore-Witten and Moore-Saulina. In particular, we construct the twisted K-theory torus which defines the partition function, and also discuss the problem from the E8 loop group picture, in which the Dixmier-Douady class is the Neveu-Schwarz field. In the process of doing this, we encounter some mathematics that is new to the physics literature. In particular, the eta differential form, which is the generalization of the eta invariant, arises naturally in this context. We conclude with several open problems in mathematics and string theory. (author)
Twisted covariant noncommutative self-dual gravity
International Nuclear Information System (INIS)
Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.
2008-01-01
A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the θ expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in θ for the Plebanski action is explicitly obtained.
Nonlinear physics of twisted magnetic field lines
International Nuclear Information System (INIS)
Yoshida, Zensho
1998-01-01
Twisted magnetic field lines appear commonly in many different plasma systems, such as magnetic ropes created through interactions between the magnetosphere and the solar wind, magnetic clouds in the solar wind, solar corona, galactic jets, accretion discs, as well as fusion plasma devices. In this paper, we study the topological characterization of twisted magnetic fields, nonlinear effect induced by the Lorentz back reaction, length-scale bounds, and statistical distributions. (author)
OAM mode converter in twisted fibers
DEFF Research Database (Denmark)
Usuga Castaneda, Mario A.; Beltran-Mejia, Felipe; Cordeiro, Cristiano
2014-01-01
We analyze the case of an OAM mode converter based on a twisted fiber, through finite element simulations where we exploit an equivalence between geometric and material transformations. The obtained converter has potential applications in MDM. © 2014 OSA.......We analyze the case of an OAM mode converter based on a twisted fiber, through finite element simulations where we exploit an equivalence between geometric and material transformations. The obtained converter has potential applications in MDM. © 2014 OSA....
Further Generalisations of Twisted Gabidulin Codes
DEFF Research Database (Denmark)
Puchinger, Sven; Rosenkilde, Johan Sebastian Heesemann; Sheekey, John
2017-01-01
We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known general constructions of linear MRD codes.......We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known general constructions of linear MRD codes....
Twisted 3D N=4 supersymmetric YM on deformed A{sub 3}{sup *} lattice
Energy Technology Data Exchange (ETDEWEB)
Saidi, El Hassan [Lab of High Energy Physics, Modeling and Simulations, Faculty of Science, University Mohamed V-Agdal, Morocco and Centre of Physics and Mathematics, CPM, Rabat (Morocco)
2014-01-15
We study a class of twisted 3D N=4 supersymmetric Yang-Mills (SYM) theory on particular 3-dimensional lattice L{sub 3D} formally denoted as L{sub 3D}{sup su{sub 3}×u{sub 1}} and given by non-trivial fibration L{sub 1D}{sup u{sub 1}}×L{sub 2D}{sup su{sub 3}} with base L{sub 2D}{sup su{sub 3}}=A{sub 2}{sup *}, the weight lattice of SU(3). We first, develop the twisted 3D N=4 SYM in continuum by using superspace method where the scalar supercharge Q is manifestly exhibited. Then, we show how to engineer the 3D lattice L{sub 3D}{sup su{sub 3}×u{sub 1}} that host this theory. After that we build the lattice action S{sub latt} invariant under the following three points: (i) U(N) gauge invariance, (ii) BRST symmetry, (iii) the S{sub 3} point group symmetry of L{sub 3D}{sup su{sub 3}×u{sub 1}}. Other features such as reduction to twisted 2D supersymmetry with 8 supercharges living on L{sub 2D}≡L{sub 2D}{sup su{sub 2}×u{sub 1}}, the extension to twisted maximal 5D SYM with 16 supercharges on lattice L{sub 5D}≡L{sub 5D}{sup su{sub 4}×u{sub 1}} as well as the relation with known results are also given.
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.
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
Soft tissue twisting injuries of the knee
International Nuclear Information System (INIS)
Magee, T.; Shapiro, M.
2001-01-01
Twisting injuries occur as a result of differential motion of different tissue types in injuries with some rotational force. These injuries are well described in brain injuries but, to our knowledge, have not been described in the musculoskeletal literature. We correlated the clinical examination and MR findings of 20 patients with twisting injuries of the soft tissues around the knee. Design and patients: We prospectively followed the clinical courses of 20 patients with knee injuries who had clinical histories and MR findings to suggest twisting injuries of the subcutaneous tissues. Patients with associated internal derangement of the knee (i.e., meniscal tears, ligamentous or bone injuries) were excluded from this study. MR findings to suggest twisting injuries included linear areas of abnormal dark signal on T1-weighted sequences and abnormal bright signal on T2-weighted or short tau inversion recovery (STIR) sequences and/or signal to suggest hemorrhage within the subcutaneous tissues. These MR criteria were adapted from those established for indirect musculotendinous junction injuries. Results: All 20 patients presented with considerable pain that suggested internal derangement on physical examination by the referring orthopedic surgeons. All presented with injuries associated with rotational force. The patients were placed on a course of protected weight-bearing of the affected extremity for 4 weeks. All patients had pain relief by clinical examination after this period of protected weight-bearing. Twisting injuries of the soft tissues can result in considerable pain that can be confused with internal derangement of the knee on physical examination. Soft tissue twisting injuries need to be recognized on MR examinations as they may be the cause of the patient's pain despite no MR evidence of internal derangement of the knee. The demonstration of soft tissue twisting injuries in a patient with severe knee pain but no documented internal derangement on MR
Method of chronokinemetrical invariants
International Nuclear Information System (INIS)
Vladimirov, Yu.S.; Shelkovenko, A.Eh.
1976-01-01
A particular case of a general dyadic method - the method of chronokinemetric invariants is formulated. The time-like dyad vector is calibrated in a chronometric way, and the space-like vector - in a kinemetric way. Expressions are written for the main physical-geometrical values of the dyadic method and for differential operators. The method developed may be useful for predetermining the reference system of a single observer, and also for studying problems connected with emission and absorption of gravitational and electromagnetic waves [ru
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
Viability, invariance and applications
Carja, Ovidiu; Vrabie, Ioan I
2007-01-01
The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In th...
Twisted electron-acoustic waves in plasmas
International Nuclear Information System (INIS)
Aman-ur-Rehman; Ali, S.; Khan, S. A.; Shahzad, K.
2016-01-01
In the paraxial limit, a twisted electron-acoustic (EA) wave is studied in a collisionless unmagnetized plasma, whose constituents are the dynamical cold electrons and Boltzmannian hot electrons in the background of static positive ions. The analytical and numerical solutions of the plasma kinetic equation suggest that EA waves with finite amount of orbital angular momentum exhibit a twist in its behavior. The twisted wave particle resonance is also taken into consideration that has been appeared through the effective wave number q_e_f_f accounting for Laguerre-Gaussian mode profiles attributed to helical phase structures. Consequently, the dispersion relation and the damping rate of the EA waves are significantly modified with the twisted parameter η, and for η → ∞, the results coincide with the straight propagating plane EA waves. Numerically, new features of twisted EA waves are identified by considering various regimes of wavelength and the results might be useful for transport and trapping of plasma particles in a two-electron component plasma.
Electrically Controllable Magnetism in Twisted Bilayer Graphene.
Gonzalez-Arraga, Luis A; Lado, J L; Guinea, Francisco; San-Jose, Pablo
2017-09-08
Twisted graphene bilayers develop highly localized states around AA-stacked regions for small twist angles. We show that interaction effects may induce either an antiferromagnetic or a ferromagnetic (FM) polarization of said regions, depending on the electrical bias between layers. Remarkably, FM-polarized AA regions under bias develop spiral magnetic ordering, with a relative 120° misalignment between neighboring regions due to a frustrated antiferromagnetic exchange. This remarkable spiral magnetism emerges naturally without the need of spin-orbit coupling, and competes with the more conventional lattice-antiferromagnetic instability, which interestingly develops at smaller bias under weaker interactions than in monolayer graphene, due to Fermi velocity suppression. This rich and electrically controllable magnetism could turn twisted bilayer graphene into an ideal system to study frustrated magnetism in two dimensions.
Monopole scattering with a twist
International Nuclear Information System (INIS)
Houghton, C.J.; Sutcliffe, P.M.
1996-01-01
By imposing certain combined inversion and rotation symmetries on the rational maps for SU(2) BPS monopoles we construct geodesics in the monopole moduli space. In the moduli space approximation these geodesics describe a novel kind of monopole scattering. During these scattering processes axial symmetry is instantaneously attained and, in some, monopoles with the symmetries of the regular solids are formed. The simplest example corresponds to a charge three monopole invariant under a combined inversion and 90 circle rotation symmetry. In this example three well-separated collinear unit charge monopoles coalesce to form first a tetrahedron, then a torus, then the dual tetrahedron and finally separate again along the same axis of motion. We explicitly construct the spectral curves in this case and use a numerical ADHMN construction to compute the energy density at various times during the motion. We find that the dynamics of the zeros of the Higgs field is extremely rich and we discover a new phenomenon; there exist charge k SU(2) BPS monopoles with more than k zeros of the Higgs field. (orig.)
Donaldson invariants in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)
Remarks on the E-invariant and the Casson invariant
International Nuclear Information System (INIS)
Seade, J.
1991-08-01
In this work a framed manifold means a pair (M,F) consisting of a closed C ∞ , stably parallelizable manifold M, together with a trivialization F of its stable tangent bundle. The purpose of this work is to understand and determine in higher dimensions the invariant h(M,F) appearing in connection with the Adams e-invariants. 28 refs
Invariant and Absolute Invariant Means of Double Sequences
Directory of Open Access Journals (Sweden)
Abdullah Alotaibi
2012-01-01
Full Text Available We examine some properties of the invariant mean, define the concepts of strong σ-convergence and absolute σ-convergence for double sequences, and determine the associated sublinear functionals. We also define the absolute invariant mean through which the space of absolutely σ-convergent double sequences is characterized.
International Nuclear Information System (INIS)
Kauffman, L.; Saleur, H.
1991-01-01
Various aspects of knot theory are discussed when fermionic degrees of freedom are taken into account in the braid group representations and in the state models. It is discussed how the R matrix for the Alexander polynomial arises from the Fox differential calculus, and how it is related to the quantum group U q gl(1,1). New families of solutions of the Yang Baxter equation obtained from ''linear'' representations of the braid group and exterior algebra are investigated. State models associated with U q sl(n,m), and in the case n=m=1 a state model for the multivariable Alexander polynomial are studied. Invariants of links in solid handlebodies are considered and it is shown how the non trivial topology lifts the boson fermion degeneracy is present in S 3 . (author) 36 refs
Wulan, Hasi
2017-01-01
This monograph summarizes the recent major achievements in Möbius invariant QK spaces. First introduced by Hasi Wulan and his collaborators, the theory of QK spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers interested in the field. Featuring a wide range of subjects, including an overview of QK spaces, QK-Teichmüller spaces, K-Carleson measures and analysis of weight functions, this book serves as an important resource for analysts interested in this area of complex analysis. Notes, numerous exercises, and a comprehensive up-to-date bibliography provide an accessible entry to anyone with a standard graduate background in real and complex analysis.
Permutationally invariant state reconstruction
DEFF Research Database (Denmark)
Moroder, Tobias; Hyllus, Philipp; Tóth, Géza
2012-01-01
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale opti...... optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.......-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum...
Higher-twist correlations in polarized hadrons
International Nuclear Information System (INIS)
Tangerman, R.D.
1996-01-01
In this thesis we studied the response of polarized hadrons to several high-energy probes, working in the framework of the field theoretic model. Emphasis is laid upon higher-twist effects such as quark transverse momentum. The inclusive DIS process is very well suited to study QCD. From general principles we were able to derive four positivity constraints on the structure functions without invoking the helicity formalism. The on-shell quark model is used to illustrate these constraints. Subseqeuently, we concentrated on the higher-twist structure function g 2 (x,Q 2 ). (orig./HSI)
Factorising the 3D topologically twisted index
Cabo-Bizet, Alejandro
2017-04-01
We explore the path integration — upon the contour of hermitian (non-auxliary) field configurations — of topologically twisted N=2 Chern-Simons-matter theory (TTCSM) on {S}_2 times a segment. In this way, we obtain the formula for the 3D topologically twisted index, first as a convolution of TTCSM on {S}_2 times halves of {S}_1 , second as TTCSM on {S}_2 times {S}_1 — with a puncture, — and third as TTCSM on {S}_2× {S}_1 . In contradistinction to the first two cases, in the third case, the vector multiplet auxiliary field D is constrained to be anti-hermitian.
A higher twist correction to heavy quark production
International Nuclear Information System (INIS)
Brodsky, S.J.; Gunion, J.F.; Soper, D.E.
1987-06-01
The leading twist prediction for heavy quark production and a model for a higher twist correction that may be important for charm production was discussed. The correction arises from the interaction of the charm quark with spectator quarks
The holonomy expansion: Invariants and approximate supersymmetry
International Nuclear Information System (INIS)
Jaffe, Arthur
2000-01-01
In this paper we give a new expansion, based on cyclicity of the trace, to study regularity properties of twisted expectations =Tr H (γU(θ)X(s)). Here X(s)=X 0 e -s 0 Q 2 X 1 e -s 1 Q 2 ...X k e -s k Q 2 is a product of operators X j , regularized by heat kernels e -s j Q 2 with s j >0. The twist groups γ(set-membership sign)Z 2 and U(θ)(set-membership sign)U(1) are commuting symmetries of Q 2 . The name ''holonomy expansion'' arises from picturing as a circular graph, with vertices in the graph representing the operators X j , in the order that they appear in the product, and the line-segment following X j representing the heat kernel e -s j Q 2 . The trace functional is cyclic, so the graph is circular. We generate our expansion by ''transporting'' a vertex X k around the circle, ending in its original position. We choose an X k that transforms under a one-dimensional representation of Z 2 xU(1). For θ in the complement of the discrete set γ sing (where the group Z 2 xU(1) acts trivially on X k ) we obtain an identity between the original expectation and some new expectations. We study an example from supersymmetric quantum mechanics, with a Dirac operator Q(λ) depending on a parameter λ and with a U(1) group of symmetries U(θ). We apply our expansion to invariants Z(λ;θ)=Z(Q(λ);θ) suggested by non-commutative geometry. These invariants are sums of expectations of the form above. We investigate this example as a first step toward developing an expansion to evaluate related invariants arising in supersymmetric quantum field theory. We establish differentiability of Z(λ; θ) in λ for λ(set-membership sign)(0,1] and show Z(λ; θ) is independent of λ. We wish to evaluate Z(λ; θ) at the endpoint λ=0, but Z(0; θ) is ill-defined. We regularize the endpoint, while preserving the U(θ)-symmetry, by replacing Q(λ) 2 with H(ε,λ)=Q(λ) 2 +ε 2 |z| 2 . The regularized function Z(ε, λ; θ) depends on all three variables ε, λ, θ; for fixed θ, it
Denjoy minimal sets and Birkhoff periodic orbits for non-exact monotone twist maps
Qin, Wen-Xin; Wang, Ya-Nan
2018-06-01
A non-exact monotone twist map φbarF is a composition of an exact monotone twist map φ bar with a generating function H and a vertical translation VF with VF ((x , y)) = (x , y - F). We show in this paper that for each ω ∈ R, there exists a critical value Fd (ω) ≥ 0 depending on H and ω such that for 0 ≤ F ≤Fd (ω), the non-exact twist map φbarF has an invariant Denjoy minimal set with irrational rotation number ω lying on a Lipschitz graph, or Birkhoff (p , q)-periodic orbits for rational ω = p / q. Like the Aubry-Mather theory, we also construct heteroclinic orbits connecting Birkhoff periodic orbits, and show that quasi-periodic orbits in these Denjoy minimal sets can be approximated by periodic orbits. In particular, we demonstrate that at the critical value F =Fd (ω), the Denjoy minimal set is not uniformly hyperbolic and can be approximated by smooth curves.
Finite type invariants and fatgraphs
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Bene, Alex; Meilhan, Jean-Baptiste Odet Thierry
2010-01-01
–Murakami–Ohtsuki of the link invariant of Andersen–Mattes–Reshetikhin computed relative to choices determined by the fatgraph G; this provides a basic connection between 2d geometry and 3d quantum topology. For each fixed G, this invariant is shown to be universal for homology cylinders, i.e., G establishes an isomorphism...
Novel topological invariants and anomalies
International Nuclear Information System (INIS)
Hirayama, M.; Sugimasa, N.
1987-01-01
It is shown that novel topological invariants are associated with a class of Dirac operators. Trace formulas which are similar to but different from Callias's formula are derived. Implications of these topological invariants to anomalies in quantum field theory are discussed. A new class of anomalies are calculated for two models: one is two dimensional and the other four dimensional
Twist operators in N=4 beta-deformed theory
de Leeuw, M.; Łukowski, T.
2010-01-01
In this paper we derive both the leading order finite size corrections for twist-2 and twist-3 operators and the next-to-leading order finite-size correction for twist-2 operators in beta-deformed SYM theory. The obtained results respect the principle of maximum transcendentality as well as
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
A topologically twisted index for three-dimensional supersymmetric theories
International Nuclear Information System (INIS)
Benini, Francesco; Zaffaroni, Alberto
2015-01-01
We provide a general formula for the partition function of three-dimensional N=2 gauge theories placed on S 2 ×S 1 with a topological twist along S 2 , which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to Ω-backgrounds, as well as two-dimensional theories on S 2 and four-dimensional theories on S 2 ×T 2 . In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants.
Hidden scale invariance of metals
DEFF Research Database (Denmark)
Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.
2015-01-01
Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general “hidden” scale invariance...... of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were...... available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant...
Static Isolated Horizons: SU(2 Invariant Phase Space, Quantization, and Black Hole Entropy
Directory of Open Access Journals (Sweden)
Alejandro Perez
2011-03-01
Full Text Available We study the classical field theoretical formulation of static generic isolated horizons in a manifestly SU(2 invariant formulation. We show that the usual classical description requires revision in the non-static case due to the breaking of diffeomorphism invariance at the horizon leading to the non-conservation of the usual pre-symplectic structure. We argue how this difficulty could be avoided by a simple enlargement of the field content at the horizon that restores diffeomorphism invariance. Restricting our attention to static isolated horizons we study the effective theories describing the boundary degrees of freedom. A quantization of the horizon degrees of freedom is proposed. By defining a statistical mechanical ensemble where only the area aH of the horizon is fixed macroscopically—states with fluctuations away from spherical symmetry are allowed—we show that it is possible to obtain agreement with the Hawkings area law (S = aH /(4l 2p without fixing the Immirzi parameter to any particular value: consistency with the area law only imposes a relationship between the Immirzi parameter and the level of the Chern-Simons theory involved in the effective description of the horizon degrees of freedom.
Twisted Frobenius Identities from Vertex Operator Superalgebras
Directory of Open Access Journals (Sweden)
Alexander Zuevsky
2017-01-01
Full Text Available In consideration of the continuous orbifold partition function and a generating function for all n-point correlation functions for the rank two free fermion vertex operator superalgebra on the self-sewing torus, we introduce the twisted version of Frobenius identity.
Magnetization Modeling of Twisted Superconducting Filaments
Satiramatekul, T; Devred, Arnaud; Leroy, Daniel
2007-01-01
This paper presents a new Finite Element numerical method to analyze the coupling between twisted filaments in a superconducting multifilament composite wire. To avoid the large number of elements required by a 3D code, the proposed method makes use of the energy balance principle in a 2D code. The relationship between superconductor critical current density and local magnetic flux density is implemented in the program for the Bean and modified Kim models. The modeled wire is made up of six filaments twisted together and embedded in a lowresistivity matrix. Computations of magnetization cycle and of the electric field pattern have been performed for various twist pitch values in the case of a pure copper matrix. The results confirm that the maximum magnetization depends on the matrix conductivity, the superconductor critical current density, the applied field frequency, and the filament twist pitch. The simulations also lead to a practical criterion for wire design that can be used to assess whether or not th...
Hilbert's Grand Hotel with a series twist
Wijeratne, Chanakya; Mamolo, Ami; Zazkis, Rina
2014-08-01
This paper presents a new twist on a familiar paradox, linking seemingly disparate ideas under one roof. Hilbert's Grand Hotel, a paradox which addresses infinite set comparisons is adapted and extended to incorporate ideas from calculus - namely infinite series. We present and resolve several variations, and invite the reader to explore his or her own variations.
On the Compton Twist-3 Asymmetries
International Nuclear Information System (INIS)
Korotkiyan, V.M.; Teryaev, O.V.
1994-01-01
The 'fermionic poles' contribution to the twist-3 single asymmetry in the gluon Compton process is calculated. The 'gluonic poles' existence seems to contradict the density matrix positivity. Qualitative predictions for the direct photon and jets asymmetries are presented. 13 refs., 2 figs
Generalized Weyl modules for twisted current algebras
Makedonskyi, I. A.; Feigin, E. B.
2017-08-01
We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and also their connection with nonsymmetric Macdonald polynomials. As an application, we compute the dimension of the classical Weyl modules in the remaining unknown case.
Hardy Inequalities in Globally Twisted Waveguides
Czech Academy of Sciences Publication Activity Database
Briet, Ph.; Hammedi, H.; Krejčiřík, David
2015-01-01
Roč. 105, č. 7 (2015), s. 939-958 ISSN 0377-9017 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : quantum waveguides * twisted tubes * Dirichlet Laplacian * Hardy inequality Subject RIV: BE - Theoretical Physics Impact factor: 1.517, year: 2015
Symplectomorphisms and discrete braid invariants
Czechowski, Aleksander; Vandervorst, Robert
2017-01-01
Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of D2, allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition, we utilize the Conley index theory of discrete braid classes as introduced in Ghrist et
Physical Invariants of Intelligence
Zak, Michail
2010-01-01
A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective
Morphing wing structure with controllable twist based on adaptive bending-twist coupling
Raither, Wolfram; Heymanns, Matthias; Bergamini, Andrea; Ermanni, Paolo
2013-06-01
A novel semi-passive morphing airfoil concept based on variable bending-twist coupling induced by adaptive shear center location and torsional stiffness is presented. Numerical parametric studies and upscaling show that the concept relying on smart materials permits effective twist control while offering the potential of being lightweight and energy efficient. By means of an experimental characterization of an adaptive beam and a scaled adaptive wing structure, effectiveness and producibility of the structural concept are demonstrated.
Morphing wing structure with controllable twist based on adaptive bending–twist coupling
International Nuclear Information System (INIS)
Raither, Wolfram; Heymanns, Matthias; Ermanni, Paolo; Bergamini, Andrea
2013-01-01
A novel semi-passive morphing airfoil concept based on variable bending–twist coupling induced by adaptive shear center location and torsional stiffness is presented. Numerical parametric studies and upscaling show that the concept relying on smart materials permits effective twist control while offering the potential of being lightweight and energy efficient. By means of an experimental characterization of an adaptive beam and a scaled adaptive wing structure, effectiveness and producibility of the structural concept are demonstrated. (paper)
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.
Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A.; Goncalves, A.E. [Universidade Estadual de Londrina, Departamento de Fisica, Londrina-Parana (Brazil)
2016-11-15
We derive formulas for the classical Chern-Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities. (orig.)
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
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
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...
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.
Hamiltonian evolutions of twisted polygons in RPn
International Nuclear Information System (INIS)
Beffa, Gloria Marì; Wang, Jing Ping
2013-01-01
In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W 3 -algebra), its projective realization in RP 2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the W n -algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. (paper)
Cohomological invariants in Galois cohomology
Garibaldi, Skip; Serre, Jean Pierre
2003-01-01
This volume is concerned with algebraic invariants, such as the Stiefel-Whitney classes of quadratic forms (with values in Galois cohomology mod 2) and the trace form of �tale algebras (with values in the Witt ring). The invariants are analogues for Galois cohomology of the characteristic classes of topology. Historically, one of the first examples of cohomological invariants of the type considered here was the Hasse-Witt invariant of quadratic forms. The first part classifies such invariants in several cases. A principal tool is the notion of versal torsor, which is an analogue of the universal bundle in topology. The second part gives Rost's determination of the invariants of G-torsors with values in H^3(\\mathbb{Q}/\\mathbb{Z}(2)), when G is a semisimple, simply connected, linear group. This part gives detailed proofs of the existence and basic properties of the Rost invariant. This is the first time that most of this material appears in print.
Mass generation within conformal invariant theories
International Nuclear Information System (INIS)
Flato, M.; Guenin, M.
1981-01-01
The massless Yang-Mills theory is strongly conformally invariant and renormalizable; however, when masses are introduced the theory becomes nonrenormalizable and weakly conformally invariant. Conditions which recover strong conformal invariance are discussed in the letter. (author)
Test of charge conjugation invariance
International Nuclear Information System (INIS)
Nefkens, B.M.K.; Prakhov, S.; Gaardestig, A.; Clajus, M.; Marusic, A.; McDonald, S.; Phaisangittisakul, N.; Price, J.W.; Starostin, A.; Tippens, W.B.; Allgower, C.E.; Spinka, H.; Bekrenev, V.; Koulbardis, A.; Kozlenko, N.; Kruglov, S.; Lopatin, I.; Briscoe, W.J.; Shafi, A.; Comfort, J.R.
2005-01-01
We report on the first determination of upper limits on the branching ratio (BR) of η decay to π 0 π 0 γ and to π 0 π 0 π 0 γ. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(η→π 0 π 0 γ) -4 at the 90% confidence level, in support of C invariance of isoscalar electromagnetic interactions of the light quarks. We have also measured BR(η→π 0 π 0 π 0 γ) -5 at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions
A novel role for Twist-1 in pulp homeostasis.
Galler, K M; Yasue, A; Cavender, A C; Bialek, P; Karsenty, G; D'Souza, R N
2007-10-01
The molecular mechanisms that maintain the equilibrium of odontoblast progenitor cells in dental pulp are unknown. Here we tested whether homeostasis in dental pulp is modulated by Twist-1, a nuclear protein that partners with Runx2 during osteoblast differentiation. Our analysis of Twist-1(+/-) mice revealed phenotypic changes that involved an earlier onset of dentin matrix formation, increased alkaline phosphatase activity, and pulp stones within the pulp. RT-PCR analyses revealed Twist-1 expression in several adult organs, including pulp. Decreased levels of Twist-1 led to higher levels of type I collagen and Dspp gene expression in perivascular cells associated with the pulp stones. In mice heterozygous for both Twist-1 and Runx2 inactivation, the phenotype of pulp stones appeared completely rescued. These findings suggest that Twist-1 plays a key role in restraining odontoblast differentiation, thus maintaining homeostasis in dental pulp. Furthermore, Twist-1 functions in dental pulp are dependent on its interaction with Runx2.
Relating measurement invariance, cross-level invariance, and multilevel reliability
Jak, S.; Jorgensen, T.D.
2017-01-01
Data often have a nested, multilevel structure, for example when data are collected from children in classrooms. This kind of data complicate the evaluation of reliability and measurement invariance, because several properties can be evaluated at both the individual level and the cluster level, as well as across levels. For example, cross-level invariance implies equal factor loadings across levels, which is needed to give latent variables at the two levels a similar interpretation. Reliabili...
Invariant and semi-invariant probabilistic normed spaces
Energy Technology Data Exchange (ETDEWEB)
Ghaemi, M.B. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: mghaemi@iust.ac.ir; Lafuerza-Guillen, B. [Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, Almeria E-04120 (Spain)], E-mail: blafuerz@ual.es; Saiedinezhad, S. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: ssaiedinezhad@yahoo.com
2009-10-15
Probabilistic metric spaces were introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger . We introduce the concept of semi-invariance among the PN spaces. In this paper we will find a sufficient condition for some PN spaces to be semi-invariant. We will show that PN spaces are normal spaces. Urysohn's lemma, and Tietze extension theorem for them are proved.
The Dynamical Invariant of Open Quantum System
Wu, S. L.; Zhang, X. Y.; Yi, X. X.
2015-01-01
The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the dynamical invariant for the closed quantum system, the evolution of the dynamical invariant for the open quantum system is no longer unitary, and the eigenvalues of it are time-dependent. Since any hermitian operator fulfilling dynamical invariant condition ...
On density of the Vassiliev invariants
DEFF Research Database (Denmark)
Røgen, Peter
1999-01-01
The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots......The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots...
Invariant measures in brain dynamics
International Nuclear Information System (INIS)
Boyarsky, Abraham; Gora, Pawel
2006-01-01
This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a 'folding' property on the space of ensembles
The invariant theory of matrices
Concini, Corrado De
2017-01-01
This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case...
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.
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)
Object recognition by implicit invariants
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Kautsky, J.; Šroubek, Filip
2007-01-01
Roč. 2007, č. 4673 (2007), s. 856-863 ISSN 0302-9743. [Computer Analysis of Images and Patterns. Vienna, 27.08.2007-29.08.2007] R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : Invariants * implicit invariants * moments * orthogonal polynomials * nonlinear object deformation Subject RIV: JD - Computer Applications, Robotics Impact factor: 0.402, year: 2005 http:// staff .utia.cas.cz/sroubekf/papers/CAIP_07.pdf
Classification of simple current invariants
Gato-Rivera, Beatriz
1992-01-01
We summarize recent work on the classification of modular invariant partition functions that can be obtained with simple currents in theories with a center (Z_p)^k with p prime. New empirical results for other centers are also presented. Our observation that the total number of invariants is monodromy-independent for (Z_p)^k appears to be true in general as well. (Talk presented in the parallel session on string theory of the Lepton-Photon/EPS Conference, Geneva, 1991.)
Affine invariants of convex polygons.
Flusser, Jan
2002-01-01
In this correspondence, we prove that the affine invariants, for image registration and object recognition, proposed recently by Yang and Cohen (see ibid., vol.8, no.7, p.934-46, July 1999) are algebraically dependent. We show how to select an independent and complete set of the invariants. The use of this new set leads to a significant reduction of the computing complexity without decreasing the discrimination power.
A New Twisting Somersault: 513XD
Tong, William; Dullin, Holger R.
2017-12-01
We present the mathematical framework of an athlete modelled as a system of coupled rigid bodies to simulate platform and springboard diving. Euler's equations of motion are generalised to non-rigid bodies and are then used to innovate a new dive sequence that in principle can be performed by real-world athletes. We begin by assuming that shape changes are instantaneous so that the equations of motion simplify enough to be solved analytically, and then use this insight to present a new dive (513XD) consisting of 1.5 somersaults and five twists using realistic shape changes. Finally, we demonstrate the phenomenon of converting pure somersaulting motion into pure twisting motion by using a sequence of impulsive shape changes, which may have applications in other fields such as space aeronautics.
Chiral tunneling in a twisted graphene bilayer.
He, Wen-Yu; Chu, Zhao-Dong; He, Lin
2013-08-09
The perfect transmission in a graphene monolayer and the perfect reflection in a Bernal graphene bilayer for electrons incident in the normal direction of a potential barrier are viewed as two incarnations of the Klein paradox. Here we show a new and unique incarnation of the Klein paradox. Owing to the different chiralities of the quasiparticles involved, the chiral fermions in a twisted graphene bilayer show an adjustable probability of chiral tunneling for normal incidence: they can be changed from perfect tunneling to partial or perfect reflection, or vice versa, by controlling either the height of the barrier or the incident energy. As well as addressing basic physics about how the chiral fermions with different chiralities tunnel through a barrier, our results provide a facile route to tune the electronic properties of the twisted graphene bilayer.
Factorising the 3D topologically twisted index
Energy Technology Data Exchange (ETDEWEB)
Cabo-Bizet, Alejandro [Instituto de Astronomía y Física del Espacio (CONICET-UBA),Ciudad Universitaria, C.P. 1428, Buenos Aires (Argentina)
2017-04-20
We explore the path integration — upon the contour of hermitian (non-auxliary) field configurations — of topologically twisted N=2 Chern-Simons-matter theory (TTCSM) on S{sub 2} times a segment. In this way, we obtain the formula for the 3D topologically twisted index, first as a convolution of TTCSM on S{sub 2} times halves of S{sub 1}, second as TTCSM on S{sub 2} times S{sub 1} — with a puncture, — and third as TTCSM on S{sub 2}×S{sub 1}. In contradistinction to the first two cases, in the third case, the vector multiplet auxiliary field D is constrained to be anti-hermitian.
IRONY IN CHARLES DICKEN'S OLIVER TWIST
Directory of Open Access Journals (Sweden)
Ika Kana Trisnawati
2016-05-01
Full Text Available This paper describes the types of irony used by Charles Dickens in his notable early work, Oliver Twist, as well as the reasons the irony was chosen. As a figurative language, irony is utilized to express one’s complex feelings without truly saying them. In Oliver Twist, Dickens brought the readers some real social issues wrapped in dark, deep written expressions of irony uttered by the characters of his novel. Undoubtedly, the novel had left an impact to the British society at the time. The irony Dickens displayed here includes verbal, situational, and dramatic irony. His choice of irony made sense as he intended to criticize the English Poor Laws and to touch the public sentiment. He wanted to let the readers go beyond what was literally written and once they discovered what the truth was, they would eventually understand Dickens’ purposes.
Valve-aided twisted Savonius rotor
Energy Technology Data Exchange (ETDEWEB)
Jaya Rajkumar, M.; Saha, U.K.
2006-05-15
Accessories, such as end plates, deflecting plates, shielding and guide vanes, may increase the power of a Savonius rotor, but make the system structurally complex. In such cases, the rotor can develop a relatively large torque at small rotational speeds and is cheap to build, however it harnesses only a small fraction of the incident wind energy. Another proposition for increasing specific output is to place non-return valves inside the concave side of the blades. Such methods have been studied experimentally with a twisted-blade Thus improving a Savonius rotor's energy capture. This new concept has been named as the 'Valve-Aided Twisted Savonius'rotor. Tests were conducted in a low-speed wind tunnel to evaluate performance. This mechanism is found to be independent of flow direction, and shows potential for large machines. [Author].
Energy Technology Data Exchange (ETDEWEB)
Anikin, I.V. [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation); Ivanov, D.Yu. [Sobolev Institute of Mathematics, 630090 Novosibirsk (Russian Federation); Pire, B., E-mail: pire@cpht.polytechnique.f [CPHT, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex (France); Szymanowski, L. [Soltan Institute for Nuclear Studies, PL-00-681 Warsaw (Poland); Wallon, S. [LPT, Universite Paris-Sud, CNRS, 91405 Orsay (France); UPMC Univ. Paris 06, faculte de physique, 4 place Jussieu, 75252 Paris Cedex 05 (France)
2010-03-21
We describe a consistent approach to factorization of scattering amplitudes for exclusive processes beyond the leading twist approximation. The method involves the Taylor expansion of the scattering amplitude in the momentum space around the dominant light-cone direction and thus naturally introduces an appropriate set of non-perturbative correlators which encode effects not only of the lowest but also of the higher Fock states of the produced particle. The reduction of original set of correlators to a set of independent ones is achieved with the help of equations of motion and invariance of the scattering amplitude under rotation on the light cone. We compare the proposed method with the covariant method formulated in the coordinate space, based on the operator product expansion. We prove the equivalence of two proposed parametrizations of the rho{sub T} distribution amplitudes. As a concrete application, we compute the expressions of the impact factor for the transition of virtual photon to transversally polarised rho-meson up to the twist 3 accuracy within these two quite different methods and show that they are identical.
Chiral Tunnelling in Twisted Graphene Bilayer
He, Wen-Yu; Chu, Zhao-Dong; He, Lin
2013-01-01
The perfect transmission in graphene monolayer and the perfect reflection in Bernal graphene bilayer for electrons incident in the normal direction of a potential barrier are viewed as two incarnations of the Klein paradox. Here we show a new and unique incarnation of the Klein paradox. Owing to the different chiralities of the quasiparticles involved, the chiral fermions in twisted graphene bilayer shows adjustable probability of chiral tunnelling for normal incidence: they can be changed fr...
Vacuum expectation value of twist fields
Belitsky, A. V.
2017-09-01
Twist fields emerge in a number of physical applications ranging from entanglement entropy to scattering amplitudes in four-dimensional gauge theories. In this work, their vacuum expectation values are studied in the path integral framework. By performing a gauge transformation, their correlation functions are reduced to field theory of matter fields in external Aharonov-Bohm vortices. The resulting functional determinants are then analyzed within the zeta-function regularization for the spectrum of Bessel zeros, and concise formulas are derived.
Exploring exotic states with twisted boundary conditions
International Nuclear Information System (INIS)
Agadjanov, Dimitri
2017-01-01
he goal of this thesis is to develop methods to study the nature and properties of exotic hadrons from lattice simulations. The main focus lies in the application of twisted boundary conditions. The thesis consists of a general introduction and the collection of three papers, represented respectively in three chapters. The introduction of the thesis reviews the theoretical background, which is further used in the rest of the thesis. Further implementing partially twisted boundary conditions in the scalar sector of lattice QCD is studied. Then we develop a method to study the content of the exotic hadrons by determining the wave function renormalization constant from lattice simulations, exploiting the dependence of the spectrum on the twisted boundary conditions. The final chapter deals with a novel method to study the multi-channel scattering problem in a finite volume, which is relevant for exotic states. Its key idea is to extract the complex hadron-hadron optical potential, avoiding the difficulties, associated with the solution of the multi-channel Luescher equation.
Exploring exotic states with twisted boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Agadjanov, Dimitri
2017-09-11
he goal of this thesis is to develop methods to study the nature and properties of exotic hadrons from lattice simulations. The main focus lies in the application of twisted boundary conditions. The thesis consists of a general introduction and the collection of three papers, represented respectively in three chapters. The introduction of the thesis reviews the theoretical background, which is further used in the rest of the thesis. Further implementing partially twisted boundary conditions in the scalar sector of lattice QCD is studied. Then we develop a method to study the content of the exotic hadrons by determining the wave function renormalization constant from lattice simulations, exploiting the dependence of the spectrum on the twisted boundary conditions. The final chapter deals with a novel method to study the multi-channel scattering problem in a finite volume, which is relevant for exotic states. Its key idea is to extract the complex hadron-hadron optical potential, avoiding the difficulties, associated with the solution of the multi-channel Luescher equation.
Transverse kink oscillations in the presence of twist
Terradas, J.; Goossens, M.
2012-12-01
Context. Magnetic twist is thought to play an important role in coronal loops. The effects of magnetic twist on stable magnetohydrodynamic (MHD) waves is poorly understood because they are seldom studied for relevant cases. Aims: The goal of this work is to study the fingerprints of magnetic twist on stable transverse kink oscillations. Methods: We numerically calculated the eigenmodes of propagating and standing MHD waves for a model of a loop with magnetic twist. The azimuthal component of the magnetic field was assumed to be small in comparison to the longitudinal component. We did not consider resonantly damped modes or kink instabilities in our analysis. Results: For a nonconstant twist the frequencies of the MHD wave modes are split, which has important consequences for standing waves. This is different from the degenerated situation for equilibrium models with constant twist, which are characterised by an azimuthal component of the magnetic field that linearly increases with the radial coordinate. Conclusions: In the presence of twist standing kink solutions are characterised by a change in polarisation of the transverse displacement along the tube. For weak twist, and in the thin tube approximation, the frequency of standing modes is unaltered and the tube oscillates at the kink speed of the corresponding straight tube. The change in polarisation is linearly proportional to the degree of twist. This has implications with regard to observations of kink modes, since the detection of this variation in polarisation can be used as an indirect method to estimate the twist in oscillating loops.
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)
Design optimization for active twist rotor blades
Mok, Ji Won
This dissertation introduces the process of optimizing active twist rotor blades in the presence of embedded anisotropic piezo-composite actuators. Optimum design of active twist blades is a complex task, since it involves a rich design space with tightly coupled design variables. The study presents the development of an optimization framework for active helicopter rotor blade cross-sectional design. This optimization framework allows for exploring a rich and highly nonlinear design space in order to optimize the active twist rotor blades. Different analytical components are combined in the framework: cross-sectional analysis (UM/VABS), an automated mesh generator, a beam solver (DYMORE), a three-dimensional local strain recovery module, and a gradient based optimizer within MATLAB. Through the mathematical optimization problem, the static twist actuation performance of a blade is maximized while satisfying a series of blade constraints. These constraints are associated with locations of the center of gravity and elastic axis, blade mass per unit span, fundamental rotating blade frequencies, and the blade strength based on local three-dimensional strain fields under worst loading conditions. Through pre-processing, limitations of the proposed process have been studied. When limitations were detected, resolution strategies were proposed. These include mesh overlapping, element distortion, trailing edge tab modeling, electrode modeling and foam implementation of the mesh generator, and the initial point sensibility of the current optimization scheme. Examples demonstrate the effectiveness of this process. Optimization studies were performed on the NASA/Army/MIT ATR blade case. Even though that design was built and shown significant impact in vibration reduction, the proposed optimization process showed that the design could be improved significantly. The second example, based on a model scale of the AH-64D Apache blade, emphasized the capability of this framework to
Simulating QCD at the physical point with Nf=2 Wilson twisted mass fermions at maximal twist
International Nuclear Information System (INIS)
Abdel-Rehim, A.; Alexandrou, C.; Cyprus Univ. Nicosia; Burger, F.
2015-12-01
We present simulations of QCD using N f =2 dynamical Wilson twisted mass lattice QCD with physical value of the pion mass and at one value of the lattice spacing. Such simulations at a∼0.09 fm became possible by adding the clover term to the action. While O(a) improvement is still guaranteed by Wilson twisted mass fermions at maximal twist, the introduction of the clover term reduces O(a 2 ) cutoff effects related to isospin symmetry breaking. We give results for a set of phenomenologically interesting observables like pseudo-scalar masses and decay constants, quark masses and the anomalous magnetic moments of leptons. We mostly find remarkably good agreement with phenomenology, even though we cannot take the continuum and thermodynamic limits.
Identification of invariant measures of interacting systems
International Nuclear Information System (INIS)
Chen Jinwen
2004-01-01
In this paper we provide an approach for identifying certain mixture representations of some invariant measures of interacting stochastic systems. This is related to the problem of ergodicity of certain extremal invariant measures that are translation invariant. Corresponding to these, results concerning the existence of invariant measures and certain weak convergence of the systems are also provided
Link invariants from finite Coxeter racks
Nelson, Sam; Wieghard, Ryan
2008-01-01
We study Coxeter racks over $\\mathbb{Z}_n$ and the knot and link invariants they define. We exploit the module structure of these racks to enhance the rack counting invariants and give examples showing that these enhanced invariants are stronger than the unenhanced rack counting invariants.
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.
The Obstruction criterion for non existence of Invariant Circles and Renormalization.
De la Llave, R
2003-01-01
We formulate a conjecture which supplements the standard renormalization scenario for the breakdown of golden circle in twist maps. We show rigorously that if the conjecture was true then: a) The stable manifold of the non-trivial fixed point would indeed be a boundary between the existence of smooth invariant tori and hyperbolic orbits with golden mean rotation number. In particular, the boundary of the set of twist maps with a torus with a golden mean rotation number would include a smooth submanifold in the space of analytic mappings. b) The obstruction criterion of [Olvera-Simo] would be sharp in the universality class of the renormalization group. c) The criterion of [Greene-79] for existence of invariant circles if and only if there the residues of approximating orbits are finite would be valid for maps in the universality class. d) If there is no invariant circle, there are hyperbolic sets with golden mean rotation number. We also provide numerical evidence which suggests that the conjecture is true an...
Ten helical twist angles of B-DNA
Energy Technology Data Exchange (ETDEWEB)
Kabsch, W; Sander, C; Trifonov, E N
1982-01-01
On the assumption that the twist angles between adjacent base-pairs in the DNA molecule are additive a linear system of 40 equations was derived from experimental measurements of the total twist angles for different pieces of DNA of known sequences. This system of equations is found to be statistically consistent providing a solution for all ten possible twist angles of B-DNA by a least squares fitting procedure. Four of the calculated twist angles were not known before. The other six twist angles calculated are very close to the experimentally measured ones. The data used were obtained by the electrophoretic band-shift method, crystallography and nuclease digestion of DNA adsorbed to mica or Ca-phosphate surface. The validity of the principle of additivity of the twist angles implies that the angle between any particular two base-pairs is a function of only these base-pairs, independent of nearest neighbors.
Nonlocal, yet translation invariant, constraints for rotationally invariant slave bosons
Ayral, Thomas; Kotliar, Gabriel
The rotationally-invariant slave boson (RISB) method is a lightweight framework allowing to study the low-energy properties of complex multiorbital problems currently out of the reach of more comprehensive, yet more computationally demanding methods such as dynamical mean field theory. In the original formulation of this formalism, the slave-boson constraints can be made nonlocal by enlarging the unit cell and viewing the quantum states enclosed in this new unit cell as molecular levels. In this work, we extend RISB to constraints which are nonlocal while preserving translation invariance. We apply this extension to the Hubbard model.
Twisted Vanes Would Enhance Fuel/Air Mixing In Turbines
Nguyen, H. Lee; Micklow, Gerald J.; Dogra, Anju S.
1994-01-01
Computations of flow show performance of high-shear airblast fuel injector in gas-turbine engine enhanced by use of appropriately proportioned twisted (instead of flat) dome swirl vanes. Resultant more nearly uniform fuel/air mixture burns more efficiently, emitting smaller amounts of nitrogen oxides. Twisted-vane high-shear airblast injectors also incorporated into paint sprayers, providing advantages of low pressure drop characteristic of airblast injectors in general and finer atomization of advanced twisted-blade design.
Knot invariants and M-theory: Proofs and derivations
Errasti Díez, Verónica
2018-01-01
We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory models. We show that this theory has indeed all required properties to host knots. Our analysis provides a unifying picture of the various recent works that attempt an understanding of knot invariants using techniques of four-dimensional physics. This is a companion paper to K. Dasgupta, V. Errasti Díez, P. Ramadevi, and R. Tatar, Phys. Rev. D 95, 026010 (2017), 10.1103/PhysRevD.95.026010, covering all but Sec. III C. It presents a detailed mathematical derivation of the main results there, as well as additional material. Among the new insights, those related to supersymmetry and the topological twist are highlighted. This paper offers an alternative, complementary formulation of the contents in the first paper, but is self-contained and can be read independently.
Twisted rudder for reducing fuel-oil consumption
Directory of Open Access Journals (Sweden)
Jung-Hun Kim
2014-09-01
Full Text Available Three twisted rudders fit for large container ships have been developed; 1 the Z-twisted rudder that is an asymmetry type taking into consideration incoming flow angles of the propeller slipstream, 2 the ZB-twisted rudder with a rudder bulb added onto the Z-twisted rudder, and 3 the ZB-F twisted rudder with a rudder fin attached to the ZB-twisted rudder. The twisted rudders have been designed computationally with the hydrodynamic characteristics in a self-propulsion condition in mind. The governing equation is the Navier-Stokes equations in an unsteady turbulent flow. The turbulence model applied is the Reynolds stress. The calculation was carried out in towing and self-propulsion conditions. The sliding mesh technique was employed to simulate the flow around the propeller. The speed performances of the ship with the twisted rudders were verified through model tests in a towing tank. The twisted versions showed greater performance driven by increased hull efficiency from less thrust deduction fraction and more effective wake fraction and decreased propeller rotating speed.
Higher twist contributions to deep-inelastic structure functions
International Nuclear Information System (INIS)
Bluemlein, J.; Boettcher, H.
2008-07-01
We report on a recent extraction of the higher twist contributions to the deep inelastic structure functions F ep,ed 2 (x,Q 2 ) in the large x region. It is shown that the size of the extracted higher twist contributions is strongly correlated with the higher order corrections applied to the leading twist part. A gradual lowering of the higher twist contributions going from NLO to N 4 LO is observed, where in the latter case only the leading large x terms were considered. (orig.)
Twisted sigma-model solitons on the quantum projective line
Landi, Giovanni
2018-04-01
On the configuration space of projections in a noncommutative algebra, and for an automorphism of the algebra, we use a twisted Hochschild cocycle for an action functional and a twisted cyclic cocycle for a topological term. The latter is Hochschild-cohomologous to the former and positivity in twisted Hochschild cohomology results into a lower bound for the action functional. While the equations for the critical points are rather involved, the use of the positivity and the bound by the topological term lead to self-duality equations (thus yielding twisted noncommutative sigma-model solitons, or instantons). We present explicit nontrivial solutions on the quantum projective line.
Bound states on the lattice with partially twisted boundary conditions
International Nuclear Information System (INIS)
Agadjanov, D.; Guo, F.-K.; Ríos, G.; Rusetsky, A.
2015-01-01
We propose a method to study the nature of exotic hadrons by determining the wave function renormalization constant Z from lattice simulations. It is shown that, instead of studying the volume-dependence of the spectrum, one may investigate the dependence of the spectrum on the twisting angle, imposing twisted boundary conditions on the fermion fields on the lattice. In certain cases, e.g., the case of the DK bound state which is addressed in detail, it is demonstrated that the partial twisting is equivalent to the full twisting up to exponentially small corrections.
Invariant probabilities of transition functions
Zaharopol, Radu
2014-01-01
The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of t...
Invariants of triangular Lie algebras
International Nuclear Information System (INIS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-01-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated
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
$\\kappa$-Minkowski star product in any dimension from symplectic realization
Pachol, Anna; Vitale, Patrizia
2015-01-01
We derive an explicit expression for the star product reproducing the $\\kappa$-Minkowski Lie algebra in any dimension $n$. The result is obtained by suitably reducing the Wick-Voros star product defined on $\\mathbb{C}^{d}_\\theta$ with $n=d+1$. It is thus shown that the new star product can be obtained from a Jordanian twist.
Dark coupling and gauge invariance
International Nuclear Information System (INIS)
Gavela, M.B.; Honorez, L. Lopez; Mena, O.; Rigolin, S.
2010-01-01
We study a coupled dark energy-dark matter model in which the energy-momentum exchange is proportional to the Hubble expansion rate. The inclusion of its perturbation is required by gauge invariance. We derive the linear perturbation equations for the gauge invariant energy density contrast and velocity of the coupled fluids, and we determine the initial conditions. The latter turn out to be adiabatic for dark energy, when assuming adiabatic initial conditions for all the standard fluids. We perform a full Monte Carlo Markov Chain likelihood analysis of the model, using WMAP 7-year data
Numeric invariants from multidimensional persistence
Energy Technology Data Exchange (ETDEWEB)
Skryzalin, Jacek [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Carlsson, Gunnar [Stanford Univ., Stanford, CA (United States)
2017-05-19
In this paper, we analyze the space of multidimensional persistence modules from the perspectives of algebraic geometry. We first build a moduli space of a certain subclass of easily analyzed multidimensional persistence modules, which we construct specifically to capture much of the information which can be gained by using multidimensional persistence over one-dimensional persistence. We argue that the global sections of this space provide interesting numeric invariants when evaluated against our subclass of multidimensional persistence modules. Lastly, we extend these global sections to the space of all multidimensional persistence modules and discuss how the resulting numeric invariants might be used to study data.
Dark Coupling and Gauge Invariance
Gavela, M B; Mena, O; Rigolin, S
2010-01-01
We study a coupled dark energy-dark matter model in which the energy-momentum exchange is proportional to the Hubble expansion rate. The inclusion of its perturbation is required by gauge invariance. We derive the linear perturbation equations for the gauge invariant energy density contrast and velocity of the coupled fluids, and we determine the initial conditions. The latter turn out to be adiabatic for dark energy, when assuming adiabatic initial conditions for all the standard fluids. We perform a full Monte Carlo Markov Chain likelihood analysis of the model, using WMAP 7-year data.
Relating measurement invariance, cross-level invariance, and multilevel reliability
Jak, S.; Jorgensen, T.D.
2017-01-01
Data often have a nested, multilevel structure, for example when data are collected from children in classrooms. This kind of data complicate the evaluation of reliability and measurement invariance, because several properties can be evaluated at both the individual level and the cluster level, as
Twisting and Writhing with George Ellery Hale
Canfield, Richard C.
2013-06-01
Early in his productive career in astronomy, George Ellery Hale developed innovative solar instrumentation that allowed him to make narrow-band images. Among the solar phenomena he discovered were sunspot vortices, which he attributed to storms akin to cyclones in our own atmosphere. Using the concept of magnetic helicity, physicists and mathematicians describe the topology of magnetic fields, including twisting and writhing. Our contemporary understanding of Hale's vortices as a consequence of large-scale twist in sunspot magnetic fields hinges on a key property of helicity: conservation. I will describe the critical role that this property plays, when applied to twist and writhe, in a fundamental aspect of global solar magnetism: the hemispheric and solar cycle dependences of active region electric currents with respect to magnetic fields. With the advent of unbroken sequences of high-resolution magnetic images, such as those presently available from the Helioseismic and Magnetic Imager on Solar Dynamics Observatory, the flux of magnetic helicity through the photosphere can be observed quantitatively. As magnetic flux tubes buoy up through the convection zone, buffeted and shredded by turbulence, they break up into fragments by repeated random bifurcation. We track these rising flux fragments in the photosphere, and calculate the flux of energy and magnetic helicity there. Using a quantitative model of coronal currents, we also track connections between these fragments to calculate the energy and magnetic helicity stored at topological interfaces that are in some ways analogous to the storage of stress at faults in the Earth's crust. Comparison of these values to solar flares and interplanetary coronal mass ejections implies that this is the primary storage mechanism for energy and magnetic helicity released in those phenomena, and suggests a useful tool for quantitative prediction of geomagnetic storms.
Twisted Polynomials and Forgery Attacks on GCM
DEFF Research Database (Denmark)
Abdelraheem, Mohamed Ahmed A. M. A.; Beelen, Peter; Bogdanov, Andrey
2015-01-01
Polynomial hashing as an instantiation of universal hashing is a widely employed method for the construction of MACs and authenticated encryption (AE) schemes, the ubiquitous GCM being a prominent example. It is also used in recent AE proposals within the CAESAR competition which aim at providing...... in an improved key recovery algorithm. As cryptanalytic applications of our twisted polynomials, we develop the first universal forgery attacks on GCM in the weak-key model that do not require nonce reuse. Moreover, we present universal weak-key forgeries for the nonce-misuse resistant AE scheme POET, which...
Optical twists in phase and amplitude
DEFF Research Database (Denmark)
Daria, Vincent R.; Palima, Darwin; Glückstad, Jesper
2011-01-01
where both phase and amplitude express a helical profile as the beam propagates in free space. Such a beam can be accurately referred to as an optical twister. We characterize optical twisters and demonstrate their capacity to induce spiral motion on particles trapped along the twisters’ path. Unlike LG...... beams, the far field projection of the twisted optical beam maintains a high photon concentration even at higher values of topological charge. Optical twisters have therefore profound applications to fundamental studies of light and atoms such as in quantum entanglement of the OAM, toroidal traps...
NMSBA - Twist Resist - Rotational Exercise Module
Energy Technology Data Exchange (ETDEWEB)
Walker, Aaron [Twist Resist, Albuquerque, NM (United States); Reece, Blake D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Berger, Jason E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Guido, Steven Frank [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Linker, Taylor [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-08-01
This report contains a summary of the work completed to develop a modular, rotational exercise device. In the report are images, diagrams, and explanations of the efforts contributed to the project since its inception. The purpose of this document is to provide a walk-through of the progress on this project, from the initial design concepts to the final design and work done, so that the customer (Twist Resist), or individuals/firms who work on this project in the future will have a springboard of ideas/concepts to work from.
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.
Processing mechanics of alternate twist ply (ATP) yarn technology
Elkhamy, Donia Said
Ply yarns are important in many textile manufacturing processes and various applications. The primary process used for producing ply yarns is cabling. The speed of cabling is limited to about 35m/min. With the world's increasing demands of ply yarn supply, cabling is incompatible with today's demand activated manufacturing strategies. The Alternate Twist Ply (ATP) yarn technology is a relatively new process for producing ply yarns with improved productivity and flexibility. This technology involves self plying of twisted singles yarn to produce ply yarn. The ATP process can run more than ten times faster than cabling. To implement the ATP process to produce ply yarns there are major quality issues; uniform Twist Profile and yarn Twist Efficiency. The goal of this thesis is to improve these issues through process modeling based on understanding the physics and processing mechanics of the ATP yarn system. In our study we determine the main parameters that control the yarn twist profile. Process modeling of the yarn twist across different process zones was done. A computational model was designed to predict the process parameters required to achieve a square wave twist profile. Twist efficiency, a measure of yarn torsional stability and bulk, is determined by the ratio of ply yarn twist to singles yarn twist. Response Surface Methodology was used to develop the processing window that can reproduce ATP yarns with high twist efficiency. Equilibrium conditions of tensions and torques acting on the yarns at the self ply point were analyzed and determined the pathway for achieving higher twist efficiency. Mechanistic modeling relating equilibrium conditions to the twist efficiency was developed. A static tester was designed to zoom into the self ply zone of the ATP yarn. A computer controlled, prototypic ATP machine was constructed and confirmed the mechanistic model results. Optimum parameters achieving maximum twist efficiency were determined in this study. The
Entendue invariance in speckle fields
International Nuclear Information System (INIS)
Medina, F.F.; Garcia-Sucerquia, J.; Henao, R.; Trivi, M.
2000-04-01
Experimental evidence is shown that confirms the Entendue invariance in speckle fields. Because of this condition, the coherence patch of the speckle field can be significantly greater than the mean size of the speckles, as is shown by double exposure speckle interferometry. (author)
Geometric Invariants and Object Recognition.
1992-08-01
University of Chicago Press. Maybank , S.J. [1992], "The Projection of Two Non-coplanar Conics", in Geometric Invariance in Machine Vision, eds. J.L...J.L. Mundy and A. Zisserman, MIT Press, Cambridge, MA. Mundy, J.L., Kapur, .. , Maybank , S.J., and Quan, L. [1992a] "Geometric Inter- pretation of
On renormalization-invariant masses
International Nuclear Information System (INIS)
Fleming, H.; Furuya, K.
1978-02-01
It is shown that spontaneous generation of renormalization invariant mass is possible in infra-red stable theories with more than one coupling constant. If relations among the coupling constants are permitted the effect can be made compatible with pertubation theory
Gauge invariance of string fields
International Nuclear Information System (INIS)
Banks, T.; Peskin, M.E.
1985-10-01
Some work done to understand the appearance of gauge bosons and gravitons in string theories is reported. An action has been constructed for free (bosonic) string field theory which is invariant under an infinite set of gauge transformations which include Yang-Mills transformations and general coordinate transformations as special cases. 15 refs., 1 tab
On reflection algebras and twisted Yangians
International Nuclear Information System (INIS)
Doikou, Anastasia
2005-01-01
It is well known that integrable models associated to rational R matrices give rise to certain non-Abelian symmetries known as Yangians. Analogously boundary symmetries arise when general but still integrable boundary conditions are implemented, as originally argued by Delius, Mackay, and Short from the field theory point of view, in the context of the principal chiral model on the half-line. In the present study we deal with a discrete quantum mechanical system with boundaries, that is the N site gl(n) open quantum spin chain. In particular, the open spin chain with two distinct types of boundary condition known as soliton preserving and soliton nonpreserving is considered. For both types of boundaries we present a unified framework for deriving the corresponding boundary nonlocal charges directly at the quantum level. The nonlocal charges are simply coproduct realizations of particular boundary quantum algebras called boundary or twisted Yangians, depending on the choice of boundary conditions. Finally, with the help of linear intertwining relations between the solutions of the reflection equation and the generators of the boundary or twisted Yangians we are able to exhibit the exact symmetry of the open spin chain, namely we show that a number of the boundary nonlocal charges are in fact conserved quantities
How the embryonic brain tube twists
Chen, Zi; Guo, Qiaohang; Forsch, Nickolas; Taber, Larry
2014-03-01
During early development, the tubular brain of the chick embryo undergoes a combination of progressive ventral bending and rightward torsion. This deformation is one of the major organ-level symmetry-breaking events in development. Available evidence suggests that bending is caused by differential growth, but the mechanism for torsion remains poorly understood. Since the heart almost always loops in the same direction that the brain twists, researchers have speculated that heart looping affects the direction of brain torsion. However, direct evidence is virtually nonexistent, nor is the mechanical origin of such torsion understood. In our study, experimental perturbations show that the bending and torsional deformations in the brain are coupled and that the vitelline membrane applies an external load necessary for torsion to occur. In addition, the asymmetry of the looping heart gives rise to the chirality of the twisted brain. A computational model is used to interpret these findings. Our work clarifies the mechanical origins of brain torsion and the associated left-right asymmetry, reminiscent of D'Arcy Thompson's view of biological form as ``diagram of forces''.
Drag Performance of Twist Morphing MAV Wing
Directory of Open Access Journals (Sweden)
Ismail N.I.
2016-01-01
Full Text Available Morphing wing is one of latest evolution found on MAV wing. However, due to few design problems such as limited MAV wing size and complicated morphing mechanism, the understanding of its aerodynamic behaviour was not fully explored. In fact, the basic drag distribution induced by a morphing MAV wing is still remained unknown. Thus, present work is carried out to compare the drag performance between a twist morphing wing with membrane and rigid MAV wing design. A quasi-static aeroelastic analysis by using the Ansys-Fluid Structure Interaction (FSI method is utilized in current works to predict the drag performance a twist morphing MAV wing design. Based on the drag pattern study, the results exhibits that the morphing wing has a partial similarities in overall drag pattern with the baseline (membrane and rigid wing. However, based CD analysis, it shows that TM wing induced higher CD magnitude (between 25% to 82% higher than to the baseline wing. In fact, TM wing also induced the largest CD increment (about 20% to 27% among the wings. The visualization on vortex structure revealed that TM wing also produce larger tip vortex structure (compared to baseline wings which presume to promote higher induce drag component and subsequently induce its higher CD performance.
Strong CP, flavor, and twisted split fermions
International Nuclear Information System (INIS)
Harnik, Roni; Perez, Gilad; Schwartz, Matthew D.; Shirman, Yuri
2005-01-01
We present a natural solution to the strong CP problem in the context of split fermions. By assuming CP is spontaneously broken in the bulk, a weak CKM phase is created in the standard model due to a twisting in flavor space of the bulk fermion wavefunctions. But the strong CP phase remains zero, being essentially protected by parity in the bulk and CP on the branes. As always in models of spontaneous CP breaking, radiative corrections to theta bar from the standard model are tiny, but even higher dimension operators are not that dangerous. The twisting phenomenon was recently shown to be generic, and not to interfere with the way that split fermions naturally weaves small numbers into the standard model. It follows that out approach to strong CP is compatible with flavor, and we sketch a comprehensive model. We also look at deconstructed version of this setup which provides a viable 4D model of spontaneous CP breaking which is not in the Nelson-Barr class. (author)
Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang
2015-01-23
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.
Quadratic Twists of Rigid Calabi–Yau Threefolds Over
DEFF Research Database (Denmark)
Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko
2013-01-01
of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...
Bend-twist coupling potential of wind turbine blades
DEFF Research Database (Denmark)
Fedorov, Vladimir; Berggreen, Christian
2014-01-01
-twist coupling magnitude of up to 0.2 is feasible to achieve in the baseline blade structure made of glass-fiber reinforced plastics. Further, by substituting the glass-fibers with carbon-fibers the coupling effect can be increased to 0.4. Additionally, the effect of introduction of bend-twist coupling...
A twisted generalization of Novikov-Poisson algebras
Yau, Donald
2010-01-01
Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products and several kinds of twistings. Necessary and sufficient conditions are given under which Hom-Novikov-Poisson algebras give rise to Hom-Poisson algebras.
Twisted Acceleration-Enlarged Newton-Hooke Hopf Algebras
International Nuclear Information System (INIS)
Daszkiewicz, M.
2010-01-01
Ten Abelian twist deformations of acceleration-enlarged Newton-Hooke Hopf algebra are considered. The corresponding quantum space-times are derived as well. It is demonstrated that their contraction limit τ → ∞ leads to the new twisted acceleration-enlarged Galilei spaces. (author)
Enhancement of heat transfer using varying width twisted tape inserts
African Journals Online (AJOL)
user
enhancement of heat transfer with twisted tape inserts as compared to plain ... studies for heat transfer and pressure drop of laminar flow in horizontal tubes ... flow in rectangular and square plain ducts and ducts with twisted-tape inserts .... presence of the insert in the pipe causes resistance to flow and increases turbulence.
Electronic and Optical Properties of Twisted Bilayer Graphene
Huang, Shengqiang
The ability to isolate single atomic layers of van der Waals materials has led to renewed interest in the electronic and optical properties of these materials as they can be fundamentally different at the monolayer limit. Moreover, these 2D crystals can be assembled together layer by layer, with controllable sequence and orientation, to form artificial materials that exhibit new features that are not found in monolayers nor bulk. Twisted bilayer graphene is one such prototype system formed by two monolayer graphene layers placed on top of each other with a twist angle between their lattices, whose electronic band structure depends on the twist angle. This thesis presents the efforts to explore the electronic and optical properties of twisted bilayer graphene by Raman spectroscopy and scanning tunneling microscopy measurements. We first synthesize twisted bilayer graphene with various twist angles via chemical vapor deposition. Using a combination of scanning tunneling microscopy and Raman spectroscopy, the twist angles are determined. The strength of the Raman G peak is sensitive to the electronic band structure of twisted bilayer graphene and therefore we use this peak to monitor changes upon doping. Our results demonstrate the ability to modify the electronic and optical properties of twisted bilayer graphene with doping. We also fabricate twisted bilayer graphene by controllable stacking of two graphene monolayers with a dry transfer technique. For twist angles smaller than one degree, many body interactions play an important role. It requires eight electrons per moire unit cell to fill up each band instead of four electrons in the case of a larger twist angle. For twist angles smaller than 0.4 degree, a network of domain walls separating AB and BA stacking regions forms, which are predicted to host topologically protected helical states. Using scanning tunneling microscopy and spectroscopy, these states are confirmed to appear on the domain walls when inversion
d $\\leq$ 1 U d $\\geq$ 25 and W constraints from BRST invariance in the C $\
Gato-Rivera, Beatriz
1992-01-01
The BRST invariance condition in a highest-weight representation of the topological ($\\equiv$ twisted $N=2$) algebra captures the `invariant' content of two-dimensional gravity coupled to matter. The standard DDK formulation is recovered by splitting the topological generators into $c=-26$ reparametrization ghosts+matter +`Liouville', while a similar splitting involving $c=-2$ ghosts gives rise to the matter dressed in exactly the way required in order that the theory be equivalent to Virasoro constraints on the KP hierarchy. The two dressings of matter with the `Liouville' differ also by their `ghost numbers', which is similar to the existence of representatives of BRST cohomologies with different ghost numbers. The topological central charge $\\ctop\
The light-front gauge-invariant energy-momentum tensor
International Nuclear Information System (INIS)
Lorce, Cedric
2015-01-01
In this study, we provide for the first time a complete parametrization for the matrix elements of the generic asymmetric, non-local and gauge-invariant canonical energy-momentum tensor, generalizing therefore former works on the symmetric, local and gauge-invariant kinetic energy-momentum tensor also known as the Belinfante-Rosenfeld energy-momentum tensor. We discuss in detail the various constraints imposed by non-locality, linear and angular momentum conservation. We also derive the relations with two-parton generalized and transverse-momentum dependent distributions, clarifying what can be learned from the latter. In particular, we show explicitly that two-parton transverse-momentum dependent distributions cannot provide any model-independent information about the parton orbital angular momentum. On the way, we recover the Burkardt sum rule and obtain similar new sum rules for higher-twist distributions
Duality and braiding in twisted quantum field theory
International Nuclear Information System (INIS)
Riccardi, Mauro; Szabo, Richard J.
2008-01-01
We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green's functions in the noncommutative and commutative theories, causality, and the absence of UV/IR mixing. We use these fields to define the functional integral formulation of twisted quantum field theory. We exploit techniques from braided tensor algebra to argue that the twisted Fock space states of these free fields obey conventional statistics. We support our claims with a detailed analysis of the modifications induced in the presence of background magnetic fields, which induces additional twists by magnetic translation operators and alters the effective noncommutative geometry seen by the twisted quantum fields. When two such field theories are dual to one another, we demonstrate that only our braided physical states are covariant under the duality
Analysis list: Twist1 [Chip-atlas[Archive
Lifescience Database Archive (English)
Full Text Available Twist1 Embryo,Neural + mm9 http://dbarchive.biosciencedbc.jp/kyushu-u/mm9/target/Tw...ist1.1.tsv http://dbarchive.biosciencedbc.jp/kyushu-u/mm9/target/Twist1.5.tsv http://dbarchive.biosciencedbc....jp/kyushu-u/mm9/target/Twist1.10.tsv http://dbarchive.biosciencedbc.jp/kyushu-u/mm9/colo/Twist1.Embryo.tsv,http://dbarchive.bioscien...cedbc.jp/kyushu-u/mm9/colo/Twist1.Neural.tsv http://dbarchive.bioscience...dbc.jp/kyushu-u/mm9/colo/Embryo.gml,http://dbarchive.biosciencedbc.jp/kyushu-u/mm9/colo/Neural.gml ...
On the performance analysis of Savonius rotor with twisted blades
Energy Technology Data Exchange (ETDEWEB)
Saha, U.K.; Rajkumar, M. Jaya [Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati-781 039 (India)
2006-09-15
The present investigation is aimed at exploring the feasibility of twisted bladed Savonius rotor for power generation. The twisted blade in a three-bladed rotor system has been tested in a low speed wind tunnel, and its performance has been compared with conventional semicircular blades (with twist angle of 0{sup o}). Performance analysis has been made on the basis of starting characteristics, static torque and rotational speed. Experimental evidence shows the potential of the twisted bladed rotor in terms of smooth running, higher efficiency and self-starting capability as compared to that of the conventional bladed rotor. Further experiments have been conducted in the same setup to optimize the twist angle. (author)
Continuous Integrated Invariant Inference, Phase I
National Aeronautics and Space Administration — The proposed project will develop a new technique for invariant inference and embed this and other current invariant inference and checking techniques in an...
Gauge-invariant cosmological density perturbations
International Nuclear Information System (INIS)
Sasaki, Misao.
1986-06-01
Gauge-invariant formulation of cosmological density perturbation theory is reviewed with special emphasis on its geometrical aspects. Then the gauge-invariant measure of the magnitude of a given perturbation is presented. (author)
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
Constructing Invariant Fairness Measures for Surfaces
DEFF Research Database (Denmark)
Gravesen, Jens; Ungstrup, Michael
1998-01-01
of the size of this vector field is used as the fairness measure on the family.Six basic 3rd order invariants satisfying two quadratic equations are defined. They form a complete set in the sense that any invariant 3rd order function can be written as a function of the six basic invariants together...
Gauge invariance and holographic renormalization
Directory of Open Access Journals (Sweden)
Keun-Young Kim
2015-10-01
Full Text Available We study the gauge invariance of physical observables in holographic theories under the local diffeomorphism. We find that gauge invariance is intimately related to the holographic renormalization: the local counter terms defined in the boundary cancel most of gauge dependences of the on-shell action as well as the divergences. There is a mismatch in the degrees of freedom between the bulk theory and the boundary one. We resolve this problem by noticing that there is a residual gauge symmetry (RGS. By extending the RGS such that it satisfies infalling boundary condition at the horizon, we can understand the problem in the context of general holographic embedding of a global symmetry at the boundary into the local gauge symmetry in the bulk.
Gauge invariant fractional electromagnetic fields
International Nuclear Information System (INIS)
Lazo, Matheus Jatkoske
2011-01-01
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.
Gauge invariant fractional electromagnetic fields
Energy Technology Data Exchange (ETDEWEB)
Lazo, Matheus Jatkoske, E-mail: matheuslazo@furg.br [Instituto de Matematica, Estatistica e Fisica - FURG, Rio Grande, RS (Brazil)
2011-09-26
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-01-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Testing CPT invariance with neutrinos
International Nuclear Information System (INIS)
Ohlsson, Tommy
2003-01-01
We investigate possible tests of CPT invariance on the level of event rates at neutrino factories. We do not assume any specific model, but phenomenological differences in the neutrino-antineutrino masses and mixing angles in a Lorentz invariance preserving context, which could be induced by physics beyond the Standard Model. We especially focus on the muon neutrino and antineutrino disappearance channels in order to obtain constraints on the neutrino-antineutrino mass and mixing angle differences. In a typical neutrino factory setup simulation, we find, for example, that vertical bar m 3 - m-bar 3 vertical bar $1.9 · 10 -4 eV and vertical bar ≡ 23 - ≡-bar 23 vertical bar < or approx. 2 deg
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-08-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Wetterich, C.
2018-06-01
We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.
Molecular invariants: atomic group valence
International Nuclear Information System (INIS)
Mundim, K.C.; Giambiagi, M.; Giambiagi, M.S. de.
1988-01-01
Molecular invariants may be deduced in a very compact way through Grassman algebra. In this work, a generalized valence is defined for an atomic group; it reduces to the Known expressions for the case of an atom in a molecule. It is the same of the correlations between the fluctions of the atomic charges qc and qd (C belongs to the group and D does not) around their average values. Numerical results agree with chemical expectation. (author) [pt
Holographic multiverse and conformal invariance
Energy Technology Data Exchange (ETDEWEB)
Garriga, Jaume [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, 08193 Barcelona (Spain); Vilenkin, Alexander, E-mail: jaume.garriga@ub.edu, E-mail: vilenkin@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, 212 College Ave., Medford, MA 02155 (United States)
2009-11-01
We consider a holographic description of the inflationary multiverse, according to which the wave function of the universe is interpreted as the generating functional for a lower dimensional Euclidean theory. We analyze a simple model where transitions between inflationary vacua occur through bubble nucleation, and the inflating part of spacetime consists of de Sitter regions separated by thin bubble walls. In this model, we present some evidence that the dual theory is conformally invariant in the UV.
Holographic multiverse and conformal invariance
International Nuclear Information System (INIS)
Garriga, Jaume; Vilenkin, Alexander
2009-01-01
We consider a holographic description of the inflationary multiverse, according to which the wave function of the universe is interpreted as the generating functional for a lower dimensional Euclidean theory. We analyze a simple model where transitions between inflationary vacua occur through bubble nucleation, and the inflating part of spacetime consists of de Sitter regions separated by thin bubble walls. In this model, we present some evidence that the dual theory is conformally invariant in the UV
Bianisotropic metamaterials based on twisted asymmetric crosses
International Nuclear Information System (INIS)
Reyes-Avendaño, J A; Sampedro, M P; Juárez-Ruiz, E; Pérez-Rodríguez, F
2014-01-01
The effective bianisotropic response of 3D periodic metal-dielectric structures, composed of crosses with asymmetrically-cut wires, is investigated within a general homogenization theory using the Fourier formalism and the form-factor division approach. It is found that the frequency dependence of the effective permittivity for a system of periodically-repeated layers of metal crosses exhibits two strong resonances, whose separation is due to the cross asymmetry. Besides, bianisotropic metamaterials, having a base of four twisted asymmetric crosses, are proposed. The designed metamaterials possess negative refractive index at frequencies determined by the cross asymmetry, the gap between the arms of adjacent crosses lying on the same plane, and the type of Bravais lattice. (papers)
Band engineering in twisted molybdenum disulfide bilayers
Zhao, Yipeng; Liao, Chengwei; Ouyang, Gang
2018-05-01
In order to explore the theoretical relationship between interlayer spacing, interaction and band offset at the atomic level in vertically stacked two-dimensional (2D) van der Waals (vdW) structures, we propose an analytical model to address the evolution of interlayer vdW coupling with random stacking configurations in MoS2 bilayers based on the atomic-bond-relaxation correlation mechanism. We found that interlayer spacing changes substantially with respect to the orientations, and the bandgap increases from 1.53 eV (AB stacking) to 1.68 eV (AA stacking). Our results reveal that the evolution of interlayer vdW coupling originates from the interlayer interaction, leading to interlayer separations and electronic properties changing with stacking configurations. Our predictions constitute a demonstration of twist engineering the band shift in the emergent class of 2D crystals, transition-metal dichalcogenides.
Unusual presentation of twisted ovarian cyst
Directory of Open Access Journals (Sweden)
Vineet V Mishra
2016-01-01
Full Text Available Ovarian torsion (also termed as adnexal torsion refers to partial or complete rotation of the ovary and a portion of fallopian tube along its supplying vascular pedicle. It occurs commonly in reproductive age group; more on the right side (60% and often presents with acute lower abdominal pain lasting for few hours and up to 24 h, accounting for 2.7% of acute gynecological conditions. It is one of the devastating conditions, hampering blood supply of ovary which may lead to total necrosis of ovarian tissue and complications, if not diagnosed and managed in time. Hence, we present a case on a twisted ovarian cyst in postmenopausal woman with unusual symptomatology leading to delayed diagnosis and loss of an ovary.
International Nuclear Information System (INIS)
Obregon, Octavio; Quevedo, Hernando; Ryan, Michael P.
2004-01-01
We construct a family of time and angular dependent, regular S-brane solutions which corresponds to a simple analytical continuation of the Zipoy-Voorhees 4-dimensional vacuum spacetime. The solutions are asymptotically flat and turn out to be free of singularities without requiring a twist in space. They can be considered as the simplest non-singular generalization of the singular S0-brane solution. We analyze the properties of a representative of this family of solutions and show that it resembles to some extent the asymptotic properties of the regular Kerr S-brane. The R-symmetry corresponds, however, to the general lorentzian symmetry. Several generalizations of this regular solution are derived which include a charged S-brane and an additional dilatonic field. (author)
Random SU(2) invariant tensors
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
Dynamical twisted mass fermions and baryon spectroscopy
International Nuclear Information System (INIS)
Drach, V.
2010-06-01
The aim of this work is an ab initio computation of the baryon masses starting from quantum chromodynamics (QCD). This theory describes the interaction between quarks and gluons and has been established at high energy thanks to one of its fundamental properties: the asymptotic freedom. This property predicts that the running coupling constant tends to zero at high energy and thus that perturbative expansions in the coupling constant are justified in this regime. On the contrary the low energy dynamics can only be understood in terms of a non perturbative approach. To date, the only known method that allows the computation of observables in this regime together with a control of its systematic effects is called lattice QCD. It consists in formulating the theory on an Euclidean space-time and to evaluating numerically suitable functional integrals. First chapter is an introduction to the QCD in the continuum and on a discrete space time. The chapter 2 describes the formalism of maximally twisted fermions used in the European Twisted Mass (ETM) collaboration. The chapter 3 deals with the techniques needed to build hadronic correlator starting from gauge configuration. We then discuss how we determine hadron masses and their statistical errors. The numerical estimation of functional integral is explained in chapter 4. It is stressed that it requires sophisticated algorithm and massive parallel computing on Blue-Gene type architecture. Gauge configuration production is an important part of the work realized during my Ph.D. Chapter 5 is a critical review on chiral perturbation theory in the baryon sector. The two last chapter are devoted to the analysis in the light and strange baryon sector. Systematics and chiral extrapolation are extensively discussed. (author)
Bioinspired twisted composites based on Bouligand structures
Pinto, F.; Iervolino, O.; Scarselli, G.; Ginzburg, D.; Meo, M.
2016-04-01
The coupling between structural support and protection makes biological systems an important source of inspiration for the development of advanced smart composite structures. In particular, some particular material configurations can be implemented into traditional composites in order to improve their impact resistance and the out-of-plane properties, which represents one of the major weakness of commercial carbon fibres reinforced polymers (CFRP) structures. Based on this premise, a three-dimensional twisted arrangement shown in a vast multitude of biological systems (such as the armoured cuticles of Scarabei, the scales of Arapaima Gigas and the smashing club of Odontodactylus Scyllarus) has been replicated to develop an improved structural material characterised by a high level of in-plane isotropy and a higher interfacial strength generated by the smooth stiffness transition between each layer of fibrils. Indeed, due to their intrinsic layered nature, interlaminar stresses are one of the major causes of failure of traditional CFRP and are generated by the mismatch of the elastic properties between plies in a traditional laminate. Since the energy required to open a crack or a delamination between two adjacent plies is due to the difference between their orientations, the gradual angle variation obtained by mimicking the Bouligand Structures could improve energy absorption and the residual properties of carbon laminates when they are subjected to low velocity impact event. Two different bioinspired laminates were manufactured following a double helicoidal approach and a rotational one and were subjected to a complete test campaign including low velocity impact loading and compared to a traditional quasi-isotropic panel. Fractography analysis via X-Ray tomography was used to understand the mechanical behaviour of the different laminates and the residual properties were evaluated via Compression After Impact (CAI) tests. Results confirmed that the biological
Indian Academy of Sciences (India)
Example 1 (Word Problem): This is taken from Em- peror's New Mind ... is as follows. We are given a set of equalities of words .... pictures without proper definitions, and without being ... a polynomial, or in other words it could be a collection of.
Conical twist fields and null polygonal Wilson loops
Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Fioravanti, Davide
2018-06-01
Using an extension of the concept of twist field in QFT to space-time (external) symmetries, we study conical twist fields in two-dimensional integrable QFT. These create conical singularities of arbitrary excess angle. We show that, upon appropriate identification between the excess angle and the number of sheets, they have the same conformal dimension as branch-point twist fields commonly used to represent partition functions on Riemann surfaces, and that both fields have closely related form factors. However, we show that conical twist fields are truly different from branch-point twist fields. They generate different operator product expansions (short distance expansions) and form factor expansions (large distance expansions). In fact, we verify in free field theories, by re-summing form factors, that the conical twist fields operator product expansions are correctly reproduced. We propose that conical twist fields are the correct fields in order to understand null polygonal Wilson loops/gluon scattering amplitudes of planar maximally supersymmetric Yang-Mills theory.
Real-space mapping of topological invariants using artificial neural networks
Carvalho, D.; García-Martínez, N. A.; Lado, J. L.; Fernández-Rossier, J.
2018-03-01
Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.
Dynamical topological invariant after a quantum quench
Yang, Chao; Li, Linhu; Chen, Shu
2018-02-01
We show how to define a dynamical topological invariant for one-dimensional two-band topological systems after a quantum quench. By analyzing general two-band models of topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifolds S2, and thus we are able to define a dynamical topological invariant on each of the spheres. We also unveil the intrinsic relation between the dynamical topological invariant and the difference in the topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.
Cartan invariants and event horizon detection
Brooks, D.; Chavy-Waddy, P. C.; Coley, A. A.; Forget, A.; Gregoris, D.; MacCallum, M. A. H.; McNutt, D. D.
2018-04-01
We show that it is possible to locate the event horizon of a black hole (in arbitrary dimensions) by the zeros of certain Cartan invariants. This approach accounts for the recent results on the detection of stationary horizons using scalar polynomial curvature invariants, and improves upon them since the proposed method is computationally less expensive. As an application, we produce Cartan invariants that locate the event horizons for various exact four-dimensional and five-dimensional stationary, asymptotically flat (or (anti) de Sitter), black hole solutions and compare the Cartan invariants with the corresponding scalar curvature invariants that detect the event horizon.
QCD factorization beyond leading twist in exclusive processes: rhoT-meson production
International Nuclear Information System (INIS)
Wallon, S.; Anikin, I.; ); Ivanov, D.; Pire, B.; Szymanowski, L.
2009-01-01
Exclusive processes in hard electroproduction with asymptotic γ * p center of mass energy is one of the best place for understanding QCD in the perturbative Regge limit. The HERA experiment recently provided precise data for rho electroproduction, including all spin density matrix elements. From QCD, it is expected that such a process should factorize between a hard (calculable) coefficient function, and hadronic (P and ρ) matrix elements. Such a factorization is up to now only proven for a longitudinally polarized rho. Within the kt-factorization approach (valid at large s γ * p), we evaluate the impact factor of the transition γ * → ρT taking into account the twist 3 contributions. We show that a gauge invariant expression is obtained with the help of QCD equations of motion. More generally, relying on these equations and on the gauge invariance of the factorized amplitude, the non-perturbative Distribution Amplitudes can be reduced to a minimal set. This opens the way to a consistent treatment of factorization for exclusive processes with a transversally polarized vector meson. (author)
Quantum communication through a spin ring with twisted boundary conditions
International Nuclear Information System (INIS)
Bose, S.; Jin, B.-Q.; Korepin, V.E.
2005-01-01
We investigate quantum communication between the sites of a spin ring with twisted boundary conditions. Such boundary conditions can be achieved by a magnetic flux through the ring. We find that a nonzero twist can improve communication through finite odd-numbered rings and enable high-fidelity multiparty quantum communication through spin rings (working near perfectly for rings of five and seven spins). We show that in certain cases, the twist results in the complete blockage of quantum-information flow to a certain site of the ring. This effect can be exploited to interface and entangle a flux qubit and a spin qubit without embedding the latter in a magnetic field
TWIST1 promotes invasion through mesenchymal change in human glioblastoma
Directory of Open Access Journals (Sweden)
Wakimoto Hiroaki
2010-07-01
Full Text Available Abstract Background Tumor cell invasion into adjacent normal brain is a mesenchymal feature of GBM and a major factor contributing to their dismal outcomes. Therefore, better understandings of mechanisms that promote mesenchymal change in GBM are of great clinical importance to address invasion. We previously showed that the bHLH transcription factor TWIST1 which orchestrates carcinoma metastasis through an epithelial mesenchymal transition (EMT is upregulated in GBM and promotes invasion of the SF767 GBM cell line in vitro. Results To further define TWIST1 functions in GBM we tested the impact of TWIST1 over-expression on invasion in vivo and its impact on gene expression. We found that TWIST1 significantly increased SNB19 and T98G cell line invasion in orthotopic xenotransplants and increased expression of genes in functional categories associated with adhesion, extracellular matrix proteins, cell motility and locomotion, cell migration and actin cytoskeleton organization. Consistent with this TWIST1 reduced cell aggregation, promoted actin cytoskeletal re-organization and enhanced migration and adhesion to fibronectin substrates. Individual genes upregulated by TWIST1 known to promote EMT and/or GBM invasion included SNAI2, MMP2, HGF, FAP and FN1. Distinct from carcinoma EMT, TWIST1 did not generate an E- to N-cadherin "switch" in GBM cell lines. The clinical relevance of putative TWIST target genes SNAI2 and fibroblast activation protein alpha (FAP identified in vitro was confirmed by their highly correlated expression with TWIST1 in 39 human tumors. The potential therapeutic importance of inhibiting TWIST1 was also shown through a decrease in cell invasion in vitro and growth of GBM stem cells. Conclusions Together these studies demonstrated that TWIST1 enhances GBM invasion in concert with mesenchymal change not involving the canonical cadherin switch of carcinoma EMT. Given the recent recognition that mesenchymal change in GBMs is
Translationally invariant and non-translationally invariant empirical effective interactions
International Nuclear Information System (INIS)
Golin, M.; Zamick, L.
1975-01-01
In this work empirical deficiencies of the core-renormalized realistic effective interactions are examined and simple corrective potentials are sought. The inability of the current realistic interactions to account for the energies of isobaric analog states is noted, likewise they are unable to reproduce the changes in the single-particle energies, as one goes from one closed shell to another. It is noted that the Schiffer interaction gives better results for these gross properties and this is attributed to a combination of several facts. First, to the inclusion of long range terms in the Schiffer potential, then to the presence of relative p-state terms (l=1), in addition to the usual relative s-state terms (l=0). The strange shape of the above interaction is further attributed to the fact that it is translationally invariant whereas the theory of core-polarization yields non-translationally invariant potentials. Consequently, as a correction to the monopole deficiencies of the realistic interactions the term Vsub(mon)=ar 2 (1)r 2 (2)+r 2 (1)+β[r 4 (1)r 2 (2)r 4 (2) ] is proposed. (Auth.)
Blossier, BenoÃ®t.; Brinet, Mariane; Guichon, Pierre; Morénas, Vincent; Pène, Olivier; Rodríguez-Quintero, Jose; Zafeiropoulos, Savvas
2015-06-01
We present a precise nonperturbative determination of the renormalization constants in the mass independent RI'-MOM scheme. The lattice implementation uses the Iwasaki gauge action and four degenerate dynamical twisted-mass fermions. The gauge configurations are provided by the ETM Collaboration. Renormalization constants for scalar, pseudoscalar, vector and axial operators, as well as the quark propagator renormalization, are computed at three different values of the lattice spacing, two volumes and several twisted-mass parameters. The method we developed allows for a precise cross-check of the running, thanks to the particular proper treatment of hypercubic artifacts. Results for the twist-2 operator O44 are also presented.
Conformal invariance in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1987-01-01
In the present paper we show how the N = 2 superconformal group is realised in harmonic superspace and examine conformal invariance of N = 2 off-shell theories. We believe that the example of N = O self-dual Yang-Mills equations can serve as an instructive introduction to the subject of harmonic superspace and this is examined. The rigid N = 2 conformal supersymmetry and its local version, i.e. N = 2 conformal supergravity is also discussed. The paper is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. (author)
Gauge invariant fractional electromagnetic fields
Lazo, Matheus Jatkoske
2011-09-01
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.
Invariant metrics for Hamiltonian systems
International Nuclear Information System (INIS)
Rangarajan, G.; Dragt, A.J.; Neri, F.
1991-05-01
In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs
Enhancement of heat transfer using varying width twisted tape inserts
African Journals Online (AJOL)
International Journal of Engineering, Science and Technology ... experimental investigations of the augmentation of turbulent flow heat transfer in a horizontal tube by means of varying width twisted tape inserts with air as the working fluid.
Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions
Energy Technology Data Exchange (ETDEWEB)
Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)
2010-05-15
In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)
The geometric Langlands twist in five and six dimensions
International Nuclear Information System (INIS)
Bak, Dongsu; Gustavsson, Andreas
2015-01-01
Abelian 6d (2,0) theory has SO(5) R symmetry. We twist this theory by identifying the R symmetry group with the SO(5) subgroup of the SO(1,5) Lorentz group. This twisted theory can be put on any five-manifold M, times R, while preserving one scalar supercharge. We subsequently assume the existence of one unit normalized Killing vector field on M, and we find a corresponding SO(4) twist that preserves two supercharges and is a generalization of the geometric Langlands twist of 4d SYM. We generalize the story to non-Abelian gauge group for the corresponding 5d SYM theories on M. We derive a vanishing theorem for BPS contact instantons by identifying the 6d potential energy and its BPS bound, in the 5d theory. To this end we need to perform a Wick rotation that complexifies the gauge field.
Static-light meson masses from twisted mass lattice QCD
International Nuclear Information System (INIS)
Jansen, Karl; Michael, Chris; Shindler, Andrea; Wagner, Marc
2008-08-01
We compute the static-light meson spectrum using two-flavor Wilson twisted mass lattice QCD. We have considered five different values for the light quark mass corresponding to 300 MeV PS S mesons. (orig.)
Higher-Twist Dynamics in Large Transverse Momentum Hadron Production
International Nuclear Information System (INIS)
Francois, Alero
2009-01-01
A scaling law analysis of the world data on inclusive large-p # perpendicular# hadron production in hadronic collisions is carried out. A significant deviation from leading-twist perturbative QCD predictions at next-to-leading order is reported. The observed discrepancy is largest at high values of x # perpendicular# = 2p # perpendicular#/√s. In contrast, the production of prompt photons and jets exhibits the scaling behavior which is close to the conformal limit, in agreement with the leading-twist expectation. These results bring evidence for a non-negligible contribution of higher-twist processes in large-p # perpendicular# hadron production in hadronic collisions, where the hadron is produced directly in the hard subprocess rather than by gluon or quark jet fragmentation. Predictions for scaling exponents at RHIC and LHC are given, and it is suggested to trigger the isolated large-p # perpendicular# hadron production to enhance higher-twist processes.
Flux Density through Guides with Microstructured Twisted Clad DB Medium
Directory of Open Access Journals (Sweden)
M. A. Baqir
2014-01-01
Full Text Available The paper deals with the study of flux density through a newly proposed twisted clad guide containing DB medium. The inner core and the outer clad sections are usual dielectrics, and the introduced twisted windings at the core-clad interface are treated under DB boundary conditions. The pitch angle of twist is supposed to greatly contribute towards the control over the dispersion characteristics of the guide. The eigenvalue equation for the guiding structure is deduced, and the analytical investigations are made to explore the propagation patterns of flux densities corresponding to the sustained low-order hybrid modes under the situation of varying pitch angles. The emphasis has been put on the effects due to the DB twisted pitch on the propagation of energy flux density through the guide.
Õnnetu saatusega Oliver Twist Polanski meelevallas / Andres Laasik
Laasik, Andres, 1960-2016
2005-01-01
Mängufilm Charles Dickensi romaani järgi "Oliver Twist" : stsenarist Ronald Harwood : režissöör Roman Polanski : nimiosas Barney Clark, Fagin - Ben Kingsley : Suurbritannia - Tšehhi - Prantsusmaa - Itaalia 2005
Study of twist boundaries in aluminium. Structure and intergranular diffusion
International Nuclear Information System (INIS)
Lemuet, Daniel
1981-01-01
This research thesis addresses the study of grain boundaries in oriented crystals, and more particularly the systematic calculation of intergranular structures and energies of twist boundaries of <001> axis in aluminium, the determination of intergranular diffusion coefficients of zinc in a set of twist bi-crystals of same axis encompassing a whole range of disorientations, and the search for a correlation between these experimental results and calculated structures
'Twisted' strings and higher level Kac-Moody representations
International Nuclear Information System (INIS)
Horvath, Z.; Palla, L.
1989-01-01
Using an orbifold-like construction the twisted sector of a closed string moving on GxG (with G simply laced) is determined. A level-two G current operating there is constructed explicitly. The decomposition of the twisted sector into products between appropriate conformal and level-two G representations is given if 2 rank G-2 dim G/(2+g)<1. (orig.)
New look at the dynamics of twisted accretion disks
International Nuclear Information System (INIS)
Hatchett, S.P.; Begelman, M.C.; Sarazin, C.L.
1981-01-01
We reexamine the dynamic response of a thin, accretion disk to twisting torques, guided by the earlier analyses by Bardeen and Petterson. We make several corrections to this earlier work, and present a new version of the twist equations consistent with their physical assumptions. By describing the distortion of the disk in terms Cartesian direction cosines rather than the Euler angles used by the earlier authors, we are able to transform the twist equations from a pair of coupled, nonlinear, partial differential equations to a single, linear, complex one. We write down formulae for the external twisting torques likley to be encountered in astrophysic, and we show that even with these driving torques our twist equation remains linear. We find exact, analytic solutions for steady state structure of a disk subject to Lense-Thirring torques by a nonaligned central Kerr black hole and also for the time-dependent problem of the structure of a slaved disk with its oscillating boundary conditions. Finally, we discuss the stability of disks against twisting modes and show that undriven disks and disks subject to time-independent driving torques are stable
Observations on discretization errors in twisted-mass lattice QCD
International Nuclear Information System (INIS)
Sharpe, Stephen R.
2005-01-01
I make a number of observations concerning discretization errors in twisted-mass lattice QCD that can be deduced by applying chiral perturbation theory including lattice artifacts. (1) The line along which the partially conserved axial current quark mass vanishes in the untwisted-mass-twisted-mass plane makes an angle to the twisted-mass axis which is a direct measure of O(a) terms in the chiral Lagrangian, and is found numerically to be large; (2) Numerical results for pionic quantities in the mass plane show the qualitative properties predicted by chiral perturbation theory, in particular, an asymmetry in slopes between positive and negative untwisted quark masses; (3) By extending the description of the 'Aoki regime' (where m q ∼a 2 Λ QCD 3 ) to next-to-leading order in chiral perturbation theory I show how the phase-transition lines and lines of maximal twist (using different definitions) extend into this region, and give predictions for the functional form of pionic quantities; (4) I argue that the recent claim that lattice artifacts at maximal twist have apparent infrared singularities in the chiral limit results from expanding about the incorrect vacuum state. Shifting to the correct vacuum (as can be done using chiral perturbation theory) the apparent singularities are summed into nonsingular, and furthermore predicted, forms. I further argue that there is no breakdown in the Symanzik expansion in powers of lattice spacing, and no barrier to simulating at maximal twist in the Aoki regime
Twisting short dsDNA with applied tension
Zoli, Marco
2018-02-01
The twisting deformation of mechanically stretched DNA molecules is studied by a coarse grained Hamiltonian model incorporating the fundamental interactions that stabilize the double helix and accounting for the radial and angular base pair fluctuations. The latter are all the more important at short length scales in which DNA fragments maintain an intrinsic flexibility. The presented computational method simulates a broad ensemble of possible molecule conformations characterized by a specific average twist and determines the energetically most convenient helical twist by free energy minimization. As this is done for any external load, the method yields the characteristic twist-stretch profile of the molecule and also computes the changes in the macroscopic helix parameters i.e. average diameter and rise distance. It is predicted that short molecules under stretching should first over-twist and then untwist by increasing the external load. Moreover, applying a constant load and simulating a torsional strain which over-twists the helix, it is found that the average helix diameter shrinks while the molecule elongates, in agreement with the experimental trend observed in kilo-base long sequences. The quantitative relation between percent relative elongation and superhelical density at fixed load is derived. The proposed theoretical model and computational method offer a general approach to characterize specific DNA fragments and predict their macroscopic elastic response as a function of the effective potential parameters of the mesoscopic Hamiltonian.
Scanning tunneling microscopy and spectroscopy of twisted trilayer graphene
Zuo, Wei-Jie; Qiao, Jia-Bin; Ma, Dong-Lin; Yin, Long-Jing; Sun, Gan; Zhang, Jun-Yang; Guan, Li-Yang; He, Lin
2018-01-01
Twist, as a simple and unique degree of freedom, could lead to enormous novel quantum phenomena in bilayer graphene. A small rotation angle introduces low-energy van Hove singularities (VHSs) approaching the Fermi level, which result in unusual correlated states in the bilayer graphene. It is reasonable to expect that the twist could also affect the electronic properties of few-layer graphene dramatically. However, such an issue has remained experimentally elusive. Here, by using scanning tunneling microscopy/spectroscopy (STM/STS), we systematically studied a twisted trilayer graphene (TTG) with two different small twist angles between adjacent layers. Two sets of VHSs, originating from the two twist angles, were observed in the TTG, indicating that the TTG could be simply regarded as a combination of two different twisted bilayers of graphene. By using high-resolution STS, we observed a split of the VHSs and directly imaged the spatial symmetry breaking of electronic states around the VHSs. These results suggest that electron-electron interactions play an important role in affecting the electronic properties of graphene systems with low-energy VHSs.
Admissible invariant distributions on reductive
Harish-Chandra; Paul J Sally, Jr
1999-01-01
Harish-Chandra presented these lectures on admissible invariant distributions for p-adic groups at the Institute for Advanced Study in the early 1970s. He published a short sketch of this material as his famous "Queen's Notes". This book, which was prepared and edited by DeBacker and Sally, presents a faithful rendering of Harish-Chandra's original lecture notes. The main purpose of Harish-Chandra's lectures was to show that the character of an irreducible admissible representation of a connected reductive p-adic group G is represented by a locally summable function on G. A key ingredient in this proof is the study of the Fourier transforms of distributions on \\mathfrak g, the Lie algebra of G. In particular, Harish-Chandra shows that if the support of a G-invariant distribution on \\mathfrak g is compactly generated, then its Fourier transform has an asymptotic expansion about any semisimple point of \\mathfrak g. Harish-Chandra's remarkable theorem on the local summability of characters for p-adic groups was ...
Scale-invariant gravity: geometrodynamics
International Nuclear Information System (INIS)
Anderson, Edward; Barbour, Julian; Foster, Brendan; Murchadha, Niall O
2003-01-01
We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's idea of a compensating field, our direct approach dispenses with this and is built by extension of the method of best matching w.r.t. scaling developed in the parallel particle dynamics paper by one of the authors. In spatially compact GR, there is an infinity of degrees of freedom that describe the shape of 3-space which interact with a single volume degree of freedom. In conformal gravity, the shape degrees of freedom remain, but the volume is no longer a dynamical variable. Further theories and formulations related to GR and conformal gravity are presented. Conformal gravity is successfully coupled to scalars and the gauge fields of nature. It should describe the solar system observations as well as GR does, but its cosmology and quantization will be completely different
Flux compactifications, twisted tori and doubled geometry
International Nuclear Information System (INIS)
Reid-Edwards, R.A.
2009-01-01
In [1] an O(D,D)-covariant sigma model describing the embedding of a closed world-sheet into the 2D-dimensional twisted torus X was proposed. Such sigma models provide a universal description of string theory with target spaces related by the action of T-duality. In this article a six-dimensional toy example is studied in detail. Different polarisations of the six-dimensional target space give different three-dimensional string backgrounds including a nilmanifold with H-flux, a T-fold with R-flux and a new class of T-folds. Global issues and connections with the doubled torus formalism are discussed. Finally, the sigma model introduced in [1], describing the embedding of a world-sheet into X, is generalised to one describing a target space which is a bundle of X over a base M d , allowing for a more complete description of the associated gauged supergravity from the world-sheet perspective to be given.
Twisted conformal field theories and Morita equivalence
Energy Technology Data Exchange (ETDEWEB)
Marotta, Vincenzo [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' and INFN, Sezione di Napoli, Compl. universitario M. Sant' Angelo, Via Cinthia, 80126 Napoli (Italy); Naddeo, Adele [CNISM, Unita di Ricerca di Salerno and Dipartimento di Fisica ' E.R. Caianiello' , Universita degli Studi di Salerno, Via Salvador Allende, 84081 Baronissi (Italy); Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Compl. universitario M. Sant' Angelo, Via Cinthia, 80126 Napoli (Italy)], E-mail: adelenaddeo@yahoo.it
2009-04-01
The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter {theta} (in appropriate units): an isomorphism is established between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space. We focus on a particular conformal field theory (CFT), the one obtained by means of the m-reduction procedure [V. Marotta, J. Phys. A 26 (1993) 3481; V. Marotta, Mod. Phys. Lett. A 13 (1998) 853; V. Marotta, Nucl. Phys. B 527 (1998) 717; V. Marotta, A. Sciarrino, Mod. Phys. Lett. A 13 (1998) 2863], and show that it is the Morita equivalent of a NCFT. Finally, the whole m-reduction procedure is shown to be the image in the ordinary space of the Morita duality. An application to the physics of a quantum Hall fluid at Jain fillings {nu}=m/(2pm+1) is explicitly discussed in order to further elucidate such a correspondence and to clarify its role in the physics of strongly correlated systems. A new picture emerges, which is very different from the existing relationships between noncommutativity and many body systems [A.P. Polychronakos, arXiv: 0706.1095].
How the embryonic chick brain twists.
Chen, Zi; Guo, Qiaohang; Dai, Eric; Forsch, Nickolas; Taber, Larry A
2016-11-01
During early development, the tubular embryonic chick brain undergoes a combination of progressive ventral bending and rightward torsion, one of the earliest organ-level left-right asymmetry events in development. Existing evidence suggests that bending is caused by differential growth, but the mechanism for the predominantly rightward torsion of the embryonic brain tube remains poorly understood. Here, we show through a combination of in vitro experiments, a physical model of the embryonic morphology and mechanics analysis that the vitelline membrane (VM) exerts an external load on the brain that drives torsion. Our theoretical analysis showed that the force is of the order of 10 micronewtons. We also designed an experiment to use fluid surface tension to replace the mechanical role of the VM, and the estimated magnitude of the force owing to surface tension was shown to be consistent with the above theoretical analysis. We further discovered that the asymmetry of the looping heart determines the chirality of the twisted brain via physical mechanisms, demonstrating the mechanical transfer of left-right asymmetry between organs. Our experiments also implied that brain flexure is a necessary condition for torsion. Our work clarifies the mechanical origin of torsion and the development of left-right asymmetry in the early embryonic brain. © 2016 The Author(s).
Complex Toda theories and twisted reality conditions
International Nuclear Information System (INIS)
Evans, J.M.
1993-01-01
The Toda equations (based on a finite-dimensional or affine Lie algebra of superalgebra) are discussed as integrable non-linear differential equations for a set of complex scalar fields. We show that such complex Toda fields can either be restricted to take real values in the standard way or else they can be subjected to a 'twisted' reality condition associated to any Z 2 symmetry of the Cartan matrix or Dynkin diagram of the underlying algebra. Different reality conditions give rise to different lagrangian field theories. In the conformal case, however, these theories have the same central charge, while in the affine case they have the same mass spectrum. The construction of N=2 superconformal theories based on the superalgebras A(n, n-1) is clarified, and a new class of conformal field theories with positive kinetic energy based on the superalgebras C(n) is presented. The ideas developed are also relevant to understanding solition solutions in affine Toda theories with imaginary coupling constant. (orig.)
The Latest Twists in Chromatin Remodeling.
Blossey, Ralf; Schiessel, Helmut
2018-01-05
In its most restrictive interpretation, the notion of chromatin remodeling refers to the action of chromatin-remodeling enzymes on nucleosomes with the aim of displacing and removing them from the chromatin fiber (the effective polymer formed by a DNA molecule and proteins). This local modification of the fiber structure can have consequences for the initiation and repression of the transcription process, and when the remodeling process spreads along the fiber, it also results in long-range effects essential for fiber condensation. There are three regulatory levels of relevance that can be distinguished for this process: the intrinsic sequence preference of the histone octamer, which rules the positioning of the nucleosome along the DNA, notably in relation to the genetic information coded in DNA; the recognition or selection of nucleosomal substrates by remodeling complexes; and, finally, the motor action on the nucleosome exerted by the chromatin remodeler. Recent work has been able to provide crucial insights at each of these three levels that add new twists to this exciting and unfinished story, which we highlight in this perspective. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Synthesizing Modular Invariants for Synchronous Code
Directory of Open Access Journals (Sweden)
Pierre-Loic Garoche
2014-12-01
Full Text Available In this paper, we explore different techniques to synthesize modular invariants for synchronous code encoded as Horn clauses. Modular invariants are a set of formulas that characterizes the validity of predicates. They are very useful for different aspects of analysis, synthesis, testing and program transformation. We describe two techniques to generate modular invariants for code written in the synchronous dataflow language Lustre. The first technique directly encodes the synchronous code in a modular fashion. While in the second technique, we synthesize modular invariants starting from a monolithic invariant. Both techniques, take advantage of analysis techniques based on property-directed reachability. We also describe a technique to minimize the synthesized invariants.
Link invariants for flows in higher dimensions
International Nuclear Information System (INIS)
Garcia-Compean, Hugo; Santos-Silva, Roberto
2010-01-01
Linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of BF theories. The linking numbers associated with n-manifolds with smooth flows generated by divergence-free p-vector fields, endowed with an invariant flow measure, are computed in the context of quantum field theory. They constitute invariants of smooth dynamical systems (for nonsingular flows) and generalize previous proposals of invariants. In particular, they generalize Arnold's asymptotic Hopf invariant from three to higher dimensions. This invariant is generalized by coupling with a non-Abelian gauge flat connection with nontrivial holonomy. The computation of the asymptotic Jones-Witten invariants for flows is naturally extended to dimension n=2p+1. Finally, we give a possible interpretation and implementation of these issues in the context of 11-dimensional supergravity and string theory.
Recent progress in invariant pattern recognition
Arsenault, Henri H.; Chang, S.; Gagne, Philippe; Gualdron Gonzalez, Oscar
1996-12-01
We present some recent results in invariant pattern recognition, including methods that are invariant under two or more distortions of position, orientation and scale. There are now a few methods that yield good results under changes of both rotation and scale. Some new methods are introduced. These include locally adaptive nonlinear matched filters, scale-adapted wavelet transforms and invariant filters for disjoint noise. Methods using neural networks will also be discussed, including an optical method that allows simultaneous classification of multiple targets.
Modular invariance, chiral anomalies and contact terms
International Nuclear Information System (INIS)
Kutasov, D.
1988-03-01
The chiral anomaly in heterotic strings with full and partial modular invariance in D=2n+2 dimensions is calculated. The boundary terms which were present in previous calculations are shown to be cancelled in the modular invariant case by contact terms, which can be obtained by an appropriate analytic continuation. The relation to the low energy field theory is explained. In theories with partial modular invariance, an expression for the anomaly is obtained and shown to be non zero in general. (author)
Mujika, Jon I; Formoso, Elena; Mercero, Jose M; Lopez, Xabier
2006-08-03
We present an ab initio study of the acid hydrolysis of a highly twisted amide and a planar amide analogue. The aim of these studies is to investigate the effect that the twist of the amide bond has on the reaction barriers and mechanism of acid hydrolysis. Concerted and stepwise mechanisms were investigated using density functional theory and polarizable continuum model calculations. Remarkable differences were observed between the mechanism of twisted and planar amide, due mainly to the preference for N-protonation of the former and O-protonation of the latter. In addition, we were also able to determine that the hydrolytic mechanism of the twisted amide will be pH dependent. Thus, there is a preference for a stepwise mechanism with formation of an intermediate in the acid hydrolysis, whereas the neutral hydrolysis undergoes a concerted-type mechanism. There is a nice agreement between the characterized intermediate and available X-ray data and a good agreement with the kinetically estimated rate acceleration of hydrolysis with respect to analogous undistorted amide compounds. This work, along with previous ab initio calculations, describes a complex and rich chemistry for the hydrolysis of highly twisted amides as a function of pH. The theoretical data provided will allow for a better understanding of the available kinetic data of the rate acceleration of amides upon twisting and the relation of the observed rate acceleration with intrinsic differential reactivity upon loss of amide bond resonance.