Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11
International Nuclear Information System (INIS)
Wang, S.; Yu, P.
2006-01-01
In this article, a systematic procedure has been explored to studying general Z q -equivariant planar polynomial Hamiltonian vector fields for the maximal number of closed orbits and the maximal number of limit cycles after perturbation. Following the procedure by taking special consideration of Z 12 -equivariant vector fields of degree 11, the maximal of 99 closed orbits are obtained under a well-defined coefficient group. Consequently, perturbation parameter control in limit cycle computation leads to the existence of 121 limit cycles in the perturbed Hamiltonian vector field, which gives rise to the lower bound of Hilbert number of 11th-order systems as H(11) ≥ 11 2 . Two conjectures are proposed regarding the maximal number of closed orbits for equivariant polynomial Hamiltonian vector fields and the maximal number of limit cycles bifurcated from the well defined Hamiltonian vector fields after perturbation
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1985-02-01
The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1984-03-01
The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained
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
Kolev, Boris
2006-01-01
23 pages; International audience; This paper is a survey article on bi-Hamiltonian systems on the dual of the Lie algebra of vector fields on the circle. We investigate the special case where one of the structures is the canonical Lie-Poisson structure and the second one is constant. These structures called affine or modified Lie-Poisson structures are involved in the integrability of certain Euler equations that arise as models of shallow water waves.
Hamiltonian representation of divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1984-11-01
Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields
Construction of alternative Hamiltonian structures for field equations
Energy Technology Data Exchange (ETDEWEB)
Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)
2001-08-10
We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)
Jacobi fields of completely integrable Hamiltonian systems
International Nuclear Information System (INIS)
Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2003-01-01
We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom make up an extended completely integrable system of 2m degrees of freedom, where m additional first integrals characterize a relative motion
Hamiltonian mechanics and divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1986-08-01
The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space
Numerical determination of the magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Kuo-Petravic, G.; Boozer, A.H.
1986-03-01
The structure of a magnetic field is determined by a one-degree of freedom, time-dependent Hamiltonian. This Hamiltonian is evaluated for a given field in a perturbed action-angle form. The location and the size of magnetic islands in the given field are determined from Hamiltonian perturbation theory and from an ordinary Poincare plot of the field line trajectories
Hamiltonian constraint in polymer parametrized field theory
International Nuclear Information System (INIS)
Laddha, Alok; Varadarajan, Madhavan
2011-01-01
Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.
Hamiltonian Anomalies from Extended Field Theories
Monnier, Samuel
2015-09-01
We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.
Quantum Hamiltonian reduction and conformal field theories
International Nuclear Information System (INIS)
Bershadsky, M.
1991-01-01
It is proved that irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL (2, R) current algebra by putting a constraint on the latter using the BRST formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra which is gauged and hidden. This construction of the Virasoro algebra is the quantum analog of the Hamiltonian reduction. The author then naturally leads to consider an SL(2, R) Wess-Zumino-Witten model. This system is related to the quantum field theory of the coadjoint orbit of the Virasoro group. Based on this result he presents the canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two dimensional gravity; it is manifestation of the SL(2, R) symmetry in the conformal field theory hidden by the quantum Hamiltonian reduction. He discusses the quantum Hamiltonian reduction of the SL(n, R) current algebra for the general type of constraints labeled by index 1 ≤ l ≤ (n - 1) and claim that it leads to the new extended conformal algebras W n l . For l = 1 he recovers the well known W n algebra introduced by A. Zamolodchikov. For SL(3, R) Wess-Zumino-Witten model there are two different possibilities of constraining it. The first possibility gives the W 3 algebra, while the second leads to the new chiral algebra W 3 2 generated by the stress-energy tensor, two bosonic supercurrents with spins 3/2 and the U(1) current. He conjectures a Kac formula that describes the highly reducible representation for this algebra. He also makes some speculations concerning the structure of W gravity
A Hamiltonian functional for the linearized Einstein vacuum field equations
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2005-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained
A Hamiltonian five-field gyrofluid model
Energy Technology Data Exchange (ETDEWEB)
Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, TX 78712 (United States)
2015-11-15
A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.
Multivector field formulation of Hamiltonian field theories: equations and symmetries
Energy Technology Data Exchange (ETDEWEB)
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)
1999-12-03
We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)
Fractal vector optical fields.
Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2016-07-15
We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.
Hamiltonian reduction of SU(2) Yang-Mills field theory
International Nuclear Information System (INIS)
Khvedelidze, A.M.; Pavel, H.-P.
1998-01-01
The unconstrained system equivalent to SU (2) Yang-Mills field theory is obtained in the framework of the generalized Hamiltonian formalism using the method of Hamiltonian reduction. The reduced system is expressed in terms of fields with 'nonrelativistic' spin-0 and spin-2
Curjel, C. R.
1990-01-01
Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...... or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic...... vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...... of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.......The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...
Hamiltonian lattice studies of chiral meson field theories
International Nuclear Information System (INIS)
Chin, S.A.
1998-01-01
The latticization of the non-linear sigma model reduces a chiral meson field theory to an O(4) spin lattice system with quantum fluctuations. The result is an interesting marriage between quantum many-body theory and classical spin systems. By solving the resulting lattice Hamiltonian by Monte Carlo methods, the dynamics and thermodynamics of pions can be determined non-perturbatively. In a variational 16 3 lattice study, the ground state chiral phase transition is shown to be first order. Moreover, as the chiral phase transition is approached, the mass gap of pionic collective modes with quantum number of the ω vector meson drops toward zero. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
New classes of nonlinear vector coherent states of generalized spin-orbit Hamiltonians
International Nuclear Information System (INIS)
Geloun, Joseph Ben; Norbert Hounkonnou, Mahouton
2009-01-01
This paper deals with an extension of our previous work (Ben Geloun and Hounkonnou 2007 J. Phys. A: Math. Theor. 40 F817) by considering an alternative construction of canonical and deformed vector coherent states (VCSs) of the Gazeau-Klauder type associated with generalized spin-orbit Hamiltonians. We define an annihilation operator which takes into account the finite-dimensional space of states induced by the k-photon transition processes of the two-level atom interacting with the single-mode radiation field. The class of nonlinear VCSs (NVCSs) corresponding to the action of the annihilation operator is deduced and expressed in terms of generalized displacement operators. Various NVCSs including their 'dual' counterparts are also discussed. Also, by using the Hilbert space structure, a new family of NVCSs parametrized by unit vectors of the S 3 sphere has been identified without making use of the annihilation operator.
Hamiltonian structure of gravitational field theory
International Nuclear Information System (INIS)
Rayski, J.
1992-01-01
Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations
A Hamiltonian structure for the linearized Einstein vacuum field equations
International Nuclear Information System (INIS)
Torres del Castillo, G.F.
1991-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)
Vector Fields on Product Manifolds
Kurz, Stefan
2011-01-01
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.
On the asymptotic form of the recursion method basis vectors for periodic Hamiltonians
International Nuclear Information System (INIS)
O'Reilly, E.P.; Weaire, D.
1984-01-01
The authors present the first detailed study of the recursion method basis vectors for the case of a periodic Hamiltonian. In the examples chosen, the probability density scales linearly with n as n → infinity, whenever the local density of states is bounded. Whenever it is unbounded and the recursion coefficients diverge, different scaling behaviour is found. These findings are explained and a scaling relationship between the asymptotic forms of the recursion coefficients and basis vectors is proposed. (author)
Directory of Open Access Journals (Sweden)
Rudowicz Czesław
2015-07-01
Full Text Available The interface between optical spectroscopy, electron magnetic resonance (EMR, and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF (or equivalently ligand field (LF Hamiltonians, and the effective spin Hamiltonians (SH, which include the zero-field splitting (ZFS Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA. Survey of recent literature has revealed that this interface, denoted CF (LF ↔ SH (ZFS, has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF, SH (ZFS, and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF ↔ SH (ZFS interface with the focus on the EMR-related problems for transition ions.
The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach
Likar, A.; Razpet, N.
2009-01-01
The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is…
Hamiltonian description of the parametrized scalar field in bounded spatial regions
International Nuclear Information System (INIS)
Barbero G, J Fernando; Margalef-Bentabol, Juan; Villaseñor, Eduardo J S
2016-01-01
We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions. We generalize the work carried out by a number of authors on parametrized field systems to the interesting case where spatial boundaries are present. The configuration space of our models contains both smooth scalar fields defined on the spatial manifold and spacelike embeddings from the spatial manifold to a target spacetime endowed with a fixed Lorentzian background metric. We pay particular attention to the geometry of the infinite dimensional manifold of embeddings and the description of the relevant geometric objects: the symplectic form on the primary constraint submanifold and the Hamiltonian vector fields defined on it. (paper)
Hyperbolic-symmetry vector fields.
Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2015-12-14
We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.
Quantum control mechanism analysis through field based Hamiltonian encoding
International Nuclear Information System (INIS)
Mitra, Abhra; Rabitz, Herschel
2006-01-01
Optimal control of quantum dynamics in the laboratory is proving to be increasingly successful. The control fields can be complex, and the mechanisms by which they operate have often remained obscure. Hamiltonian encoding (HE) has been proposed as a method for understanding mechanisms in quantum dynamics. In this context mechanism is defined in terms of the dominant quantum pathways leading to the final state of the controlled system. HE operates by encoding a special modulation into the Hamiltonian and decoding its signature in the dynamics to determine the dominant pathway amplitudes. Earlier work encoded the modulation directly into the Hamiltonian operators. This present work introduces the alternative scheme of field based HE, where the modulation is encoded into the control field and not directly into the Hamiltonian operators. This distinct form of modulation yields a new perspective on mechanism and is computationally faster than the earlier approach. Field based encoding is also an important step towards a laboratory based algorithm for HE as it is the only form of encoding that may be experimentally executed. HE is also extended to cover systems with noise and uncertainty and finally, a hierarchical algorithm is introduced to reveal mechanism in a stepwise fashion of ever increasing detail as desired. This new hierarchical algorithm is an improvement over earlier approaches to HE where the entire mechanism was determined in one stroke. The improvement comes from the use of less complex modulation schemes, which leads to fewer evaluations of Schroedinger's equation. A number of simulations are presented on simple systems to illustrate the new field based encoding technique for mechanism assessment
Fermion Bag Approach to Lattice Hamiltonian Field Theories
Huffman, Emilie
2018-03-01
Using a model in the Gross-Neveu Ising universality class, we show how the fermion bag idea can be applied to develop algorithms to Hamiltonian lattice field theories. We argue that fermion world lines suggest an alternative method to the traditional techniques for calculating ratios of determinants in a stable manner. We show the power behind these ideas by extracting the physics of the model on large lattices.
Estimation of Motion Vector Fields
DEFF Research Database (Denmark)
Larsen, Rasmus
1993-01-01
This paper presents an approach to the estimation of 2-D motion vector fields from time varying image sequences. We use a piecewise smooth model based on coupled vector/binary Markov random fields. We find the maximum a posteriori solution by simulated annealing. The algorithm generate sample...... fields by means of stochastic relaxation implemented via the Gibbs sampler....
Hamiltonian description of toroidal magnetic fields in vacuum
International Nuclear Information System (INIS)
Lewis, H.R.; Bates, J.W.
1996-01-01
An investigation of vacuum magnetic fields in toroidal geometry has been initiated. Previously, the general form of the magnetic scalar potential for fields regular at the poloidal axis was given. Here, these results have been expanded to obtain the magnetic scalar potential in a vacuum region that may surround a toroidal current distribution. Using this generalized magnetic scalar potential in conjunction with Boozer's canonical representation of a magnetic field, a field-line Hamiltonian for nonaxisymmetric vacuum fields has been derived. These fields axe being examined using a novel, open-quotes time-dependentclose quotes perturbation theory, which permits the iterative construction of invariants associated with magnetic field-line Hamiltonians that consist of an axisymmetric zeroth-order term, plus a nonaxisymmetric perturbation. By choosing appropriate independent variables, an explicit constructive procedure is developed which involves only a single canonical transformation. Such invariants are of interest because they provide a means of investigating the topology of magnetic field lines. Our objective is to elucidate the existence of magnetic surfaces for nonaxisymmetric vacuum configurations, as well as to provide an approach for studying the onset of stochastic behavior
Simplified Representation of Vector Fields
Telea, Alexandru; Wijk, Jarke J. van
1999-01-01
Vector field visualization remains a difficult task. Although many local and global visualization methods for vector fields such as flow data exist, they usually require extensive user experience on setting the visualization parameters in order to produce images communicating the desired insight. We
Stable piecewise polynomial vector fields
Directory of Open Access Journals (Sweden)
Claudio Pessoa
2012-09-01
Full Text Available Let $N={y>0}$ and $S={y<0}$ be the semi-planes of $mathbb{R}^2$ having as common boundary the line $D={y=0}$. Let $X$ and $Y$ be polynomial vector fields defined in $N$ and $S$, respectively, leading to a discontinuous piecewise polynomial vector field $Z=(X,Y$. This work pursues the stability and the transition analysis of solutions of $Z$ between $N$ and $S$, started by Filippov (1988 and Kozlova (1984 and reformulated by Sotomayor-Teixeira (1995 in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields $Z_{epsilon}$, defined by averaging $X$ and $Y$. This family approaches $Z$ when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002 providing conditions on $(X,Y$ for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on $mathbb{R}^2$. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.
Covariant description of Hamiltonian form for field dynamics
International Nuclear Information System (INIS)
Ozaki, Hiroshi
2005-01-01
Hamiltonian form of field dynamics is developed on a space-like hypersurface in space-time. A covariant Poisson bracket on the space-like hypersurface is defined and it plays a key role to describe every algebraic relation into a covariant form. It is shown that the Poisson bracket has the same symplectic structure that was brought in the covariant symplectic approach. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in which the interaction Hamiltonian density generates a deformation of the space-like hypersurface. The equation just corresponds to the Yang-Feldman equation in the Heisenberg pictures in quantum field theory. By converting the covariant Poisson bracket on the space-like hypersurface to four-dimensional commutator, we can pass over to quantum field theory in the Heisenberg picture without spoiling the explicit relativistic covariance. As an example the canonical QCD is displayed in a covariant way on a space-like hypersurface
Analytic approximations to hamiltonian lattice field theories. Pt. 2
International Nuclear Information System (INIS)
Surany, P.
1983-01-01
It is shown that at weak coupling physical quantities in hamiltonian U(1) lattice gauge (or global symmetric) theories of arbitrary dimension are provided as expectation values in a d - 1 dimensional lagrangian Z(2) gauge (or spin) theory with calculable long-range interactions. Confinement and the existence of a magnetic mass gap are equivalent to the existence of infinite-range plaquette-plaquette (or link-link) correlations in the spin field. The existence of infinite range correlations is simply related to the dimension of the lattice and the transformation property of the order parameter. As expected, only the d = 2 + 1 U(1) gauge theory confines electric charges at all non-vanishing coupling. (orig.)
Elliptic-symmetry vector optical fields.
Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Kong, Ling-Jun; Tu, Chenghou; Wang, Hui-Tian
2014-08-11
We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.
Hamiltonian truncation approach to quenches in the Ising field theory
Directory of Open Access Journals (Sweden)
T. Rakovszky
2016-10-01
Full Text Available In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.
Vector fields on nonorientable surfaces
Directory of Open Access Journals (Sweden)
Ilie Barza
2003-01-01
X, and the space of vector fields on X are proved by using a symmetrisation process. An example related to the normal derivative on the border of the Möbius strip supports the nontriviality of the concepts introduced in this paper.
On vector fields having properties of Reeb fields
Hajduk, Boguslaw; Walczak, Rafal
2011-01-01
We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional manifold have geodesible vector fields.
International Nuclear Information System (INIS)
Ammari, Zied
2000-01-01
Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure point spectrum outside its thresholds. We study the asymptotic fields and the existence of the wave operators. Finally we show asymptotic completeness for the Nelson Hamiltonian
Problems of vector Lagrangians in field theories
International Nuclear Information System (INIS)
Krivsky, I.Yu.; Simulik, V.M.
1997-01-01
A vector Lagrange approach to the Dirac spinor field and the relationship between the vector Lagrangians for the spinor and electromagnetic fields are considered. A vector Lagrange approach for the system of interacting electromagnetic B=(B μ υ)=(E-bar,H-bar) and spinor Ψ fields is constructed. New Lagrangians (scalar and vector) for electromagnetic field in terms of field strengths are found. The foundations of two new QED models are formulated
Vector fields and gravity on the lattice
International Nuclear Information System (INIS)
Khatsymovsky, V.M.
1988-01-01
The problem of discretization of vector field on Regge lattice is considered. Our approach is based on geometrical interpretation of the vector field as the field of infinitesimal coordinate transformation. A discrete version of the vector field action is obtained as a particular case of the continuum action, and it is shown to have the true continuum limit
Diagnostics of vector magnetic fields
Stenflo, J. O.
1985-01-01
It is shown that the vector magnetic fields derived from observations with a filter magnetograph will be severely distorted if the spatially unresolved magnetic structure is not properly accounted for. Thus the apparent vector field will appear much more horizontal than it really is, but this distortion is strongly dependent on the area factor and the temperature line weakenings. As the available fluxtube models are not sufficiently well determined, it is not possible to correct the filter magnetograph observations for these effects in a reliable way, although a crude correction is of course much better than no correction at all. The solution to this diagnostic problem is to observe simultaneously in suitable combinations of spectral lines, and/or use Stokes line profiles recorded with very high spectral resolution. The diagnostic power of using a Fourier transform spectrometer for polarimetry is shown and some results from I and V spectra are illustrated. The line asymmetries caused by mass motions inside the fluxtubes adds an extra complication to the diagnostic problem, in particular as there are indications that the motions are nonstationary in nature. The temperature structure appears to be a function of fluxtube diameter, as a clear difference between plage and network fluxtubes was revealed. The divergence of the magnetic field with height plays an essential role in the explanation of the Stokes V asymmetries (in combination with the mass motions). A self consistent treatment of the subarcsec field geometry may be required to allow an accurate derivation of the spatially averaged vector magnetic field from spectrally resolved data.
Constraints and Hamiltonian in light-front quantized field theory
International Nuclear Information System (INIS)
Srivastava, P.P.
1993-01-01
Self-consistent hamiltonian formulation of scalar theory on the null plane is constructed and quantized following the Dirac procedure. The theory contains also constraint equations which would give, if solved, to a nonlocal Hamiltonian. In contrast to the equal-time formulation we obtain a different description of the spontaneous symmetry breaking in the continuum and the symmetry generators are found to annihilate the light-front vacuum. Two examples are given where the procedure cannot be applied self-consistently. The corresponding theories are known to be ill-defined from the equal-time quantization. (author)
Transversals of Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
Vector fields in the complex plane are defined by assigning the vector determined by the value P(z) to each point z in the complex plane, where P is a polynomial of one complex variable. We consider special families of so-called rotated vector fields that are determined by a polynomial multiplied...... by rotational constants. Transversals are a certain class of curves for such a family of vector fields that represent the bifurcation states for this family of vector fields. More specifically, transversals are curves that coincide with a homoclinic separatrix for some rotation of the vector field. Given...... a concrete polynomial, it seems to take quite a bit of work to prove that it is generic, i.e. structurally stable. This has been done for a special class of degree d polynomial vector fields having simple equilibrium points at the d roots of unity, d odd. In proving that such vector fields are generic...
Vector Fields and Flows on Differentiable Stacks
DEFF Research Database (Denmark)
A. Hepworth, Richard
2009-01-01
This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined 2-cell. This extends the usual result on the existence...... of vector fields....
Visualizing vector field topology in fluid flows
Helman, James L.; Hesselink, Lambertus
1991-01-01
Methods of automating the analysis and display of vector field topology in general and flow topology in particular are discussed. Two-dimensional vector field topology is reviewed as the basis for the examination of topology in three-dimensional separated flows. The use of tangent surfaces and clipping in visualizing vector field topology in fluid flows is addressed.
Introduction to Vector Field Visualization
Kao, David; Shen, Han-Wei
2010-01-01
Vector field visualization techniques are essential to help us understand the complex dynamics of flow fields. These can be found in a wide range of applications such as study of flows around an aircraft, the blood flow in our heart chambers, ocean circulation models, and severe weather predictions. The vector fields from these various applications can be visually depicted using a number of techniques such as particle traces and advecting textures. In this tutorial, we present several fundamental algorithms in flow visualization including particle integration, particle tracking in time-dependent flows, and seeding strategies. For flows near surfaces, a wide variety of synthetic texture-based algorithms have been developed to depict near-body flow features. The most common approach is based on the Line Integral Convolution (LIC) algorithm. There also exist extensions of LIC to support more flexible texture generations for 3D flow data. This tutorial reviews these algorithms. Tensor fields are found in several real-world applications and also require the aid of visualization to help users understand their data sets. Examples where one can find tensor fields include mechanics to see how material respond to external forces, civil engineering and geomechanics of roads and bridges, and the study of neural pathway via diffusion tensor imaging. This tutorial will provide an overview of the different tensor field visualization techniques, discuss basic tensor decompositions, and go into detail on glyph based methods, deformation based methods, and streamline based methods. Practical examples will be used when presenting the methods; and applications from some case studies will be used as part of the motivation.
A covariant formulation of the relativistic Hamiltonian theory on the light cone (fields with spin)
International Nuclear Information System (INIS)
Atakishiev, N.M.; Mir-Kasimov, R.M.; Nagiyev, Sh.M.
1978-01-01
A Hamiltonian formulation of quantum field theory on the light cone, developed earlier, is extended to the case of particles with spin. The singularities accompanying each field theory in light-front variables are removed by the introduction of an infinite number of counterterms of a new type, which can be included into the interaction Hamiltonian. A three-dimensional diagram technique is formulated, which is applied to calculate the fermion self-energy in the lowest order of perturbation theory
Symmetry-adaptation and selection rules for effective crystal field Hamiltonians
International Nuclear Information System (INIS)
Tuszynski, J.A.
1986-01-01
The intention of this paper is to systematically derive an effective Hamiltonian in the presence of crystal fields in such a way as to incorporate relativistic effects and higher order perturbation corrections including configuration mixing. This Hamiltonian will then be conveniently represented as a symmetry-adapted series of one- and two-body double tensor operators whose matrix elements will be analyzed for selection rules. 16 references, 4 tables
Weaving Knotted Vector Fields with Tunable Helicity.
Kedia, Hridesh; Foster, David; Dennis, Mark R; Irvine, William T M
2016-12-30
We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot, and its generalizations. As finite-energy physical fields, they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knotted fields. The construction can be used to generate isolated knotted flux tubes, filled by knots encoded in the lines of the vector field. Lastly, we give examples of manifestly knotted vector fields with vanishing helicity. Our results provide building blocks for analytical models and simulations alike.
Hawking radiation of a vector field and gravitational anomalies
International Nuclear Information System (INIS)
Murata, Keiju; Miyamoto, Umpei
2007-01-01
Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with the Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is available. It is found that the total energy emitted from the horizon for the electromagnetic field is just (d-2) times that for a scalar field. The results support the picture that Hawking radiation can be regarded as an anomaly eliminator on horizons. Possible extensions and applications of the analysis are discussed
Multi-task Vector Field Learning.
Lin, Binbin; Yang, Sen; Zhang, Chiyuan; Ye, Jieping; He, Xiaofei
2012-01-01
Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously and identifying the shared information among tasks. Most of existing MTL methods focus on learning linear models under the supervised setting. We propose a novel semi-supervised and nonlinear approach for MTL using vector fields. A vector field is a smooth mapping from the manifold to the tangent spaces which can be viewed as a directional derivative of functions on the manifold. We argue that vector fields provide a natural way to exploit the geometric structure of data as well as the shared differential structure of tasks, both of which are crucial for semi-supervised multi-task learning. In this paper, we develop multi-task vector field learning (MTVFL) which learns the predictor functions and the vector fields simultaneously. MTVFL has the following key properties. (1) The vector fields MTVFL learns are close to the gradient fields of the predictor functions. (2) Within each task, the vector field is required to be as parallel as possible which is expected to span a low dimensional subspace. (3) The vector fields from all tasks share a low dimensional subspace. We formalize our idea in a regularization framework and also provide a convex relaxation method to solve the original non-convex problem. The experimental results on synthetic and real data demonstrate the effectiveness of our proposed approach.
Nonconformal scalar field in uniform isotropic space and the method of Hamiltonian diagonalization
International Nuclear Information System (INIS)
Pavlov, Yu.V.
2001-01-01
One diagonalized metric Hamiltonian of scalar field with arbitrary relation with curvature in N-dimensional uniform isotropic space. One derived spectrum of energies of the appropriate quasi-particles. One calculated energy of quasi-particle appropriate to the canonical Hamiltonian diagonal shape. One structured a modified tensor of energy-pulse with the following features. In case of conformal scalar field it coincides with the metric tensor of energy-pulse. When it is diagonalized the energies of the appropriate particles of nonconformal field are equal to oscillation frequency and the number of such particles produced in non-stationary metric is the finite one. It is shown that Hamiltonian calculated on the basis of the modified tensor of energy-pulse may be derived as a canonical one at certain selection of variables [ru
Vector fields and differential operators: noncommutative case
International Nuclear Information System (INIS)
Borowiec, A.
1997-01-01
A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed previously. In this paper an outline is given of the construction of a noncommutative analogy of the algebra of differential operators as well as its (algebraic) Fock space realization. Co-universal vector fields and covariant derivatives will also be discussed
Measurements of Solar Vector Magnetic Fields
Hagyard, M. J. (Editor)
1985-01-01
Various aspects of the measurement of solar magnetic fields are presented. The four major subdivisions of the study are: (1) theoretical understanding of solar vector magnetic fields; (3) techniques for interpretation of observational data; and (4) techniques for data display.
Measurements of Solar Vector Magnetic Fields
International Nuclear Information System (INIS)
Hagyard, M.J.
1985-05-01
Various aspects of the measurement of solar magnetic fields are presented. The four major subdivisions of the study are: (1) theoretical understanding of solar vector magnetic fields; (3) techniques for interpretation of observational data; and (4) techniques for data display
Clifford Fourier transform on vector fields.
Ebling, Julia; Scheuermann, Gerik
2005-01-01
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.
Euclidean fields: vector mesons and photons
International Nuclear Information System (INIS)
Loffelholz, J.
1979-01-01
Free transverse vector fields of mass >= 0 are studied. The model is related to the usual free vector meson and electromagnetic quantum field theories by extension of the field operators from transverse to arbitrary test functions. The one-particle states in transverse gauge and their localization are described. Reflexion positivity is proved and derived are free Feynman-Kac-Nelson formulas. An Euclidean approach to a photon field in a spherical world using dilatation covariance and inversions is given
Oscillatory regime in the multidimensional homogeneous cosmological models induced by a vector field
International Nuclear Information System (INIS)
Benini, R; Kirillov, A A; Montani, Giovanni
2005-01-01
We show that in multidimensional gravity, vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists in all spatial dimensions and for all homogeneous models. By analysing the Hamiltonian equations we derive the Poincare return map associated with the Kasner indexes and fix the rules according to which the Kasner vectors rotate. In correspondence to a four-dimensional spacetime, the oscillatory regime here constructed overlaps the usual Belinski-Khalatnikov-Liftshitz one
Ab initio Hamiltonian approach to light nuclei and quantum field theory
International Nuclear Information System (INIS)
Vary, James P.
2009-01-01
A basis-function approach that has proven successful for solving the nonrelativistic strongly interacting nuclear many-body problem and appears promising for solving relativistic field theory in a light-front Hamiltonian framework is presented. Both conventional nuclear manybody theory and light-front field theory face common issues within the Hamiltonian approach - i.e. how to; (1) define the Hamiltonian; (2) renormalize to a finite space; (3) solve for non-perturbative observables, preserving as many symmetries as possible; and (4) take the continuum limit. Each of these challenges requires a substantial undertaking but appears solvable. Advances in computational physics, both algorithms and parallel computers, have proven essential to the recent progress. I will present results that illustrate the recent advances and indicate the path forward to ever more realistic applications
Vector fields satisfying the barycenter property
Directory of Open Access Journals (Sweden)
Lee Manseob
2018-04-01
Full Text Available We show that if a vector field X has the C1 robustly barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, if a generic C1-vector field has the barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, we apply the results to the divergence free vector fields. It is an extension of the results of the barycenter property for generic diffeomorphisms and volume preserving diffeomorphisms [1].
Existence for stationary mean-field games with congestion and quadratic Hamiltonians
Gomes, Diogo A.; Mitake, Hiroyoshi
2015-01-01
Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular
Versatile generation of optical vector fields and vector beams using a non-interferometric approach.
Tripathi, Santosh; Toussaint, Kimani C
2012-05-07
We present a versatile, non-interferometric method for generating vector fields and vector beams which can produce all the states of polarization represented on a higher-order Poincaré sphere. The versatility and non-interferometric nature of this method is expected to enable exploration of various exotic properties of vector fields and vector beams. To illustrate this, we study the propagation properties of some vector fields and find that, in general, propagation alters both their intensity and polarization distribution, and more interestingly, converts some vector fields into vector beams. In the article, we also suggest a modified Jones vector formalism to represent vector fields and vector beams.
Meromorphic Vector Fields and Circle Packings
DEFF Research Database (Denmark)
Dias, Kealey
The objective of the Ph.D. project is to initiate a classification of bifurcations of meromorphic vector fields and to clarify their relation to circle packings. Technological applications are to image analysis and to effective grid generation using discrete conformal mappings. The two branches...... of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions or meromorphic (allowing poles...... as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic vector fields. Restricting...
Magnetic vector field tag and seal
Johnston, Roger G.; Garcia, Anthony R.
2004-08-31
One or more magnets are placed in a container (preferably on objects inside the container) and the magnetic field strength and vector direction are measured with a magnetometer from at least one location near the container to provide the container with a magnetic vector field tag and seal. The location(s) of the magnetometer relative to the container are also noted. If the position of any magnet inside the container changes, then the measured vector fields at the these locations also change, indicating that the tag has been removed, the seal has broken, and therefore that the container and objects inside may have been tampered with. A hollow wheel with magnets inside may also provide a similar magnetic vector field tag and seal. As the wheel turns, the magnets tumble randomly inside, removing the tag and breaking the seal.
Massive vector fields and black holes
International Nuclear Information System (INIS)
Frolov, V.P.
1977-04-01
A massive vector field inside the event horizon created by the static sources located outside the black hole is investigated. It is shown that the back reaction of such a field on the metric near r = 0 cannot be neglected. The possibility of the space-time structure changing near r = 0 due to the external massive field is discussed
Hamiltonian lattice field theory: Computer calculations using variational methods
International Nuclear Information System (INIS)
Zako, R.L.
1991-01-01
I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. I show how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems
Hamiltonian lattice field theory: Computer calculations using variational methods
International Nuclear Information System (INIS)
Zako, R.L.
1991-01-01
A variational method is developed for systematic numerical computation of physical quantities-bound state energies and scattering amplitudes-in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. An algorithm is presented for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. It is shown how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. It is shown how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. The author discusses the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, the author does not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. The method is applied to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. The author describes a computer implementation of the method and present numerical results for simple quantum mechanical systems
Hamiltonian field description of two-dimensional vortex fluids and guiding center plasmas
International Nuclear Information System (INIS)
Morrison, P.J.
1981-03-01
The equations that describe the motion of two-dimensional vortex fluids and guiding center plasmas are shown to possess underlying field Hamiltonian structure. A Poisson bracket which is given in terms of the vorticity, the physical although noncanonical dynamical variable, casts these equations into Heisenberg form. The Hamiltonian density is the kinetic energy density of the fluid. The well-known conserved quantities are seen to be in involution with respect to this Poisson bracket. Expanding the vorticity in terms of a Fourier-Dirac series transforms the field description given here into the usual canonical equations for discrete vortex motion. A Clebsch potential representation of the vorticity transforms the noncanonical field description into a canonical description
Institute of Scientific and Technical Information of China (English)
Hua WANG; ALATANCANG; Junjie HUANG
2011-01-01
The authors investigate the completeness of the system of eigen or root vectors of the 2 x 2 upper triangular infinite-dimensional Hamiltonian operator H0.First,the geometrical multiplicity and the algebraic index of the eigenvalue of H0 are considered.Next,some necessary and sufficient conditions for the completeness of the system of eigen or root vectors of H0 are obtained. Finally,the obtained results are tested in several examples.
Vector supersymmetry in topological field theories
International Nuclear Information System (INIS)
Gieres, F.; Grimstrup, J.; Pisar, T.; Schweda, M.
2000-01-01
We present a simple derivation of vector supersymmetry transformations for topological field theories of Schwarz- and Witten-type. Our method is similar to the derivation of BRST-transformations from the so-called horizontality conditions or Russian formulae. We show that this procedure reproduces in a concise way the known vector supersymmetry transformations of various topological models and we use it to obtain some new transformations of this type for 4d topological YM-theories in different gauges. (author)
International Nuclear Information System (INIS)
Skachkov, N.; Solovtsov, I.
1979-01-01
Based on the hamiltonian formulation of quantum field theory proposed by Kadyshevsky the three-dimensional relativistic approach is developed for describing the form factors of composite systems. The main features of the diagram technique appearing in the covariant hamiltonian formulation of field theory are discussed. The three-dimensional relativistic equation for the vertex function is derived and its connection with that for the quasipotential wave function is found. The expressions are obtained for the form factor of the system through equal-time two-particle wave functions both in momentum and relativistic configurational representations. An explicit expression for the form factor is found for the case of two-particle interaction through the Coulomb potential
Existence for stationary mean-field games with congestion and quadratic Hamiltonians
Gomes, Diogo A.
2015-09-03
Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel
Determination of key parameters of vector multifractal vector fields
Schertzer, D. J. M.; Tchiguirinskaia, I.
2017-12-01
For too long time, multifractal analyses and simulations have been restricted to scalar-valued fields (Schertzer and Tchiguirinskaia, 2017a,b). For instance, the wind velocity multifractality has been mostly analysed in terms of scalar structure functions and with the scalar energy flux. This restriction has had the unfortunate consequences that multifractals were applicable to their full extent in geophysics, whereas it has inspired them. Indeed a key question in geophysics is the complexity of the interactions between various fields or they components. Nevertheless, sophisticated methods have been developed to determine the key parameters of scalar valued fields. In this communication, we first present the vector extensions of the universal multifractal analysis techniques to multifractals whose generator belong to a Levy-Clifford algebra (Schertzer and Tchiguirinskaia, 2015). We point out further extensions noting the increased complexity. For instance, the (scalar) index of multifractality becomes a matrice. Schertzer, D. and Tchiguirinskaia, I. (2015) `Multifractal vector fields and stochastic Clifford algebra', Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p. 123127. doi: 10.1063/1.4937364. Schertzer, D. and Tchiguirinskaia, I. (2017) `An Introduction to Multifractals and Scale Symmetry Groups', in Ghanbarian, B. and Hunt, A. (eds) Fractals: Concepts and Applications in Geosciences. CRC Press, p. (in press). Schertzer, D. and Tchiguirinskaia, I. (2017b) `Pandora Box of Multifractals: Barely Open ?', in Tsonis, A. A. (ed.) 30 Years of Nonlinear Dynamics in Geophysics. Berlin: Springer, p. (in press).
Optical currents in vector fields
DEFF Research Database (Denmark)
Angelsky, O. V.; Gorsky, M. P.; Maksimyak, P. P.
2011-01-01
The influence of phase relations and the degree of mutual coherence of superimposing waves in the arrangements of twowave superposition on the characteristics of the microparticle's motion has been analyzed. The prospects of studying temporal coherence using the proposed approach are made. For th....... For the first time, we have shown experimentally the possibility of diagnostics the optical currents in liquids caused by polarization characteristics of an optical field alone, using test metallic particles of nanoscale....
The optical analogy for vector fields
Parker, E. N. (Editor)
1991-01-01
This paper develops the optical analogy for a general vector field. The optical analogy allows the examination of certain aspects of a vector field that are not otherwise readily accessible. In particular, in the cases of a stationary Eulerian flow v of an ideal fluid and a magnetostatic field B, the vectors v and B have surface loci in common with their curls. The intrinsic discontinuities around local maxima in absolute values of v and B take the form of vortex sheets and current sheets, respectively, the former playing a fundamental role in the development of hydrodyamic turbulence and the latter playing a major role in heating the X-ray coronas of stars and galaxies.
Polynomial Vector Fields in One Complex Variable
DEFF Research Database (Denmark)
Branner, Bodil
In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias.......In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias....
Vector Fields European user group meeting
2007-01-01
The "Vector Fields European user group meeting" will take place at CERN on 26 and 27 September 2007. Within this framework two workshops are organized at the CERN Training Centre: 24 September 2007 Modelling Magnets with Opera 25 September 2007 Modelling of Charged Particle Beam Devices with Opera If you are interested in attending the workshop or the user group meeting please contact Julie Shepherd (Vector Fields) or Pierre Baehler (CERN) directly at: Julie.Shepherd@vectorfields.co.uk, +44 (0) 1865 854933 or +44 (0) 1865 370151 Pierre.Baehler@cern.ch, 75016 / 160156.
Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics
Energy Technology Data Exchange (ETDEWEB)
Bauer, Sebastian; Tavan, Paul; Mathias, Gerald, E-mail: gerald.mathias@physik.uni-muenchen.de [Lehrstuhl für BioMolekulare Optik, Ludig-Maximilians Universität München, Oettingenstr. 67, 80538 München (Germany)
2014-03-14
In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call “Hamiltonian dielectric solvent” (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.
On bounded and unbounded dynamics of the Hamiltonian system for unified scalar field cosmology
International Nuclear Information System (INIS)
Starkov, Konstantin E.
2016-01-01
This paper is devoted to the research of global dynamics for the Hamiltonian system formed by the unified scalar field cosmology. We prove that this system possesses only unbounded dynamics in the space of negative curvature. It is found the invariant domain filled only by unbounded dynamics for the space with positive curvature. Further, we construct a set of polytopes depending on the Hamiltonian level surface that contain all compact invariant sets. Besides, one invariant two dimensional plane is described. Finally, we establish nonchaoticity of dynamics in one special case. - Highlights: • Unbounded dynamics is stated in case of negative curvature. • Domain with unbounded dynamics is got in case of positive curvature. • Localization polytope for compact invariant sets is computed. • One two dimensional invariant plane is described. • Nonchaotic dynamics is stated in one special case.
Fermion bag approach to Hamiltonian lattice field theories in continuous time
Huffman, Emilie; Chandrasekharan, Shailesh
2017-12-01
We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the 3 d Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find η =0.54 (6 ) and ν =0.88 (2 ) using lattices up to N =2304 sites. We argue that even sizes up to N =10 ,000 sites should be accessible with supercomputers available today.
On bounded and unbounded dynamics of the Hamiltonian system for unified scalar field cosmology
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E., E-mail: kstarkov@ipn.mx
2016-05-27
This paper is devoted to the research of global dynamics for the Hamiltonian system formed by the unified scalar field cosmology. We prove that this system possesses only unbounded dynamics in the space of negative curvature. It is found the invariant domain filled only by unbounded dynamics for the space with positive curvature. Further, we construct a set of polytopes depending on the Hamiltonian level surface that contain all compact invariant sets. Besides, one invariant two dimensional plane is described. Finally, we establish nonchaoticity of dynamics in one special case. - Highlights: • Unbounded dynamics is stated in case of negative curvature. • Domain with unbounded dynamics is got in case of positive curvature. • Localization polytope for compact invariant sets is computed. • One two dimensional invariant plane is described. • Nonchaotic dynamics is stated in one special case.
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E., E-mail: kstarkov@ipn.mx
2015-06-12
In this paper we study some features of global dynamics for one Hamiltonian system arisen in cosmology which is formed by the minimally coupled field; this system was introduced by Maciejewski et al. in 2007. We establish that under some simple conditions imposed on parameters of this system all trajectories are unbounded in both of time directions. Further, we present other conditions for system parameters under which we localize the domain with unbounded dynamics; this domain is defined with help of bounds for values of the Hamiltonian level surface parameter. We describe the case when our system possesses periodic orbits which are found explicitly. In the rest of the cases we get some localization bounds for compact invariant sets. - Highlights: • Domain with unbounded dynamics is localized. • Equations for periodic orbits are given in one level set. • Localizations for compact invariant sets are got.
ESTIMATING ELECTRIC FIELDS FROM VECTOR MAGNETOGRAM SEQUENCES
International Nuclear Information System (INIS)
Fisher, G. H.; Welsch, B. T.; Abbett, W. P.; Bercik, D. J.
2010-01-01
Determining the electric field distribution on the Sun's photosphere is essential for quantitative studies of how energy flows from the Sun's photosphere, through the corona, and into the heliosphere. This electric field also provides valuable input for data-driven models of the solar atmosphere and the Sun-Earth system. We show how observed vector magnetogram time series can be used to estimate the photospheric electric field. Our method uses a 'poloidal-toroidal decomposition' (PTD) of the time derivative of the vector magnetic field. These solutions provide an electric field whose curl obeys all three components of Faraday's Law. The PTD solutions are not unique; the gradient of a scalar potential can be added to the PTD electric field without affecting consistency with Faraday's Law. We then present an iterative technique to determine a potential function consistent with ideal MHD evolution; but this field is also not a unique solution to Faraday's Law. Finally, we explore a variational approach that minimizes an energy functional to determine a unique electric field, a generalization of Longcope's 'Minimum Energy Fit'. The PTD technique, the iterative technique, and the variational technique are used to estimate electric fields from a pair of synthetic vector magnetograms taken from an MHD simulation; and these fields are compared with the simulation's known electric fields. The PTD and iteration techniques compare favorably to results from existing velocity inversion techniques. These three techniques are then applied to a pair of vector magnetograms of solar active region NOAA AR8210, to demonstrate the methods with real data. Careful examination of the results from all three methods indicates that evolution of the magnetic vector by itself does not provide enough information to determine the true electric field in the photosphere. Either more information from other measurements, or physical constraints other than those considered here are necessary to find
Circular Conditional Autoregressive Modeling of Vector Fields.
Modlin, Danny; Fuentes, Montse; Reich, Brian
2012-02-01
As hurricanes approach landfall, there are several hazards for which coastal populations must be prepared. Damaging winds, torrential rains, and tornadoes play havoc with both the coast and inland areas; but, the biggest seaside menace to life and property is the storm surge. Wind fields are used as the primary forcing for the numerical forecasts of the coastal ocean response to hurricane force winds, such as the height of the storm surge and the degree of coastal flooding. Unfortunately, developments in deterministic modeling of these forcings have been hindered by computational expenses. In this paper, we present a multivariate spatial model for vector fields, that we apply to hurricane winds. We parameterize the wind vector at each site in polar coordinates and specify a circular conditional autoregressive (CCAR) model for the vector direction, and a spatial CAR model for speed. We apply our framework for vector fields to hurricane surface wind fields for Hurricane Floyd of 1999 and compare our CCAR model to prior methods that decompose wind speed and direction into its N-S and W-E cardinal components.
Linearization of germs of hyperbolic vector fields
Bonckaert, P; Naudot, [No Value; Yang, JZ
2003-01-01
We develop a normal form to express asymptotically a conjugacy between a germ of resonant vector field and its linear part. We show that such an asymptotic expression can be written in terms of functions of the Logarithmic Mourtada type. To cite this article: P Bonckaert et al., C. R. Acad. Sci.
Null vectors in superconformal quantum field theory
International Nuclear Information System (INIS)
Huang Chaoshang
1993-01-01
The superspace formulation of the N=1 superconformal field theory and superconformal Ward identities are used to give a precise definition of fusion. Using the fusion procedure, superconformally covariant differential equations are derived and consequently a complete and straightforward algorithm for finding null vectors in Verma modules of the Neveu-Schwarz algebra is given. (orig.)
Normal equivariant forms of vector fields
International Nuclear Information System (INIS)
Sanchez Bringas, F.
1992-07-01
We prove a theorem of linearization of type Siegel and a theorem of normal forms of type Poincare-Dulac for germs of holomorphic vector fields in the origin of C 2 , Γ -equivariants, where Γ is a finite subgroup of GL (2,C). (author). 5 refs
Hamiltonian quantization of self-dual tensor fields and a bosonic Nielsen-Ninomiya theorem
International Nuclear Information System (INIS)
Tang Waikeung
1989-01-01
The quantization of self-dual tensor fields is carried out following the procedure of Batalin and Fradkin. The (anti) self-duality constraints (either fermionic or bosonic) in the action leads to the gravitational anomaly. In the process of gauge fixing, the impossibility of the co-existence of a positive hamiltonian and covariant action is shown. A version of the Nielsen-Ninomiya theorem applies to self-dual tensor fields viz. the lattice version of the theory shows species doubling with zero net chirality. (orig.)
Field-strength formulation of gauge theories. The Hamiltonian approach in the Abelian theory
International Nuclear Information System (INIS)
Mendel, E.; Durand, L.
1984-01-01
We develop a Hamiltonian approach to the field-strength or dual formation of the Abelian gauge theory in which the potential A/sup μ/ is eliminated as a dynamical variable. Our work is based on the covariant gauge x/sup μ/A/sub μ/(x) = 0 which allows a simple elimination of A/sup μ/ in terms of the field strengths F/sup munu/. We obtain complete results for the generating functional for the Green's functions of the theory, Z = Z[f,g], where f and g are nonlocal currents coupled to E and B, and illustrate some unfamiliar aspects of the new formalism
The significance of vector magnetic field measurements
Hagyard, M. J.
1990-01-01
Observations of four flaring solar active regions, obtained during 1980-1986 with the NASA Marshall vector magnetograph (Hagyard et al., 1982 and 1985), are presented graphically and characterized in detail, with reference to nearly simultaneous Big Bear Solar Observatory and USAF ASW H-alpha images. It is shown that the flares occurred where local photospheric magnetic fields differed most from the potential field, with initial brightening on either side of a magnetic-neutral line near the point of maximum angular shear (rather than that of maximum magnetic-field strength, typically 1 kG or greater). Particular emphasis is placed on the fact that these significant nonpotential features were detected only by measuring all three components of the vector magnetic field.
Screening vector field modifications of general relativity
International Nuclear Information System (INIS)
Beltrán Jiménez, Jose; Delvas Fróes, André Luís; Mota, David F.
2013-01-01
A screening mechanism for conformal vector–tensor modifications of general relativity is proposed. The conformal factor depends on the norm of the vector field and makes the field to vanish in high dense regions, whereas drives it to a non-null value in low density environments. Such process occurs due to a spontaneous symmetry breaking mechanism and gives rise to both the screening of fifth forces as well as Lorentz violations. The cosmology and local constraints are also computed
``Massless'' vector field in de Sitter universe
Garidi, T.; Gazeau, J.-P.; Rouhani, S.; Takook, M. V.
2008-03-01
We proceed to the quantization of the massless vector field in the de Sitter (dS) space. This work is the natural continuation of a previous article devoted to the quantization of the dS massive vector field [J. P. Gazeau and M. V. Takook, J. Math. Phys. 41, 5920 (2000); T. Garidi et al., ibid. 43, 6379 (2002).] The term ``massless'' is used by reference to conformal invariance and propagation on the dS lightcone whereas ``massive'' refers to those dS fields which unambiguously contract to Minkowskian massive fields at zero curvature. Due to the combined occurrences of gauge invariance and indefinite metric, the covariant quantization of the massless vector field requires an indecomposable representation of the de Sitter group. We work with the gauge fixing corresponding to the simplest Gupta-Bleuler structure. The field operator is defined with the help of coordinate-independent de Sitter waves (the modes). The latter are simple to manipulate and most adapted to group theoretical approaches. The physical states characterized by the divergencelessness condition are, for instance, easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemannian manifold for the modes and the two-point function.
''Massless'' vector field in de Sitter universe
International Nuclear Information System (INIS)
Garidi, T.; Gazeau, J.-P.; Rouhani, S.; Takook, M. V.
2008-01-01
We proceed to the quantization of the massless vector field in the de Sitter (dS) space. This work is the natural continuation of a previous article devoted to the quantization of the dS massive vector field [J. P. Gazeau and M. V. Takook, J. Math. Phys. 41, 5920 (2000); T. Garidi et al., ibid. 43, 6379 (2002).] The term ''massless'' is used by reference to conformal invariance and propagation on the dS lightcone whereas ''massive'' refers to those dS fields which unambiguously contract to Minkowskian massive fields at zero curvature. Due to the combined occurrences of gauge invariance and indefinite metric, the covariant quantization of the massless vector field requires an indecomposable representation of the de Sitter group. We work with the gauge fixing corresponding to the simplest Gupta-Bleuler structure. The field operator is defined with the help of coordinate-independent de Sitter waves (the modes). The latter are simple to manipulate and most adapted to group theoretical approaches. The physical states characterized by the divergencelessness condition are, for instance, easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemannian manifold for the modes and the two-point function
Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches
Antonowicz, Marek; Szczyrba, Wiktor
1985-06-01
We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.
Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches
International Nuclear Information System (INIS)
Antonowicz, M.; Szczyrba, W.
1985-01-01
We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8 = 12 independent degrees of freedom in the phase space
Perturbations of ultralight vector field dark matter
Energy Technology Data Exchange (ETDEWEB)
Cembranos, J.A.R.; Maroto, A.L.; Jareño, S.J. Núñez [Departamento de Física Teórica I, Universidad Complutense de Madrid, E-28040 Madrid (Spain)
2017-02-13
We study the dynamics of cosmological perturbations in models of dark matter based on ultralight coherent vector fields. Very much as for scalar field dark matter, we find two different regimes in the evolution: for modes with k{sup 2}≪Hma, we have a particle-like behaviour indistinguishable from cold dark matter, whereas for modes with k{sup 2}≫Hma, we get a wave-like behaviour in which the sound speed is non-vanishing and of order c{sub s}{sup 2}≃k{sup 2}/m{sup 2}a{sup 2}. This implies that, also in these models, structure formation could be suppressed on small scales. However, unlike the scalar case, the fact that the background evolution contains a non-vanishing homogeneous vector field implies that, in general, the evolution of the three kinds of perturbations (scalar, vector and tensor) can no longer be decoupled at the linear level. More specifically, in the particle regime, the three types of perturbations are actually decoupled, whereas in the wave regime, the three vector field perturbations generate one scalar-tensor and two vector-tensor perturbations in the metric. Also in the wave regime, we find that a non-vanishing anisotropic stress is present in the perturbed energy-momentum tensor giving rise to a gravitational slip of order (Φ−Ψ)/Φ∼c{sub s}{sup 2}. Moreover in this regime the amplitude of the tensor to scalar ratio of the scalar-tensor modes is also h/Φ∼c{sub s}{sup 2}. This implies that small-scale density perturbations are necessarily associated to the presence of gravity waves in this model. We compare their spectrum with the sensitivity of present and future gravity waves detectors.
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
Antisymmetric tensor generalizations of affine vector fields.
Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro
2016-02-01
Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.
Hamiltonian field description of the one-dimensional Poisson-Vlasov equations
International Nuclear Information System (INIS)
Morrison, P.J.
1981-07-01
The one-dimensional Poisson-Vlasov equations are cast into Hamiltonian form. A Poisson Bracket in terms of the phase space density, as sole dynamical variable, is presented. This Poisson bracket is not of the usual form, but possesses the commutator properties of antisymmetry, bilinearity, and nonassociativity by virtue of the Jacobi requirement. Clebsch potentials are seen to yield a conventional (canonical) formulation. This formulation is discretized by expansion in terms of an arbitrary complete set of basis functions. In particular, a wave field representation is obtained
Multifractal vector fields and stochastic Clifford algebra.
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Multifractal vector fields and stochastic Clifford algebra
Energy Technology Data Exchange (ETDEWEB)
Schertzer, Daniel, E-mail: Daniel.Schertzer@enpc.fr; Tchiguirinskaia, Ioulia, E-mail: Ioulia.Tchiguirinskaia@enpc.fr [University Paris-Est, Ecole des Ponts ParisTech, Hydrology Meteorology and Complexity HM& Co, Marne-la-Vallée (France)
2015-12-15
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Energy-momentum tensor of intermediate vector bosons in an external electromagnetic field
International Nuclear Information System (INIS)
Mostepanenko, V.M.; Sokolov, I.Yu.
1988-01-01
Expressions are obtained for the canonical and metric energy-momentum tensors of the vector field of intermediate bosons in an external electromagnetic field. It is shown that in the case of a gyromagnetic ratio not equal to unity the energy-momentum tensor cannot be symmetrized on its indices, and an additional term proportional to the anomalous magnetic moment appears in the conservation laws. A modification of the canonical formalism for scalar and vector fields in an external field is proposed in accordance with which the Hamiltonian density is equal to the 00 component of the energy-momentum tensor. An expression for the energy-momentum tensor of a closed system containing a gauge field of intermediate bosons and an electromagnetic field is obtained
The vector structure of active magnetic fields
Parker, E. N.
1985-01-01
Observations are needed to show the form of the strains introduced into the fields above the surface of the Sun. The longitudinal component alone does not provide the basic information, so that it has been necessary in the past to use the filamentary structure observed in H sub alpha to supplement the longitudinal information. Vector measurements provide the additional essential information to determine the strains, with the filamentary structure available as a check for consistency. It is to be expected, then, that vector measurements will permit a direct mapping of the strains imposed on the magnetic fields of active regions. It will be interesting to study the relation of those strains to the emergence of magnetic flux, flares, eruptive prominences, etc. In particular we may hope to study the relaxation of the strains via the dynamical nonequilibrium.
Efficient morse decompositions of vector fields.
Chen, Guoning; Mischaikow, Konstantin; Laramee, Robert S; Zhang, Eugene
2008-01-01
Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits, and separatrices that are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field analysis unsuitable for rigorous interpretations. We advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of a vector field in the form of a directed graph, called a Morse connection graph (MCG). While an MCG exists for every vector field, it need not be unique. Previous techniques for computing MCG's, while fast, are overly conservative and usually results in MCG's that are too coarse to be useful for the applications. To address this issue, we present a new technique for performing Morse decomposition based on the concept of tau-maps, which typically provides finer MCG's than existing techniques. Furthermore, the choice of tau provides a natural tradeoff between the fineness of the MCG's and the computational costs. We provide efficient implementations of Morse decomposition based on tau-maps, which include the use of forward and backward mapping techniques and an adaptive approach in constructing better approximations of the images of the triangles in the meshes used for simulation.. Furthermore, we propose the use of spatial tau-maps in addition to the original temporal tau-maps. These techniques provide additional trade-offs between the quality of the MCGs and the speed of computation. We demonstrate the utility of our technique with various examples in the plane and on surfaces including engine simulation data sets.
Gauge structure of neutral-vector field theory. [Massive vector fields, massless limits
Energy Technology Data Exchange (ETDEWEB)
Kubo, R; Yokoyama, [Hiroshima univ., Takehara (Japan). Research Inst. for Theoretical Physics
1975-03-01
General aspects of gauge structure of neutral-vector field theory are investigated from an extended standpoint, where massive vector fields are treated in a form corresponding to the electromagnetic fields in a general gauge formalism reported previously. All results obtained are shown to have unique massless limits. It is shown that a generalized q-number gauge transformation for fields makes the theory invariant in cooperation with a simultaneous transformation for relevant gauge parameters. A method of differentiation with respect to a gauge variable is found to clarify some essential features of the gauge structure. Two possible types of gauge structure also emerge correspondingly to the massless case. A neutral-vector field theory proposed in a preceding paper is included in the present framework as the most preferable case.
Hamiltonian Light-Front Field Theory: Recent Progress and Tantalizing Prospects
International Nuclear Information System (INIS)
Vary, J. P.
2012-01-01
Fundamental theories, such as quantum electrodynamics and quantum chromodynamics promise great predictive power addressing phenomena over vast scales from the microscopic to cosmic scales. However, new non-perturbative tools are required for physics to span from one scale to the next. I outline recent theoretical and computational progress to build these bridges and provide illustrative results for Hamiltonian Light Front Field Theory. One key area is our development of basis function approaches that cast the theory as a Hamiltonian matrix problem while preserving a maximal set of symmetries. Regulating the theory with an external field that can be removed to obtain the continuum limit offers additional possibilities as seen in an application to the anomalous magnetic moment of the electron. Recent progress capitalizes on algorithm and computer developments for setting up and solving very large sparse matrix eigenvalue problems. Matrices with dimensions of 20 billion basis states are now solved on leadership-class computers for their low-lying eigenstates and eigenfunctions. (author)
Integrable and nonintegrable non-KAM Hamiltonians and magnetic field topology
International Nuclear Information System (INIS)
Salat, A.
1986-01-01
The integrability of Hamiltonians H(P 1 , P 2 , Q 1 , Q 2 )=P 1 G 1 (Q 1 ,Q 2 )+P 2 G 2 (Q 1 ,Q 2 ), with arbitrary analytic G 1 and G 2 , 2π-periodic in Q 1 and Q 2 , is analytically investigated. Such H cannot be separated into two parts, H=H 0 +H 21 , such that the KAM theorem would apply for vertical strokeH 1 vertical stroke 0 vertical stroke. For G 2 =const such Hamiltonians correspond to toroidal magnetic fields with constant rotational transform. Integrability is then equivalent to the existence of closed magnetic surfaces. The winding number w of the Q 1 , Q 2 flow (i.e. the rotational transform) is rational in 'tongue'-like domains in (ω 2 /ω 1 ,A) diagrams. Here ω i = i > is the average over both Q 1 and Q 2 , G i =ω i +F i , i=1, 2, and A is an amplitude parameter of F i (F i =0 for A=0). Integrability is proved almost everywhere in the complementary domains, namely where w is sufficiently irrational. In the generic case ('conditional') nonintegrability is proved for the class dG 1 /dQ 1 +dG 2 /dQ 2 =0 in the tongues, which in this case shrink to lines with w=ω 1 /ω 2 . It is shown that if the number of dimensions in the Hamiltonian were larger than two, qualitatively different results would be expected. (orig.)
On Discrete Killing Vector Fields and Patterns on Surfaces
Ben-Chen, Mirela; Butscher, Adrian; Solomon, Justin; Guibas, Leonidas
2010-01-01
, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis. Journal
Hamiltonian term for a uniform dc electric field under the adiabatic approximation
Siu, Zhuo Bin; Jalil, Mansoor B. A.; Tan, Seng Ghee
2018-02-01
In this work, we show that the disorder-free Kubo formula for the nonequilibrium value of an observable due to a dc electric field, represented by Exx ̂ in the Hamiltonian, can be interpreted as the standard time-independent theory response of the observable due to a time- and position-independent perturbation HMF. We derive the explicit expression for HMF and show that it originates from the adiabatic approximation to Kubo formula and the time-independent perturbation theory, as well as the Sundaram-Niu wave-packet formalism, we show that HMF reproduces the effect of the E field, i.e., Exx ̂ , up to the first order. This replacement suggests the emergence of a spin current term that is not captured by the standard Kubo formula spin current calculation. We illustrate this via the exemplary spin current for the heavy-hole spin-3/2 Luttinger system.
Mandrà, Salvatore; Zhu, Zheng; Katzgraber, Helmut G
2017-02-17
We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated with a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)NJOPFM1367-263010.1088/1367-2630/11/7/073021]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.
The Hamiltonian formulation of regular rth-order Lagrangian field theories
International Nuclear Information System (INIS)
Shadwick, W.F.
1982-01-01
A Hamiltonian formulation of regular rth-order Lagrangian field theories over an m-dimensional manifold is presented in terms of the Hamilton-Cartan formalism. It is demonstrated that a uniquely determined Cartan m-form may be associated to an rth-order Lagrangian by imposing conditions of congruence modulo a suitably defined system of contact m-forms. A geometric regularity condition is given and it is shown that, for a regular Lagrangian, the momenta defined by the Hamilton-Cartan formalism, together with the coordinates on the (r-1)st-order jet bundle, are a minimal set of local coordinates needed to express the Euler-Lagrange equations. When r is greater than one, the number of variables required is strictly less than the dimension of the (2r-1)st order jet bundle. It is shown that, in these coordinates, the Euler-Lagrange equations take the first-order Hamiltonian form given by de Donder. It is also shown that the geometrically natural generalization of the Hamilton-Jacobi procedure for finding extremals is equivalent to de Donder's Hamilton-Jacobi equation. (orig.)
Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
International Nuclear Information System (INIS)
Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo; Zanelli, Jorge
2007-01-01
We examine anti-de Sitter gravity minimally coupled to a self-interacting scalar field in D>=4 dimensions when the mass of the scalar field is in the range m * 2 = 2 * 2 +l -2 . Here, l is the AdS radius, and m * 2 is the Breitenlohner-Freedman mass. We show that even though the scalar field generically has a slow fall-off at infinity which back reacts on the metric so as to modify its standard asymptotic behavior, one can still formulate asymptotic conditions (i) that are anti-de Sitter invariant; and (ii) that allows the construction of well-defined and finite Hamiltonian generators for all elements of the anti-de Sitter algebra. This requires imposing a functional relationship on the coefficients a, b that control the two independent terms in the asymptotic expansion of the scalar field. The anti-de Sitter charges are found to involve a scalar field contribution. Subtleties associated with the self-interactions of the scalar field as well as its gravitational back reaction, not discussed in previous treatments, are explicitly analyzed. In particular, it is shown that the fields develop extra logarithmic branches for specific values of the scalar field mass (in addition to the known logarithmic branch at the B-F bound)
Conformal Vector Fields on Doubly Warped Product Manifolds and Applications
Directory of Open Access Journals (Sweden)
H. K. El-Sayied
2016-01-01
Full Text Available This article aimed to study and explore conformal vector fields on doubly warped product manifolds as well as on doubly warped spacetime. Then we derive sufficient conditions for matter and Ricci collineations on doubly warped product manifolds. A special attention is paid to concurrent vector fields. Finally, Ricci solitons on doubly warped product spacetime admitting conformal vector fields are considered.
n-Characteristic Vector Fields of Contact Manifoldss
Hassanzadeh, Babak
2017-01-01
In present paper we define and study $n$-characteristic vector fields. We present definition of Tanaka-Webster connection, then use it for studying the behavior of $n$-characteristic vector fields. Also we show some results about of these vector fields by Tanaka-Webster connection.
Directory of Open Access Journals (Sweden)
Galimzian G. Islamov
2015-12-01
Full Text Available It is shown that a simple postulate “The displacement field of the vacuum is a normalized electric field”, is equivalent to three parametric representation of the displacement field of the vacuum: $$ u(x;t = P(x \\cos k(xt + Q(x \\sin k(xt. $$ Here $t$ — time; $k(x$ — frequency vibrations at the point of three-dimensional Euclidean space; $P(x, Q(x$ — a pair of stationary orthonormal vector fields; $(k,P, Q$ — parameter list of the displacement field. In this case, the normalization factor has dimension $T^{-2}$. The speed of the displacement field $$ v(x;t = \\frac{\\partial u(x;t}{\\partial t} = k(x(Q(x \\cos k(xt - P(x \\sin k(xt. $$ The electric field corresponding to this distribution of the displacement field of vacuum, is given by the formula $$ E(x;t = -\\frac{\\partial v(x;t}{\\partial t} = k^2(xu(x;t. $$ Moreover, the magnetic induction $$ B(x;t = \\mathop{\\mathrm{rot }} v(x; t. $$ These constructions are used in the determination of local and global solutions of Maxwell's equations describing the dynamics of electromagnetic fields.
Xu, Danfeng; Gu, Bing; Rui, Guanghao; Zhan, Qiwen; Cui, Yiping
2016-02-22
We present an arbitrary vector field with hybrid polarization based on the combination of a pair of orthogonal elliptically polarized base vectors on the Poincaré sphere. It is shown that the created vector field is only dependent on the latitude angle 2χ but is independent on the longitude angle 2ψ on the Poincaré sphere. By adjusting the latitude angle 2χ, which is related to two identical waveplates in a common path interferometric arrangement, one could obtain arbitrary type of vector fields. Experimentally, we demonstrate the generation of such kind of vector fields and confirm the distribution of state of polarization by the measurement of Stokes parameters. Besides, we investigate the tight focusing properties of these vector fields. It is found that the additional degree of freedom 2χ provided by arbitrary vector field with hybrid polarization allows one to control the spatial structure of polarization and to engineer the focusing field.
International Nuclear Information System (INIS)
Dahmen, Bernd
1994-01-01
A systematic method to obtain strong coupling expansions for scattering quantities in hamiltonian lattice field theories is presented. I develop the conceptual ideas for the case of the hamiltonian field theory analogue of the Ising model, in d space and one time dimension. The main result is a convergent series representation for the scattering states and the transition matrix. To be explicit, the special cases of d=1 and d=3 spatial dimensions are discussed in detail. I compute the next-to-leading order approximation for the phase shifts. The application of the method to investigate low-energy scattering phenomena in lattice gauge theory and QCD is proposed. ((orig.))
Coherent states of quantum systems. [Hamiltonians, variable magnetic field, adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
Trifonov, D A
1975-01-01
Time-evolution of coherent states and uncertainty relations for quantum systems are considered as well as the relation between the various types of coherent states. The most general form of the Hamiltonians that keep the uncertainty products at a minimum is found using the coherent states. The minimum uncertainty packets are shown to be coherent states of the type nonstationary-system coherent states. Two specific systems, namely that of a generalized N-dimensional oscillator and that of a charged particle moving in a variable magnetic field, are treated as examples. The adiabatic approximation to the uncertainty products for these systems is also discussed and the minimality is found to be retained with an exponential accuracy.
Small traveling clusters in attractive and repulsive Hamiltonian mean-field models.
Barré, Julien; Yamaguchi, Yoshiyuki Y
2009-03-01
Long-lasting small traveling clusters are studied in the Hamiltonian mean-field model by comparing between attractive and repulsive interactions. Nonlinear Landau damping theory predicts that a Gaussian momentum distribution on a spatially homogeneous background permits the existence of traveling clusters in the repulsive case, as in plasma systems, but not in the attractive case. Nevertheless, extending the analysis to a two-parameter family of momentum distributions of Fermi-Dirac type, we theoretically predict the existence of traveling clusters in the attractive case; these findings are confirmed by direct N -body numerical simulations. The parameter region with the traveling clusters is much reduced in the attractive case with respect to the repulsive case.
Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion
International Nuclear Information System (INIS)
Kluepfel, Peter
2008-01-01
This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)
Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion
Energy Technology Data Exchange (ETDEWEB)
Kluepfel, Peter
2008-07-29
This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)
Gauge anomaly with vector and axial-vector fields in 6D curved space
Yajima, Satoshi; Eguchi, Kohei; Fukuda, Makoto; Oka, Tomonori
2018-03-01
Imposing the conservation equation of the vector current for a fermion of spin 1/2 at the quantum level, a gauge anomaly for the fermion coupling with non-Abelian vector and axial-vector fields in 6D curved space is expressed in tensorial form. The anomaly consists of terms that resemble the chiral U(1) anomaly and the commutator terms that disappear if the axial-vector field is Abelian.
Comments on conformal Killing vector fields and quantum field theory
International Nuclear Information System (INIS)
Brown, M.R.; Ottewill, A.C.; Siklos, S.T.C.
1982-01-01
We give a comprehensive analysis of those vacuums for flat and conformally flat space-times which can be defined by timelike, hypersurface-orthogonal, conformal Killing vector fields. We obtain formulas for the difference in stress-energy density between any two such states and display the correspondence with the renormalized stress tensors. A brief discussion is given of the relevance of these results to quantum-mechanical measurements made by noninertial observers moving through flat space
Vector optical fields with bipolar symmetry of linear polarization.
Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Si, Yu; Tu, Chenghou; Wang, Hui-Tian
2013-09-15
We focus on a new kind of vector optical field with bipolar symmetry of linear polarization instead of cylindrical and elliptical symmetries, enriching members of family of vector optical fields. We design theoretically and generate experimentally the demanded vector optical fields and then explore some novel tightly focusing properties. The geometric configurations of states of polarization provide additional degrees of freedom assisting in engineering the field distribution at the focus to the specific applications such as lithography, optical trapping, and material processing.
International Nuclear Information System (INIS)
Hotta, Ryuuichi; Morozumi, Takuya; Takata, Hiroyuki
2012-01-01
We develop the method analyzing particle number non-conserving phenomena with non-equilibrium quantum field-theory. In this study, we consider a CP violating model with interaction Hamiltonian that breaks particle number conservation. To derive the quantum Boltzmann equation for the particle number, we solve Schwinger-Dyson equation, which are obtained from two particle irreducible closed-time-path (2PI CTP) effective action. In this calculation, we show the contribution from interaction Hamiltonian to the time evolution of expectation value of particle number.
Robust point matching via vector field consensus.
Jiayi Ma; Ji Zhao; Jinwen Tian; Yuille, Alan L; Zhuowen Tu
2014-04-01
In this paper, we propose an efficient algorithm, called vector field consensus, for establishing robust point correspondences between two sets of points. Our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences, or outliers, in addition to a limited number of true correspondences (inliers). Next, we solve for correspondence by interpolating a vector field between the two point sets, which involves estimating a consensus of inlier points whose matching follows a nonparametric geometrical constraint. We formulate this a maximum a posteriori (MAP) estimation of a Bayesian model with hidden/latent variables indicating whether matches in the putative set are outliers or inliers. We impose nonparametric geometrical constraints on the correspondence, as a prior distribution, using Tikhonov regularizers in a reproducing kernel Hilbert space. MAP estimation is performed by the EM algorithm which by also estimating the variance of the prior model (initialized to a large value) is able to obtain good estimates very quickly (e.g., avoiding many of the local minima inherent in this formulation). We illustrate this method on data sets in 2D and 3D and demonstrate that it is robust to a very large number of outliers (even up to 90%). We also show that in the special case where there is an underlying parametric geometrical model (e.g., the epipolar line constraint) that we obtain better results than standard alternatives like RANSAC if a large number of outliers are present. This suggests a two-stage strategy, where we use our nonparametric model to reduce the size of the putative set and then apply a parametric variant of our approach to estimate the geometric parameters. Our algorithm is computationally efficient and we provide code for others to use it. In addition, our approach is general and can be applied to other problems, such as learning with a badly corrupted training data set.
A new look at the free electromagnetic field. The Gauss law as a hamiltonian equation of motion
International Nuclear Information System (INIS)
Aldaya, V.; Navarro-Salas, J.
1992-01-01
A new canonical formalism for the free electromagnetic field is proposed in terms of an infinite-dimensional Lie group. The Gauss law is derived as a hamiltonian equation of motion and the quantum theory is obtained by constructing the irreducible representation of the group. The quantum Gauss law thus appears as an additional polarization equation and not as a constraint equation. (orig.)
Spectral Analysis of Vector Magnetic Field Profiles
Parker, Robert L.; OBrien, Michael S.
1997-01-01
We investigate the power spectra and cross spectra derived from the three components of the vector magnetic field measured on a straight horizontal path above a statistically stationary source. All of these spectra, which can be estimated from the recorded time series, are related to a single two-dimensional power spectral density via integrals that run in the across-track direction in the wavenumber domain. Thus the measured spectra must obey a number of strong constraints: for example, the sum of the two power spectral densities of the two horizontal field components equals the power spectral density of the vertical component at every wavenumber and the phase spectrum between the vertical and along-track components is always pi/2. These constraints provide powerful checks on the quality of the measured data; if they are violated, measurement or environmental noise should be suspected. The noise due to errors of orientation has a clear characteristic; both the power and phase spectra of the components differ from those of crustal signals, which makes orientation noise easy to detect and to quantify. The spectra of the crustal signals can be inverted to obtain information about the cross-track structure of the field. We illustrate these ideas using a high-altitude Project Magnet profile flown in the southeastern Pacific Ocean.
Multiscale vector fields for image pattern recognition
Low, Kah-Chan; Coggins, James M.
1990-01-01
A uniform processing framework for low-level vision computing in which a bank of spatial filters maps the image intensity structure at each pixel into an abstract feature space is proposed. Some properties of the filters and the feature space are described. Local orientation is measured by a vector sum in the feature space as follows: each filter's preferred orientation along with the strength of the filter's output determine the orientation and the length of a vector in the feature space; the vectors for all filters are summed to yield a resultant vector for a particular pixel and scale. The orientation of the resultant vector indicates the local orientation, and the magnitude of the vector indicates the strength of the local orientation preference. Limitations of the vector sum method are discussed. Investigations show that the processing framework provides a useful, redundant representation of image structure across orientation and scale.
Parallel Vector Fields and Einstein Equations of Gravity | Mahara ...
African Journals Online (AJOL)
In this paper, we prove that no nontrivial timelike or spacelike parallel vector field exists in a region where the gravitational field created by macroscopic bodies and governed by Einstein's equations does not vanish. In other words, we prove that the existence of such vector fields in a region implies the vanishing of the ...
Ab-initio Hamiltonian approach to light nuclei and to quantum field ...
Indian Academy of Sciences (India)
A successful microscopic non-perturbative Hamiltonian approach to low- ... sparse matrix eigenvalue problem with the Lanczos algorithm on leadership class .... which allows for an arbitrary phase factor eiα that we have taken to be unity. The.
Derivation of Hamiltonians for accelerators
Energy Technology Data Exchange (ETDEWEB)
Symon, K.R.
1997-09-12
In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.
Lagrangian vector field and Lagrangian formulation of partial differential equations
Directory of Open Access Journals (Sweden)
M.Chen
2005-01-01
Full Text Available In this paper we consider the Lagrangian formulation of a system of second order quasilinear partial differential equations. Specifically we construct a Lagrangian vector field such that the flows of the vector field satisfy the original system of partial differential equations.
The Curl of a Vector Field: Beyond the Formula
Burch, Kimberly Jordan; Choi, Youngna
2006-01-01
It has been widely acknowledged that there is some discrepancy in the teaching of vector calculus in mathematics courses and other applied fields. The curl of a vector field is one topic many students can calculate without understanding its significance. In this paper, we explain the origin of the curl after presenting the standard mathematical…
Space-times carrying a quasirecurrent pairing of vector fields
International Nuclear Information System (INIS)
Rosca, R.; Ianus, S.
1977-01-01
A quasirecurrent pairing of vector fields(X 1 ,X 2 ,) defined previously by Rosca (C.R. Acad. Sci. 282 (1976)) is investigated on a space-time in two cases: (1) X 1 is spacelike and X 2 is timelike; (2) X 1 is null and X 2 is spacelike. The physical interpretation of these vector fields is given. (author)
Avoiding ergodicity and turbulence in R3 vector fields
International Nuclear Information System (INIS)
Ancochea, J.M.; Campoamor-Stursberg, R.; Gonzalez-Gascon, F.
2003-01-01
We show that analytic R 3 vector fields having the property of being transversal to either analytic functions or foliations F 2 , or parallel to a foliation, are free from ergodicity and turbulence. The absence of turbulence and ergodicity via induced vector fields is also proven
Design of 2D Time-Varying Vector Fields
Chen, Guoning; Kwatra, Vivek; Wei, Li-Yi; Hansen, Charles D.; Zhang, Eugene
2012-01-01
Design of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces. Our system supports the creation and modification of various time-varying vector fields with desired spatial and temporal characteristics through several design metaphors, including streamlines, pathlines, singularity paths, and bifurcations. These design metaphors are integrated into an element-based design to generate the time-varying vector fields via a sequence of basis field summations or spatial constrained optimizations at the sampled times. The key-frame design and field deformation are also introduced to support other user design scenarios. Accordingly, a spatial-temporal constrained optimization and the time-varying transformation are employed to generate the desired fields for these two design scenarios, respectively. We apply the time-varying vector fields generated using our design system to a number of important computer graphics applications that require controllable dynamic effects, such as evolving surface appearance, dynamic scene design, steerable crowd movement, and painterly animation. Many of these are difficult or impossible to achieve via prior simulation-based methods. In these applications, the time-varying vector fields have been applied as either orientation fields or advection fields to control the instantaneous appearance or evolving trajectories of the dynamic effects. © 1995-2012 IEEE.
Design of 2D time-varying vector fields.
Chen, Guoning; Kwatra, Vivek; Wei, Li-Yi; Hansen, Charles D; Zhang, Eugene
2012-10-01
Design of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces. Our system supports the creation and modification of various time-varying vector fields with desired spatial and temporal characteristics through several design metaphors, including streamlines, pathlines, singularity paths, and bifurcations. These design metaphors are integrated into an element-based design to generate the time-varying vector fields via a sequence of basis field summations or spatial constrained optimizations at the sampled times. The key-frame design and field deformation are also introduced to support other user design scenarios. Accordingly, a spatial-temporal constrained optimization and the time-varying transformation are employed to generate the desired fields for these two design scenarios, respectively. We apply the time-varying vector fields generated using our design system to a number of important computer graphics applications that require controllable dynamic effects, such as evolving surface appearance, dynamic scene design, steerable crowd movement, and painterly animation. Many of these are difficult or impossible to achieve via prior simulation-based methods. In these applications, the time-varying vector fields have been applied as either orientation fields or advection fields to control the instantaneous appearance or evolving trajectories of the dynamic effects.
Design of 2D Time-Varying Vector Fields
Chen, Guoning
2012-10-01
Design of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces. Our system supports the creation and modification of various time-varying vector fields with desired spatial and temporal characteristics through several design metaphors, including streamlines, pathlines, singularity paths, and bifurcations. These design metaphors are integrated into an element-based design to generate the time-varying vector fields via a sequence of basis field summations or spatial constrained optimizations at the sampled times. The key-frame design and field deformation are also introduced to support other user design scenarios. Accordingly, a spatial-temporal constrained optimization and the time-varying transformation are employed to generate the desired fields for these two design scenarios, respectively. We apply the time-varying vector fields generated using our design system to a number of important computer graphics applications that require controllable dynamic effects, such as evolving surface appearance, dynamic scene design, steerable crowd movement, and painterly animation. Many of these are difficult or impossible to achieve via prior simulation-based methods. In these applications, the time-varying vector fields have been applied as either orientation fields or advection fields to control the instantaneous appearance or evolving trajectories of the dynamic effects. © 1995-2012 IEEE.
Renormalization of Hamiltonian QCD
International Nuclear Information System (INIS)
Andrasi, A.; Taylor, John C.
2009-01-01
We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.
Student difficulties regarding symbolic and graphical representations of vector fields
Directory of Open Access Journals (Sweden)
Laurens Bollen
2017-08-01
Full Text Available The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person’s understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing, and switching between representations of vector fields, using both qualitative and quantitative methods. We first identified to what extent students are fluent with the use of field vector plots, field line diagrams, and symbolic expressions of vector fields by conducting individual student interviews and analyzing in-class student activities. Based on those findings, we designed the Vector Field Representations test, a free response assessment tool that has been given to 196 second- and third-year physics, mathematics, and engineering students from four different universities. From the obtained results we gained a comprehensive overview of typical errors that students make when switching between vector field representations. In addition, the study allowed us to determine the relative prevalence of the observed difficulties. Although the results varied greatly between institutions, a general trend revealed that many students struggle with vector addition, fail to recognize the field line density as an indication of the magnitude of the field, confuse characteristics of field lines and equipotential lines, and do not choose the appropriate coordinate system when writing out mathematical expressions of vector fields.
Student difficulties regarding symbolic and graphical representations of vector fields
Bollen, Laurens; van Kampen, Paul; Baily, Charles; Kelly, Mossy; De Cock, Mieke
2017-12-01
The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person's understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing, and switching between representations of vector fields, using both qualitative and quantitative methods. We first identified to what extent students are fluent with the use of field vector plots, field line diagrams, and symbolic expressions of vector fields by conducting individual student interviews and analyzing in-class student activities. Based on those findings, we designed the Vector Field Representations test, a free response assessment tool that has been given to 196 second- and third-year physics, mathematics, and engineering students from four different universities. From the obtained results we gained a comprehensive overview of typical errors that students make when switching between vector field representations. In addition, the study allowed us to determine the relative prevalence of the observed difficulties. Although the results varied greatly between institutions, a general trend revealed that many students struggle with vector addition, fail to recognize the field line density as an indication of the magnitude of the field, confuse characteristics of field lines and equipotential lines, and do not choose the appropriate coordinate system when writing out mathematical expressions of vector fields.
Classification of complex polynomial vector fields in one complex variable
DEFF Research Database (Denmark)
Branner, Bodil; Dias, Kealey
2010-01-01
This paper classifies the global structure of monic and centred one-variable complex polynomial vector fields. The classification is achieved by means of combinatorial and analytic data. More specifically, given a polynomial vector field, we construct a combinatorial invariant, describing...... the topology, and a set of analytic invariants, describing the geometry. Conversely, given admissible combinatorial and analytic data sets, we show using surgery the existence of a unique monic and centred polynomial vector field realizing the given invariants. This is the content of the Structure Theorem......, the main result of the paper. This result is an extension and refinement of Douady et al. (Champs de vecteurs polynomiaux sur C. Unpublished manuscript) classification of the structurally stable polynomial vector fields. We further review some general concepts for completeness and show that vector fields...
On Discrete Killing Vector Fields and Patterns on Surfaces
Ben-Chen, Mirela
2010-09-21
Symmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape\\'s aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape. Continuous intrinsic symmetries can be represented using infinitesimal rigid transformations, which are given as tangent vector fields on the surface - known as Killing Vector Fields. As exact symmetries are quite rare, especially when considering noisy sampled surfaces, we propose a method for relaxing the exact symmetry constraint to allow for approximate symmetries and approximate Killing Vector Fields, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis. Journal compilation © 2010 The Eurographics Association and Blackwell Publishing Ltd.
Phase transition in the non-degenerate Hubbard Hamiltonian
International Nuclear Information System (INIS)
Chaves, C.M.; Lederer, P.; Gomes, A.A.
1976-01-01
Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques, using the epsilon = 4 - d expansion to first order in epsilon, is studied. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. The possibility of tricritical behavior then emerges. The effects of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E., E-mail: kstarkov@ipn.mx
2015-07-03
In this paper we study invariant domains with unbounded dynamics for one cosmological Hamiltonian system which is formed by the conformally coupled field; this system was introduced by Maciejewski et al. (2007). We find a few groups of conditions imposed on parameters of this system for which all trajectories are unbounded in both of time directions. Further, we present a few groups of other conditions imposed on system parameters under which we localize the invariant domain with unbounded dynamics; this domain is defined with help of bounds for values of the Hamiltonian level surface parameter. We describe one group of conditions when our system possesses two periodic orbits found explicitly. In some of rest cases we get localization bounds for compact invariant sets. - Highlights: • Equations for periodic orbits are got for many level sets. • Domains with unbounded dynamics are localized. • Localizations for compact invariant sets are obtained.
Gaussian vector fields on triangulated surfaces
DEFF Research Database (Denmark)
Ipsen, John H
2016-01-01
proven to be very useful to resolve the complex interplay between in-plane ordering of membranes and membrane conformations. In the present work we have developed a procedure for realistic representations of Gaussian models with in-plane vector degrees of freedoms on a triangulated surface. The method...
The divergence theorem for unbounded vector fields
De Pauw, Thierry; Pfeffer, Washek F.
2007-01-01
In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector. elds that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is. nite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.
Measuring magnetic field vector by stimulated Raman transitions
International Nuclear Information System (INIS)
Wang, Wenli; Wei, Rong; Lin, Jinda; Wang, Yuzhu; Dong, Richang; Zou, Fan; Chen, Tingting
2016-01-01
We present a method for measuring the magnetic field vector in an atomic fountain by probing the line strength of stimulated Raman transitions. The relative line strength for a Λ-type level system with an existing magnetic field is theoretically analyzed. The magnetic field vector measured by our proposed method is consistent well with that by the traditional bias magnetic field method with an axial resolution of 6.1 mrad and a radial resolution of 0.16 rad. Dependences of the Raman transitions on laser polarization schemes are also analyzed. Our method offers the potential advantages for magnetic field measurement without requiring additional bias fields, beyond the limitation of magnetic field intensity, and extending the spatial measurement range. The proposed method can be widely used for measuring magnetic field vector in other precision measurement fields.
Interpolation of vector fields from human cardiac DT-MRI
International Nuclear Information System (INIS)
Yang, F; Zhu, Y M; Rapacchi, S; Robini, M; Croisille, P; Luo, J H
2011-01-01
There has recently been increased interest in developing tensor data processing methods for the new medical imaging modality referred to as diffusion tensor magnetic resonance imaging (DT-MRI). This paper proposes a method for interpolating the primary vector fields from human cardiac DT-MRI, with the particularity of achieving interpolation and denoising simultaneously. The method consists of localizing the noise-corrupted vectors using the local statistical properties of vector fields, removing the noise-corrupted vectors and reconstructing them by using the thin plate spline (TPS) model, and finally applying global TPS interpolation to increase the resolution in the spatial domain. Experiments on 17 human hearts show that the proposed method allows us to obtain higher resolution while reducing noise, preserving details and improving direction coherence (DC) of vector fields as well as fiber tracking. Moreover, the proposed method perfectly reconstructs azimuth and elevation angle maps.
Phase transitions in the Hubbard Hamiltonian
International Nuclear Information System (INIS)
Chaves, C.M.; Lederer, P.; Gomes, A.A.
1977-05-01
Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques is studied, using the epsilon = 4 - d expansion to first order in epsilon. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences on the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed
The index of a vector field under blow ups
International Nuclear Information System (INIS)
Seade, J.
1991-08-01
A useful technique when studying the behaviour of holomorphic vector fields around their isolated singularities is that of blowing up the singular points. On the other hand, the most basic invariant of a vector field with isolated singularities is its local index, as defined by Poincare and Hopf. It is thus natural to ask how does the index of a vector field behaves under blowing ups? The purpose of this work is to study and answer this question, by taking a rather general point of view and bearing in mind that complex manifolds have a powerful birational invariant, the Todd genus. 20 refs
Visualizing Vector Fields Using Line Integral Convolution and Dye Advection
Shen, Han-Wei; Johnson, Christopher R.; Ma, Kwan-Liu
1996-01-01
We present local and global techniques to visualize three-dimensional vector field data. Using the Line Integral Convolution (LIC) method to image the global vector field, our new algorithm allows the user to introduce colored 'dye' into the vector field to highlight local flow features. A fast algorithm is proposed that quickly recomputes the dyed LIC images. In addition, we introduce volume rendering methods that can map the LIC texture on any contour surface and/or translucent region defined by additional scalar quantities, and can follow the advection of colored dye throughout the volume.
Reciprocity relationships in vector acoustics and their application to vector field calculations.
Deal, Thomas J; Smith, Kevin B
2017-08-01
The reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. A similar equation that governs the orthogonal components of the particle velocity field is needed to enable this computational method to be used for acoustic vector sensors. This paper derives a general reciprocity equation that accounts for both monopole and dipole sources. This vector-scalar reciprocity equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each vector field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-dependent environment using a parabolic equation model.
Henan Zhao; Bryant, Garnett W; Griffin, Wesley; Terrill, Judith E; Jian Chen
2017-06-01
We designed and evaluated SplitVectors, a new vector field display approach to help scientists perform new discrimination tasks on large-magnitude-range scientific data shown in three-dimensional (3D) visualization environments. SplitVectors uses scientific notation to display vector magnitude, thus improving legibility. We present an empirical study comparing the SplitVectors approach with three other approaches - direct linear representation, logarithmic, and text display commonly used in scientific visualizations. Twenty participants performed three domain analysis tasks: reading numerical values (a discrimination task), finding the ratio between values (a discrimination task), and finding the larger of two vectors (a pattern detection task). Participants used both mono and stereo conditions. Our results suggest the following: (1) SplitVectors improve accuracy by about 10 times compared to linear mapping and by four times to logarithmic in discrimination tasks; (2) SplitVectors have no significant differences from the textual display approach, but reduce cluttering in the scene; (3) SplitVectors and textual display are less sensitive to data scale than linear and logarithmic approaches; (4) using logarithmic can be problematic as participants' confidence was as high as directly reading from the textual display, but their accuracy was poor; and (5) Stereoscopy improved performance, especially in more challenging discrimination tasks.
Non-existence of limit cycles for planar vector fields
Directory of Open Access Journals (Sweden)
Jaume Gine
2014-03-01
Full Text Available This article presents sufficient conditions for the non-existence of limit cycles for planar vector fields. Classical methods for the nonexistence of limit cycles are connected with the theory developed here.
Lipschitz estimates for convex functions with respect to vector fields
Directory of Open Access Journals (Sweden)
Valentino Magnani
2012-12-01
Full Text Available We present Lipschitz continuity estimates for a class of convex functions with respect to Hörmander vector fields. These results have been recently obtained in collaboration with M. Scienza, [22].
2D Vector Field Simplification Based on Robustness
Skraba, Primoz; Wang, Bei; Chen, Guoning; Rosen, Paul
2014-01-01
Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification
Finite-size scaling theory and quantum hamiltonian Field theory: the transverse Ising model
International Nuclear Information System (INIS)
Hamer, C.J.; Barber, M.N.
1979-01-01
Exact results for the mass gap, specific heat and susceptibility of the one-dimensional transverse Ising model on a finite lattice are generated by constructing a finite matrix representation of the Hamiltonian using strong-coupling eigenstates. The critical behaviour of the limiting infinite chain is analysed using finite-size scaling theory. In this way, excellent estimates (to within 1/2% accuracy) are found for the critical coupling and the exponents α, ν and γ
Yépez-Martínez, T.; Amor Quiroz, D. A.; Hess, P. O.; Civitarese, O.
2017-07-01
We present the low energy meson spectrum of a Coulomb gauge QCD motivated Hamiltonian for light and strange quarks. We have used the harmonic oscillator as a trial basis and performed a pre-diagonalization of the kinetic energy term in order to get an effective basis where quark and anti-quark degrees of freedom are defined. For the relevant interactions between quarks and anti-quarks, we have implemented a confining interaction between color sources, in order to account in an effective way for the gluonic degrees of freedom. The low energy meson spectrum is obtained from the implementation of the TDA and RPA many-body-methods. The physical states have been described as TDA and RPA collective states with a relatively good agreement. Particularly, the particle-hole correlations of the RPA ground state improve the RPA pion-like state (159.7 MeV) close to its physical value while the TDA one remains at a higher energy (269.2 MeV).
Invariant hyperplanes and Darboux integrability of polynomial vector fields
International Nuclear Information System (INIS)
Zhang Xiang
2002-01-01
This paper is composed of two parts. In the first part, we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in n variables. This result generalizes those given in Artes et al (1998 Pac. J. Math. 184 207-30) and Llibre and Rodriguez (2000 Bull. Sci. Math. 124 599-619). The second part gives an extension of the Darboux theory of integrability to polynomial vector fields on algebraic varieties
Creation of a new vector field and focusing engineering
Wang, Xi-Lin; Chen, Jing; Li, Yongnan; Ding, Jianping; Guo, Cheng-Shan; Wang, Hui-Tian
2009-01-01
Recently many methods have been proposed to create the vector fields, due to the academic interest and a variety of attractive applications such as for particle acceleration, optical trapping, particle manipulation, and fluorescence imaging. For the most of the created vector fields, the spatial distribution in states of polarization (SoPs) is dependent of azimuthal angle only. It is very interesting and crucial that if we can introduce the radial controlling freedom, which undoubtedly opens ...
International Nuclear Information System (INIS)
Huang, Qiu; Peng, Qiyu; Huang, Bin; Cheryauka, Arvi; Gullberg, Grant T.
2008-01-01
The measurement of flow obtained using continuous wave Doppler ultrasound is formulated as a directional projection of a flow vector field. When a continuous ultrasound wave bounces against a flowing particle, a signal is backscattered. This signal obtains a Doppler frequency shift proportional to the speed of the particle along the ultrasound beam. This occurs for each particle along the beam, giving rise to a Doppler velocity spectrum. The first moment of the spectrum provides the directional projection of the flow along the ultrasound beam. Signals reflected from points further away from the detector will have lower amplitude than signals reflected from points closer to the detector. The effect is very much akin to that modeled by the attenuated Radon transform in emission computed tomography.A least-squares method was adopted to reconstruct a 2D vector field from directional projection measurements. Attenuated projections of only the longitudinal projections of the vector field were simulated. The components of the vector field were reconstructed using the gradient algorithm to minimize a least-squares criterion. This result was compared with the reconstruction of longitudinal projections of the vector field without attenuation. If attenuation is known, the algorithm was able to accurately reconstruct both components of the full vector field from only one set of directional projection measurements. A better reconstruction was obtained with attenuation than without attenuation implying that attenuation provides important information for the reconstruction of flow vector fields.This confirms previous work where we showed that knowledge of the attenuation distribution helps in the reconstruction of MRI diffusion tensor fields from fewer than the required measurements. In the application of ultrasound the attenuation distribution is obtained with pulse wave transmission computed tomography and flow information is obtained with continuous wave Doppler
Controllability of linear vector fields on Lie groups
International Nuclear Information System (INIS)
Ayala, V.; Tirao, J.
1994-11-01
In this paper, we shall deal with a linear control system Σ defined on a Lie group G with Lie algebra g. The dynamic of Σ is determined by the drift vector field which is an element in the normalizer of g in the Lie algebra of all smooth vector field on G and by the control vectors which are elements in g considered as left-invariant vector fields. We characterize the normalizer of g identifying vector fields on G with C ∞ -functions defined on G into g. For this class of control systems we study algebraic conditions for the controllability problem. Indeed, we prove that if the drift vector field has a singularity then the Lie algebra rank condition is necessary for the controllability property, but in general this condition does not determine this property. On the other hand, we show that the rank (ad-rank) condition is sufficient for the controllability of Σ. In particular, we extend the fundamental Kalman's theorem when G is an Abelian connected Lie group. Our work is related with a paper of L. Markus and we also improve his results. (author). 7 refs
Energy preserving integration of bi-Hamiltonian partial differential equations
Karasozen, B.; Simsek, G.
2013-01-01
The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the
How the geomagnetic field vector reverses polarity
Prevot, M.; Mankinen, E.A.; Gromme, C.S.; Coe, R.S.
1985-01-01
A highly detailed record of both the direction and intensity of the Earth's magnetic field as it reverses has been obtained from a Miocene volcanic sequence. The transitional field is low in intensity and is typically non-axisymmetric. Geomagnetic impulses corresponding to astonishingly high rates of change of the field sometimes occur, suggesting that liquid velocity within the Earth's core increases during geomagnetic reversals. ?? 1985 Nature Publishing Group.
On the domain of the Nelson Hamiltonian
Griesemer, M.; Wünsch, A.
2018-04-01
The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.
Intertwined Hamiltonians in two-dimensional curved spaces
International Nuclear Information System (INIS)
Aghababaei Samani, Keivan; Zarei, Mina
2005-01-01
The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle
Effective Hamiltonians for phosphorene and silicene
DEFF Research Database (Denmark)
Voon, L. C. Lew Yan; Lopez-Bezanilla, A.; Wang, J.
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field andmagnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (NewJ. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene.......For phosphorene, it is shown that the bands near the Brillouin zone center only have terms ineven powers of the wave vector. We predict that the energies change quadratically in the presence of aperpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to thosefor silicene...
Stable solutions of inflation driven by vector fields
Energy Technology Data Exchange (ETDEWEB)
Emami, Razieh [Institute for Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Mukohyama, Shinji [Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto (Japan); Namba, Ryo [Department of Physics, McGill University, Montréal, QC, H3A 2T8 (Canada); Zhang, Ying-li, E-mail: iasraziehm@ust.hk, E-mail: shinji.mukohyama@yukawa.kyoto-u.ac.jp, E-mail: namba@physics.mcgill.ca, E-mail: yingli@bao.ac.cn [National Astronomy Observatories, Chinese Academy of Science, Beijing 100012 (China)
2017-03-01
Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models, we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.
Stable solutions of inflation driven by vector fields
International Nuclear Information System (INIS)
Emami, Razieh; Mukohyama, Shinji; Namba, Ryo; Zhang, Ying-li
2017-01-01
Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models, we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.
Computation of Surface Integrals of Curl Vector Fields
Hu, Chenglie
2007-01-01
This article presents a way of computing a surface integral when the vector field of the integrand is a curl field. Presented in some advanced calculus textbooks such as [1], the technique, as the author experienced, is simple and applicable. The computation is based on Stokes' theorem in 3-space calculus, and thus provides not only a means to…
A Chargeless Complex Vector Matter Field in Supersymmetric Scenario
Directory of Open Access Journals (Sweden)
L. P. Colatto
2015-01-01
Full Text Available We construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two nochiral scalar superfields in order to take the vector component field to build the chargeless complex vector superpartner where the respective field strength transforms into matter fields by a global U1 gauge symmetry. For the aim of dealing with consistent terms without breaking the global U1 symmetry we imposes a choice to the complex combination revealing a kind of symmetry between the choices and eliminates the extra degrees of freedom which is consistent with the supersymmetry. As the usual case the mass supersymmetric sector contributes as a complement to dynamics of the model. We obtain the equations of motion of the Proca’s type field for the chiral spinor fields and for the scalar field on the mass-shell which show the same mass as expected. This work establishes the first steps to extend the analysis of charged massive vector field in a supersymmetric scenario.
Linearized interactions of scalar and vector fields with the higher spin field in AdSD
International Nuclear Information System (INIS)
Mkrtchyan, K.
2011-01-01
The explicit form of linearized gauge and generalized 'Weyl invariant' interactions of scalar and general higher even spin fields in the AdS D space is reviewed. Also a linearized interaction of vector field with general higher even spin gauge field is obtained. It is shown that the gauge-invariant action of linearized vector field interacting with the higher spin field also includes the whole tower of invariant actions for couplings of the same vector field with the gauge fields of smaller even spin
International Nuclear Information System (INIS)
Molique, H.; Dudek, J.
1997-01-01
A particle-number conserving approach is presented to solve the nuclear mean-field plus pairing Hamiltonian problem with a realistic deformed Woods-Saxon single-particle potential. The method is designed for the state-dependent monopole pairing Hamiltonian H pair =summation αβ G αβ c α † c bar α † c bar β c β with an arbitrary set of matrix elements G αβ . Symmetries of the Hamiltonians on the many-body level are discussed using the language of P symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of P symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to p∼40 particles on n∼80 levels and for several dozens of lowest lying states with precision ∼(1 endash 2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority s=0 solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei. copyright 1997 The American Physical Society
Managing focal fields of vector beams with multiple polarization singularities.
Han, Lei; Liu, Sheng; Li, Peng; Zhang, Yi; Cheng, Huachao; Gan, Xuetao; Zhao, Jianlin
2016-11-10
We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.
Center type performance of differentiable vector fields in R2
International Nuclear Information System (INIS)
Rabanal, Roland
2007-08-01
Let X : R 2 / D → R 2 be a differentiable vector field, where D is compact. If the eigenvalues of the jacobian matrix DX z are (nonzero) purely imaginary, for all z element of R 2 / D . Then, X + v has a center type performance at infinity, for some v element of R 2 . More precisely, X + v has a periodic trajectory Γ subset of R2/ D which is surrounding D such that in the unbounded component of (R 2 / D )/ Γ all the trajectories of X + v are nontrivial cycles. In the case of global vector fields Y : R 2 → R 2 with Y (0) = 0, we prove that such eigenvalue condition implies the topological equivalency of Y with the linear vector field (x, y) → (-y, x). (author)
Combinatorial vector fields and the valley structure of fitness landscapes.
Stadler, Bärbel M R; Stadler, Peter F
2010-12-01
Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vector fields and in return associate these combinatorial vector fields with weights that measure their steepness across the landscape. We show that the combinatorial vector fields and their weights have a product structure that is governed by the neutrality of the landscape. This product structure makes practical computations feasible. The framework presented here also provides an alternative, and mathematically more convenient, way of defining notions of valleys, saddle points, and barriers in landscape. As an application, we propose a refined approximation for transition rates between macrostates that are associated with the valleys of the landscape.
The Lie Bracket of Adapted Vector Fields on Wiener Spaces
International Nuclear Information System (INIS)
Driver, B. K.
1999-01-01
Let W(M) be the based (at o element of M) path space of a compact Riemannian manifold M equipped with Wiener measure ν . This paper is devoted to considering vector fields on W(M) of the form X s h (σ )=P s (σ)h s (σ ) where P s (σ ) denotes stochastic parallel translation up to time s along a Wiener path σ element of W(M) and {h s } i sanelementof [0,1] is an adapted T o M -valued process on W(M). It is shown that there is a large class of processes h (called adapted vector fields) for which we may view X h as first-order differential operators acting on functions on W(M) . Moreover, if h and k are two such processes, then the commutator of X h with X k is again a vector field on W(M) of the same form
Inferring Lower Boundary Driving Conditions Using Vector Magnetic Field Observations
Schuck, Peter W.; Linton, Mark; Leake, James; MacNeice, Peter; Allred, Joel
2012-01-01
Low-beta coronal MHD simulations of realistic CME events require the detailed specification of the magnetic fields, velocities, densities, temperatures, etc., in the low corona. Presently, the most accurate estimates of solar vector magnetic fields are made in the high-beta photosphere. Several techniques have been developed that provide accurate estimates of the associated photospheric plasma velocities such as the Differential Affine Velocity Estimator for Vector Magnetograms and the Poloidal/Toroidal Decomposition. Nominally, these velocities are consistent with the evolution of the radial magnetic field. To evolve the tangential magnetic field radial gradients must be specified. In addition to estimating the photospheric vector magnetic and velocity fields, a further challenge involves incorporating these fields into an MHD simulation. The simulation boundary must be driven, consistent with the numerical boundary equations, with the goal of accurately reproducing the observed magnetic fields and estimated velocities at some height within the simulation. Even if this goal is achieved, many unanswered questions remain. How can the photospheric magnetic fields and velocities be propagated to the low corona through the transition region? At what cadence must we observe the photosphere to realistically simulate the corona? How do we model the magnetic fields and plasma velocities in the quiet Sun? How sensitive are the solutions to other unknowns that must be specified, such as the global solar magnetic field, and the photospheric temperature and density?
Vector optical fields with polarization distributions similar to electric and magnetic field lines.
Pan, Yue; Li, Si-Min; Mao, Lei; Kong, Ling-Jun; Li, Yongnan; Tu, Chenghou; Wang, Pei; Wang, Hui-Tian
2013-07-01
We present, design and generate a new kind of vector optical fields with linear polarization distributions modeling to electric and magnetic field lines. The geometric configurations of "electric charges" and "magnetic charges" can engineer the spatial structure and symmetry of polarizations of vector optical field, providing additional degrees of freedom assisting in controlling the field symmetry at the focus and allowing engineering of the field distribution at the focus to the specific applications.
The local structure of a Liouville vector field
International Nuclear Information System (INIS)
Ciriza, E.
1990-05-01
In this work we investigate the local structure of a Liouville vector field ξ of a Kaehler manifold (P,Ω) which vanishes on an isotropic submanifold Q of P. Some of the eigenvalues of its linear part at the singular points are zero and the remaining ones are in resonance. We show that there is a C 1 -smooth linearizing conjugation between the Liouville vector field ξ and its linear part. To do this we construct Darboux coordinates adapted to the unstable foliation which is provided by the Centre Manifold Theorem. We then apply recent linearization results due to G. Sell. (author). 11 refs
Generalized Proca action for an Abelian vector field
International Nuclear Information System (INIS)
Allys, Erwan; Peter, Patrick; Rodríguez, Yeinzon
2016-01-01
We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetime (Minkowski) case, we obtain all the possible terms containing products of up to five first-order derivatives of the vector field, and provide a conjecture about higher-order terms. Rendering the metric dynamical, we covariantize the results and add all possible terms implying curvature
Energy Technology Data Exchange (ETDEWEB)
Li Xunjun; Dudek, J.; Romain, P. (Centre de Recherches Nucleaires, IN2P3-CNRS, Univ. Louis Pasteur, 67 - Strasbourg (France))
1991-11-21
Symmetry properties of the general average-field hamiltonian-matrix resulting from the geometrical symmetries of the hamiltonian itself are derived and discussed. The corresponding numerical algorithms are constructed. Total energy calculations for superdeformed nuclei are then extended to include the usually neglected deformation modes {alpha}{sub {lambda}=3{mu}{ne}0} in the expansion of the nuclear surface expression R({theta}, {phi}; {l brace}{alpha}{r brace})=c({l brace}{alpha}{r brace})R{sub 0}(1+{Sigma}{sub {lambda}} {Sigma}{sub {mu}=-{lambda}}{sup {lambda}} {alpha}{sub {lambda}{mu}}{sup *}{Upsilon}{sub {lambda}{mu}}({theta}, {phi})). The general trends in the shell-energy dependence on {alpha}{sub {lambda}=3{mu}} and the implied instabilities in the superdeformed configurations of the rare earth nuclei are studied using the Strutinsky formula with the macroscopic part taken in the form of the folded-Yukawa plus exponential interaction. A possibility of new (double superdeformed minimum) structures coexisting in some nuclei and resulting from the proton shell effects is predicted and illustrated. No significant neutron effects are found in the rare earth superdeformed nuclei considered. (orig.).
Vector fields in a tight laser focus: comparison of models.
Peatross, Justin; Berrondo, Manuel; Smith, Dallas; Ware, Michael
2017-06-26
We assess several widely used vector models of a Gaussian laser beam in the context of more accurate vector diffraction integration. For the analysis, we present a streamlined derivation of the vector fields of a uniformly polarized beam reflected from an ideal parabolic mirror, both inside and outside of the resulting focus. This exact solution to Maxwell's equations, first developed in 1920 by V. S. Ignatovsky, is highly relevant to high-intensity laser experiments since the boundary conditions at a focusing optic dictate the form of the focus in a manner analogous to a physical experiment. In contrast, many models simply assume a field profile near the focus and develop the surrounding vector fields consistent with Maxwell's equations. In comparing the Ignatovsky result with popular closed-form analytic vector models of a Gaussian beam, we find that the relatively simple model developed by Erikson and Singh in 1994 provides good agreement in the paraxial limit. Models involving a Lax expansion introduce a divergences outside of the focus while providing little if any improvement in the focal region. Extremely tight focusing produces a somewhat complicated structure in the focus, and requires the Ignatovsky model for accurate representation.
Vector field statistical analysis of kinematic and force trajectories.
Pataky, Todd C; Robinson, Mark A; Vanrenterghem, Jos
2013-09-27
When investigating the dynamics of three-dimensional multi-body biomechanical systems it is often difficult to derive spatiotemporally directed predictions regarding experimentally induced effects. A paradigm of 'non-directed' hypothesis testing has emerged in the literature as a result. Non-directed analyses typically consist of ad hoc scalar extraction, an approach which substantially simplifies the original, highly multivariate datasets (many time points, many vector components). This paper describes a commensurately multivariate method as an alternative to scalar extraction. The method, called 'statistical parametric mapping' (SPM), uses random field theory to objectively identify field regions which co-vary significantly with the experimental design. We compared SPM to scalar extraction by re-analyzing three publicly available datasets: 3D knee kinematics, a ten-muscle force system, and 3D ground reaction forces. Scalar extraction was found to bias the analyses of all three datasets by failing to consider sufficient portions of the dataset, and/or by failing to consider covariance amongst vector components. SPM overcame both problems by conducting hypothesis testing at the (massively multivariate) vector trajectory level, with random field corrections simultaneously accounting for temporal correlation and vector covariance. While SPM has been widely demonstrated to be effective for analyzing 3D scalar fields, the current results are the first to demonstrate its effectiveness for 1D vector field analysis. It was concluded that SPM offers a generalized, statistically comprehensive solution to scalar extraction's over-simplification of vector trajectories, thereby making it useful for objectively guiding analyses of complex biomechanical systems. © 2013 Published by Elsevier Ltd. All rights reserved.
Thompson, J. D.; McClarty, P. A.; Prabhakaran, D.; Cabrera, I.; Guidi, T.; Coldea, R.
2017-08-01
The frustrated pyrochlore magnet Yb2 Ti2 O7 has the remarkable property that it orders magnetically but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe, in addition to dispersive magnons, a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measurements we find that the low- and high-field regions are smoothly connected with no sharp phase transition, with the spin gap increasing monotonically in field. Through fits to an extensive data set of dispersion relations combined with magnetization measurements, we reevaluate the spin Hamiltonian, finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields.
Thompson, J D; McClarty, P A; Prabhakaran, D; Cabrera, I; Guidi, T; Coldea, R
2017-08-04
The frustrated pyrochlore magnet Yb_{2}Ti_{2}O_{7} has the remarkable property that it orders magnetically but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe, in addition to dispersive magnons, a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measurements we find that the low- and high-field regions are smoothly connected with no sharp phase transition, with the spin gap increasing monotonically in field. Through fits to an extensive data set of dispersion relations combined with magnetization measurements, we reevaluate the spin Hamiltonian, finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields.
Transitive Lie algebras of vector fields: an overview
Draisma, J.
2011-01-01
This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary differential equations, these algebras, or infinitesimal groups, are a recurring theme in 20th-century research on
Interactive exploratory visualization of 2D vector fields
Isenberg, Tobias; Everts, Maarten H.; Grubert, Jens; Carpendale, Sheelagh
In this paper we present several techniques to interactively explore representations of 2D vector fields. Through a set of simple hand postures used on large, touch-sensitive displays, our approach allows individuals to custom design glyphs (arrows, lines, etc.) that best reveal patterns of the
Desingularization strategies for three-dimensional vector fields
Torres, Felipe Cano
1987-01-01
For a vector field #3, where Ai are series in X, the algebraic multiplicity measures the singularity at the origin. In this research monograph several strategies are given to make the algebraic multiplicity of a three-dimensional vector field decrease, by means of permissible blowing-ups of the ambient space, i.e. transformations of the type xi=x'ix1, 2s. A logarithmic point of view is taken, marking the exceptional divisor of each blowing-up and by considering only the vector fields which are tangent to this divisor, instead of the whole tangent sheaf. The first part of the book is devoted to the logarithmic background and to the permissible blowing-ups. The main part corresponds to the control of the algorithms for the desingularization strategies by means of numerical invariants inspired by Hironaka's characteristic polygon. Only basic knowledge of local algebra and algebraic geometry is assumed of the reader. The pathologies we find in the reduction of vector fields are analogous to pathologies in the pro...
Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion
Energy Technology Data Exchange (ETDEWEB)
Kluepfel, Peter
2008-07-29
This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)
Off disk-center potential field calculations using vector magnetograms
Venkatakrishnan, P.; Gary, G. Allen
1989-01-01
A potential field calculation for off disk-center vector magnetograms that uses all the three components of the measured field is investigated. There is neither any need for interpolation of grid points between the image plane and the heliographic plane nor for an extension or a truncation to a heliographic rectangle. Hence, the method provides the maximum information content from the photospheric field as well as the most consistent potential field independent of the viewing angle. The introduction of polarimetric noise produces a less tolerant extrapolation procedure than using the line-of-sight extrapolation, but the resultant standard deviation is still small enough for the practical utility of this method.
Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.
2015-01-01
Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of
Time dependent drift Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1982-04-01
The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)
Existence of solutions for Hamiltonian field theories by the Hamilton-Jacobi technique
International Nuclear Information System (INIS)
Bruno, Danilo
2011-01-01
The paper is devoted to prove the existence of a local solution of the Hamilton-Jacobi equation in field theory, whence the general solution of the field equations can be obtained. The solution is adapted to the choice of the submanifold where the initial data of the field equations are assigned. Finally, a technique to obtain the general solution of the field equations, starting from the given initial manifold, is deduced.
Determination of Coronal Magnetic Fields from Vector Magnetograms
Mikic, Zoran
1997-01-01
During the course of the present contract we developed an 'evolutionary technique' for the determination of force-free coronal magnetic fields from vector magnetograph observations. The method can successfully generate nonlinear force- free fields (with non-constant-a) that match vector magnetograms. We demonstrated that it is possible to determine coronal magnetic fields from photospheric measurements, and we applied it to vector magnetograms of active regions. We have also studied theoretical models of coronal fields that lead to disruptions. Specifically, we have demonstrated that the determination of force-free fields from exact boundary data is a well-posed mathematical problem, by verifying that the computed coronal field agrees with an analytic force-free field when boundary data for the analytic field are used; demonstrated that it is possible to determine active-region coronal magnetic fields from photospheric measurements, by computing the coronal field above active region 5747 on 20 October 1989, AR6919 on 15 November 1991, and AR7260 on 18 August 1992, from data taken with the Stokes Polarimeter at Mees Solar Observatory, University of Hawaii; started to analyze active region 7201 on 19 June 1992 using measurements made with the Advanced Stokes Polarimeter at NSO/Sac Peak; investigated the effects of imperfections in the photospheric data on the computed coronal magnetic field; documented the coronal field structure of AR5747 and compared it to the morphology of footpoint emission in a flare, showing that the 'high- pressure' H-alpha footpoints are connected by coronal field lines; shown that the variation of magnetic field strength along current-carrying field lines is significantly different from the variation in a potential field, and that the resulting near-constant area of elementary flux tubes is consistent with observations; begun to develop realistic models of coronal fields which can be used to study flare trigger mechanisms; demonstrated that
Magnetic monopole and vector field of the spin 0
International Nuclear Information System (INIS)
Pantyushin, A.A.
2001-01-01
The motion of electrically charged particles in uniform magnetic field by time is considered. It is found out that additional force acting on eclectically charged particle from the spin 0 vector field side is proportional to the magnetic field. Proportion coefficient is equal to eg/4π (g - unknown parameter, determining of the rate and character of source non-preservation) - the analogue of constant thin structure α=e 2 /4π. Obtained results give evidence to suppose that for explanation of indicated experiments the monopole introduction is not essential
Alternative Hamiltonian representation for gravity
Energy Technology Data Exchange (ETDEWEB)
Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)
2007-11-15
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.
Alternative Hamiltonian representation for gravity
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2007-01-01
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity
Firpo, M.-C.; Constantinescu, D.
2011-03-01
The issue of magnetic confinement in magnetic fusion devices is addressed within a purely magnetic approach. Using some Hamiltonian models for the magnetic field lines, the dual impact of low magnetic shear is shown in a unified way. Away from resonances, it induces a drastic enhancement of magnetic confinement that favors robust internal transport barriers (ITBs) and stochastic transport reduction. When low shear occurs for values of the winding of the magnetic field lines close to low-order rationals, the amplitude thresholds of the resonant modes that break internal transport barriers by allowing a radial stochastic transport of the magnetic field lines may be quite low. The approach can be applied to assess the robustness versus magnetic perturbations of general (almost) integrable magnetic steady states, including nonaxisymmetric ones such as the important single-helicity steady states. This analysis puts a constraint on the tolerable mode amplitudes compatible with ITBs and may be proposed as a possible explanation of diverse experimental and numerical signatures of their collapses.
Relativistic gravitation from massless systems of scalar and vector fields
International Nuclear Information System (INIS)
Fonseca Teixeira, A.F. da.
1979-01-01
Under the laws of Einstein's gravitational theory, a massless system consisting of the diffuse sources of two fields is discussed. One fields is scalar, of long range, the other is a vector field of short range. A proportionality between the sources is assumed. Both fields are minimally coupled to gravitation, and contribute positive definitely to the time component of the energy momentum tensor. A class of static, spherically symmetric solutions of the equations is obtained, in the weak field limit. The solutions are regular everywhere, stable, and can represent large or small physical systems. The gravitational field presents a Schwarzschild-type asymptotic behavior. The dependence of the energy on the various parameters characterizing the system is discussed in some detail. (Author) [pt
New techniques in 3D scalar and vector field visualization
International Nuclear Information System (INIS)
Max, N.; Crawfis, R.; Becker, B.
1993-01-01
At Lawrence Livermore National Laboratory (LLNL) we have recently developed several techniques for volume visualization of scalar and vector fields, all of which use back-to-front compositing. The first renders volume density clouds by compositing polyhedral volume cells or their faces. The second is a ''splatting'' scheme which composites textures used to reconstruct the scalar or vector fields. One version calculates the necessary texture values in software, and another takes advantage of hardware texture mapping. The next technique renders contour surface polygons using semi-transparent textures, which adjust appropriately when the surfaces deform in a flow, or change topology. The final one renders the ''flow volume'' of smoke or dye tracer swept out by a fluid flowing through a small generating polygon. All of these techniques are applied to a climate model data set, to visualize cloud density and wind velocity
New techniques in 3D scalar and vector field visualization
Energy Technology Data Exchange (ETDEWEB)
Max, N.; Crawfis, R.; Becker, B.
1993-05-05
At Lawrence Livermore National Laboratory (LLNL) we have recently developed several techniques for volume visualization of scalar and vector fields, all of which use back-to-front compositing. The first renders volume density clouds by compositing polyhedral volume cells or their faces. The second is a ``splatting`` scheme which composites textures used to reconstruct the scalar or vector fields. One version calculates the necessary texture values in software, and another takes advantage of hardware texture mapping. The next technique renders contour surface polygons using semi-transparent textures, which adjust appropriately when the surfaces deform in a flow, or change topology. The final one renders the ``flow volume`` of smoke or dye tracer swept out by a fluid flowing through a small generating polygon. All of these techniques are applied to a climate model data set, to visualize cloud density and wind velocity.
Electric field vector measurements in a surface ionization wave discharge
International Nuclear Information System (INIS)
Goldberg, Benjamin M; Adamovich, Igor V; Lempert, Walter R; Böhm, Patrick S; Czarnetzki, Uwe
2015-01-01
This work presents the results of time-resolved electric field vector measurements in a short pulse duration (60 ns full width at half maximum), surface ionization wave discharge in hydrogen using a picosecond four-wave mixing technique. Electric field vector components are measured separately, using pump and Stokes beams linearly polarized in the horizontal and vertical planes, and a polarizer placed in front of the infrared detector. The time-resolved electric field vector is measured at three different locations across the discharge gap, and for three different heights above the alumina ceramic dielectric surface, ∼100, 600, and 1100 μm (total of nine different locations). The results show that after breakdown, the discharge develops as an ionization wave propagating along the dielectric surface at an average speed of 1 mm ns −1 . The surface ionization wave forms near the high voltage electrode, close to the dielectric surface (∼100 μm). The wave front is characterized by significant overshoot of both vertical and horizontal electric field vector components. Behind the wave front, the vertical field component is rapidly reduced. As the wave propagates along the dielectric surface, it also extends further away from the dielectric surface, up to ∼1 mm near the grounded electrode. The horizontal field component behind the wave front remains quite significant, to sustain the electron current toward the high voltage electrode. After the wave reaches the grounded electrode, the horizontal field component experiences a secondary rise in the quasi-dc discharge, where it sustains the current along the near-surface plasma sheet. The measurement results indicate presence of a cathode layer formed near the grounded electrode with significant cathode voltage fall, ≈3 kV, due to high current density in the discharge. The peak reduced electric field in the surface ionization wave is 85–95 Td, consistent with dc breakdown field estimated from the Paschen
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.
Lovelock vacua with a recurrent null vector field
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello
2018-01-01
Roč. 97, č. 4 (2018), č. článku 044051. ISSN 2470-0010 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : Lovelock gravity * recurrent null vector field Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.97.044051
Algebraic characterization of vector supersymmetry in topological field theories
International Nuclear Information System (INIS)
Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G.; Sorella, S.P.
1997-01-01
An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact anti-field dependent cocycles with negative ghost number, according to the cohomological reformulation of the Noether theorem given by M. Henneaux et al. (author)
Algebraic characterization of vector supersymmetry in topological field theories
Energy Technology Data Exchange (ETDEWEB)
Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Sorella, S.P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica. Dept. de Fisica Teorica
1997-01-01
An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact anti-field dependent cocycles with negative ghost number, according to the cohomological reformulation of the Noether theorem given by M. Henneaux et al. (author). 32 refs., 5 tabs.
Lovelock vacua with a recurrent null vector field
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello
2018-01-01
Roč. 97, č. 4 (2018), č. článku 044051. ISSN 2470-0010 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : Lovelock gravity * recurrent null vector field Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.97.044051
Rotation invariants of vector fields from orthogonal moments
Czech Academy of Sciences Publication Activity Database
Yang, B.; Kostková, Jitka; Flusser, Jan; Suk, Tomáš; Bujack, R.
2018-01-01
Roč. 74, č. 1 (2018), s. 110-121 ISSN 0031-3203 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Vector field * Total rotation * Invariants * Gaussian–Hermite moments * Zernike moments * Numerical stability Subject RIV: JD - Computer Applications, Robotics Impact factor: 4.582, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/flusser-0478329.pdf
Renormalization of Hamiltonians
International Nuclear Information System (INIS)
Glazek, S.D.; Wilson, K.G.
1993-01-01
This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method
Improvement of vector compensation method for vehicle magnetic distortion field
Energy Technology Data Exchange (ETDEWEB)
Pang, Hongfeng, E-mail: panghongfeng@126.com; Zhang, Qi; Li, Ji; Luo, Shitu; Chen, Dixiang; Pan, Mengchun; Luo, Feilu
2014-03-15
Magnetic distortions such as eddy-current field and low frequency magnetic field have not been considered in vector compensation methods. A new compensation method is proposed to suppress these magnetic distortions and improve compensation performance, in which the magnetic distortions related to measurement vectors and time are considered. The experimental system mainly consists of a three-axis fluxgate magnetometer (DM-050), an underwater vehicle and a proton magnetometer, in which the scalar value of magnetic field is obtained with the proton magnetometer and considered to be the true value. Comparing with traditional compensation methods, experimental results show that the magnetic distortions can be further reduced by two times. After compensation, error intensity and RMS error are reduced from 11684.013 nT and 7794.604 nT to 16.219 nT and 5.907 nT respectively. It suggests an effective way to improve the compensation performance of magnetic distortions. - Highlights: • A new vector compensation method is proposed for vehicle magnetic distortion. • The proposed model not only includes magnetometer error but also considers magnetic distortion. • Compensation parameters are computed directly by solving nonlinear equations. • Compared with traditional methods, the proposed method is not related with rotation angle rate. • Error intensity and RMS error can be reduced to 1/2 of the error with traditional methods.
Improvement of vector compensation method for vehicle magnetic distortion field
International Nuclear Information System (INIS)
Pang, Hongfeng; Zhang, Qi; Li, Ji; Luo, Shitu; Chen, Dixiang; Pan, Mengchun; Luo, Feilu
2014-01-01
Magnetic distortions such as eddy-current field and low frequency magnetic field have not been considered in vector compensation methods. A new compensation method is proposed to suppress these magnetic distortions and improve compensation performance, in which the magnetic distortions related to measurement vectors and time are considered. The experimental system mainly consists of a three-axis fluxgate magnetometer (DM-050), an underwater vehicle and a proton magnetometer, in which the scalar value of magnetic field is obtained with the proton magnetometer and considered to be the true value. Comparing with traditional compensation methods, experimental results show that the magnetic distortions can be further reduced by two times. After compensation, error intensity and RMS error are reduced from 11684.013 nT and 7794.604 nT to 16.219 nT and 5.907 nT respectively. It suggests an effective way to improve the compensation performance of magnetic distortions. - Highlights: • A new vector compensation method is proposed for vehicle magnetic distortion. • The proposed model not only includes magnetometer error but also considers magnetic distortion. • Compensation parameters are computed directly by solving nonlinear equations. • Compared with traditional methods, the proposed method is not related with rotation angle rate. • Error intensity and RMS error can be reduced to 1/2 of the error with traditional methods
Lagrangian and Hamiltonian dynamics
Mann, Peter
2018-01-01
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...
Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle
Wang, Hong
2017-09-01
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.
Ohkitani, K.
2010-05-01
We study some of the key quantities arising in the theory of [Arnold "Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits," Annales de l'institut Fourier 16, 319 (1966)] of the incompressible Euler equations both in two and three dimensions. The sectional curvatures for the Taylor-Green vortex and the ABC flow initial conditions are calculated exactly in three dimensions. We trace the time evolution of the Jacobi fields by direct numerical simulations and, in particular, see how the sectional curvatures get more and more negative in time. The spatial structure of the Jacobi fields is compared to the vorticity fields by visualizations. The Jacobi fields are found to grow exponentially in time for the flows with negative sectional curvatures. In two dimensions, a family of initial data proposed by Arnold (1966) is considered. The sectional curvature is observed to change its sign quickly even if it starts from a positive value. The Jacobi field is shown to be correlated with the passive scalar gradient in spatial structure. On the basis of Rouchon's physical-space based expression for the sectional curvature (1984), the origin of negative curvature is investigated. It is found that a "potential" αξ appearing in the definition of covariant time derivative plays an important role, in that a rapid growth in its gradient makes a major contribution to the negative curvature.
Bernabé Ferreira, Miguel Jorge; Ibieta Jimenez, Juan Pablo; Padmanabhan, Pramod; Teôtonio Sobrinho, Paulo
2015-12-01
State sum constructions, such as Kuperberg’s algorithm, give partition functions of physical systems, like lattice gauge theories, in various dimensions by associating local tensors or weights with different parts of a closed triangulated manifold. Here we extend this construction by including matter fields to build partition functions in both two and three space-time dimensions. The matter fields introduce new weights to the vertices and they correspond to Potts spin configurations described by an {A}-module with an inner product. Performing this construction on a triangulated manifold with a boundary we obtain transfer matrices which are decomposed into a product of local operators acting on vertices, links and plaquettes. The vertex and plaquette operators are similar to the ones appearing in the quantum double models (QDMs) of Kitaev. The link operator couples the gauge and the matter fields, and it reduces to the usual interaction terms in known models such as {{{Z}}}2 gauge theory with matter fields. The transfer matrices lead to Hamiltonians that are frustration-free and are exactly solvable. According to the choice of the initial input, that of the gauge group and a matter module, we obtain interesting models which have a new kind of ground state degeneracy that depends on the number of equivalence classes in the matter module under gauge action. Some of the models have confined flux excitations in the bulk which become deconfined at the surface. These edge modes are protected by an energy gap provided by the link operator. These properties also appear in ‘confined Walker-Wang’ models which are 3D models having interesting surface states. Apart from the gauge excitations there are also excitations in the matter sector which are immobile and can be thought of as defects like in the Ising model. We only consider bosonic matter fields in this paper.
Initial geomagnetic field model from Magsat vector data
Langel, R. A.; Mead, G. D.; Lancaster, E. R.; Estes, R. H.; Fabiano, E. B.
1980-01-01
Magsat data from the magnetically quiet days of November 5-6, 1979, were used to derive a thirteenth degree and order spherical harmonic geomagnetic field model, MGST(6/80). The model utilized both scalar and high-accuracy vector data and fit that data with root-mean-square deviations of 8.2, 6.9, 7.6 and 7.4 nT for the scalar magnitude, B(r), B(theta), and B(phi), respectively. The model includes the three first-order coefficients of the external field. Comparison with averaged Dst indicates that zero Dst corresponds with 25 nT of horizontal field from external sources. When compared with earlier models, the earth's dipole moment continues to decrease at a rate of about 26 nT/yr. Evaluation of earlier models with Magsat data shows that the scalar field at the Magsat epoch is best predicted by the POGO(2/72) model but that the WC80, AWC/75 and IGS/75 are better for predicting vector fields.
Localization of vector field on dynamical domain wall
Directory of Open Access Journals (Sweden)
Masafumi Higuchi
2017-03-01
Full Text Available In the previous works (arXiv:1202.5375 and arXiv:1402.1346, the dynamical domain wall, where the four dimensional FRW universe is embedded in the five dimensional space–time, has been realized by using two scalar fields. In this paper, we consider the localization of vector field in three formulations. The first formulation was investigated in the previous paper (arXiv:1510.01099 for the U(1 gauge field. In the second formulation, we investigate the Dvali–Shifman mechanism (arXiv:hep-th/9612128, where the non-abelian gauge field is confined in the bulk but the gauge symmetry is spontaneously broken on the domain wall. In the third formulation, we investigate the Kaluza–Klein modes coming from the five dimensional graviton. In the Randall–Sundrum model, the graviton was localized on the brane. We show that the (5,μ components (μ=0,1,2,3 of the graviton are also localized on the domain wall and can be regarded as the vector field on the domain wall. There are, however, some corrections coming from the bulk extra dimension if the domain wall universe is expanding.
An example of a vector field with the oriented shadowing property
Tikhomirov, Sergey
2014-01-01
We consider shadowing properties for vector fields corresponding to different type of reparametrisations. We give an example of a vector field which has the oriented shadowing properties, but does not have the standard shadowing property.
Time-varying vector fields and their flows
Jafarpour, Saber
2014-01-01
This short book provides a comprehensive and unified treatment of time-varying vector fields under a variety of regularity hypotheses, namely finitely differentiable, Lipschitz, smooth, holomorphic, and real analytic. The presentation of this material in the real analytic setting is new, as is the manner in which the various hypotheses are unified using functional analysis. Indeed, a major contribution of the book is the coherent development of locally convex topologies for the space of real analytic sections of a vector bundle, and the development of this in a manner that relates easily to classically known topologies in, for example, the finitely differentiable and smooth cases. The tools used in this development will be of use to researchers in the area of geometric functional analysis.
External field-induced chaos in classical and quantum Hamiltonian systems
International Nuclear Information System (INIS)
Lin, W.C.
1986-01-01
Classical nonlinear nonintegrable systems exhibit dense sets of resonance zones in phase space. Global chaotic motion appears when neighboring resonance zones overlap. The chaotic motion signifies the destruction of a quasi constant of motion. The motion of a particle, trapped in one of the wells of a sinusoidal, potential driven by a monochromatic external field was studied. Global chaotic behavior sets in when the amplitude of the external field reaches a critical value. The particle then escapes the well. The critical values are found to be in good agreement with a resonance overlap criterion rather than a renormalization-group scheme. A similar system was then studied, but with the particle being confined in an infinite square well potential instead. A stochastic layer is found in the low-energy part of the phase space. The resonance zone structure is found to be in excellent agreement with predictions. The critical values for the onset of global chaotic behavior are found to be in excellent agreement with the renormalization group scheme. The quantum version of the second model above was then considered. In a similar fashion, the external field induces quantum resonance zones. The spectral statistics were computed, and a transition of statistics from Poissonian to Wigner-like was found as overlap of quantum resonances occurs. This also signifies the destruction of a quasi-constant of motion
Hamiltonian indices and rational spectral densities
Byrnes, C. I.; Duncan, T. E.
1980-01-01
Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.
Killing vector fields in three dimensions: a method to solve massive gravity field equations
Energy Technology Data Exchange (ETDEWEB)
Guerses, Metin, E-mail: gurses@fen.bilkent.edu.t [Department of Mathematics, Faculty of Sciences, Bilkent University, 06800 Ankara (Turkey)
2010-10-21
Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.
Vilasi, Gaetano
2001-01-01
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m
A dynamic mean-field glass model with reversible mode coupling and a trivial Hamiltonian
International Nuclear Information System (INIS)
Kawasaki, Kyozi; Kim, Bongsoo
2002-01-01
Often the current mode coupling theory (MCT) of glass transitions is compared with mean field theories. We explore this possible correspondence. After showing a simple-minded derivation of MCT with some difficulties we give a concise account of our toy model developed to gain more insight into MCT. We then reduce this toy model by adiabatically eliminating rapidly varying velocity-like variables to obtain a Fokker-Planck equation for the slowly varying density-like variables where the diffusion matrix can be singular. This gives room for non-ergodic stationary solutions of the above equation. (author)
Efficient and Enhanced Diffusion of Vector Field for Active Contour Model
Liu, Guoqi; Sun, Lin; Liu, Shangwang
2015-01-01
Gradient vector flow (GVF) is an important external force field for active contour models. Various vector fields based on GVF have been proposed. However, these vector fields are obtained with many iterations and have difficulty in capturing the whole image area. On the other hand, the ability to converge to deep and complex concavity with these vector fields is also needed to improve. In this paper, by analyzing the diffusion equation of GVF, a normalized set is defined and a dynamically nor...
VECTOR MAGNETIC FIELDS AND ELECTRIC CURRENTS FROM THE IMAGING VECTOR MAGNETOGRAPH
International Nuclear Information System (INIS)
Li Jing; Mickey, Don; Van Ballegooijen, A. A.
2009-01-01
First, we describe a general procedure to produce high-quality vector magnetograms using the Imaging Vector Magnetograph (IVM) at Mees Solar Observatory. Two IVM effects are newly discussed and taken into account: (1) the central wavelength of the Fabry-Perot is found to drift with time as a result of undiagnosed thermal or mechanical instabilities in the instrument; (2) the Stokes V-sign convention built into the IVM is found to be opposite to the conventional definition used in the study of radiative transfer of polarized radiation. At the spatial resolution 2'' x 2'', the Stokes Q, U, V uncertainty reaches ∼1 x 10 -3 to 5 x 10 -4 in time-averaged data over 1 hr in the quiet Sun. When vector magnetic fields are inferred from the time-averaged Stokes spectral images of FeI 6302.5 A, the resulting uncertainties are on the order of 10 G for the longitudinal fields (B || ), 40 G for the transverse field strength (B perpendicular ) and ∼9 0 for the magnetic azimuth (φ). The magnetic field inversion used in this work is the 'Triplet' code, which was developed and implemented in the IVM software package by the late B. J. LaBonte. The inversion code is described in detail in the Appendix. Second, we solve for the absolute value of the vertical electric current density, |J z |, accounting for the above IVM problems, for two different active regions. One is a single sunspot region (NOAA 10001 observed on 2002 June 20) while the other is a more complex, quadrupolar region (NOAA10030 observed on 2002 July 15). We use a calculation that does not require disambiguation of 180 0 in the transverse field directions. The |J z | uncertainty is on the order of ∼7.0 mA m -2 . The vertical current density increases with increasing vertical magnetic field. The rate of increase is about 1-2 times as large in the quadrupolar NOAA 10030 region as in the simple NOAA 10001, and it is more spatially variable over NOAA 10030 than over NOAA 10001.
Hamiltonian formulation of the supermembrane
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Tanii, Y.
1987-06-01
The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence free 2-vectors are unfixed. (author). 10 refs
International Nuclear Information System (INIS)
Peggs, S.; Talman, R.
1987-01-01
As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases
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.
Helicons in uniform fields. II. Poynting vector and angular momenta
Stenzel, R. L.; Urrutia, J. M.
2018-03-01
The orbital and spin angular momenta of helicon modes have been determined quantitatively from laboratory experiments. The current density is obtained unambiguously from three dimensional magnetic field measurements. The only approximation made is to obtain the electric field from Hall Ohm's law which is usually the case for low frequency whistler modes. This allows the evaluation of the Poynting vector from which the angular momentum is obtained. Comparing two helicon modes (m = 0 and m = 1), one can separate the contribution of angular momentum of a rotating and non-rotating wave field. The orbital angular momentum is important to assess the wave-particle interaction by the transverse Doppler shift of rotating waves which has not been considered so far.
HEIGHT VARIATION OF THE VECTOR MAGNETIC FIELD IN SOLAR SPICULES
Energy Technology Data Exchange (ETDEWEB)
Suárez, D. Orozco; Ramos, A. Asensio; Bueno, J. Trujillo, E-mail: dorozco@iac.es [Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife (Spain)
2015-04-20
Proving the magnetic configuration of solar spicules has hitherto been difficult due to the lack of spatial resolution and image stability during off-limb ground-based observations. We report spectropolarimetric observations of spicules taken in the He i 1083 nm spectral region with the Tenerife Infrared Polarimeter II at the German Vacuum Tower Telescope of the Observatorio del Teide (Tenerife, Canary Islands, Spain). The data provide the variation with geometrical height of the Stokes I, Q, U, and V profiles, whose encoded information allows the determination of the magnetic field vector by means of the HAZEL inversion code. The inferred results show that the average magnetic field strength at the base of solar spicules is about 80 gauss, and then it decreases rapidly with height to about 30 gauss at a height of 3000 km above the visible solar surface. Moreover, the magnetic field vector is close to vertical at the base of the chromosphere and has mid-inclinations (about 50°) above 2 Mm height.
Observations of vector magnetic fields in flaring active regions
Chen, Jimin; Wang, Haimin; Zirin, Harold; Ai, Guoxiang
1994-01-01
We present vector magnetograph data of 6 active regions, all of which produced major flares. Of the 20 M-class (or above) flares, 7 satisfy the flare conditions prescribed by Hagyard (high shear and strong transverse fields). Strong photospheric shear, however, is not necessarily a condition for a flare. We find an increase in the shear for two flares, a 6-deg shear increase along the neutral line after a X-2 flare and a 13-deg increase after a M-1.9 flare. For other flares, we did not detect substantial shear changes.
The intermittency of vector fields and random-number generators
Kalinin, A. O.; Sokoloff, D. D.; Tutubalin, V. N.
2017-09-01
We examine how well natural random-number generators can reproduce the intermittency phenomena that arise in the transfer of vector fields in random media. A generator based on the analysis of financial indices is suggested as the most promising random-number generator. Is it shown that even this generator, however, fails to reproduce the phenomenon long enough to confidently detect intermittency, while the C++ generator successfully solves this problem. We discuss the prospects of using shell models of turbulence as the desired generator.
The Local Stellar Velocity Field via Vector Spherical Harmonics
Markarov, V. V.; Murphy, D. W.
2007-01-01
We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism. We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not corrected for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star. The Oort parameters determined by a straightforward least-squares adjustment in vector spherical harmonics are A=14.0 +/- 1.4, B=13.1 +/- 1.2, K=1.1 +/- 1.8, and C=2.9 +/- 1.4 km s(exp -1) kpc(exp -1). The physical meaning and the implications of these parameters are discussed in the framework of a general linear model of the velocity field. We find a few statistically significant higher degree harmonic terms that do not correspond to any parameters in the classical linear model. One of them, a third-degree electric harmonic, is tentatively explained as the response to a negative linear gradient of rotation velocity with distance from the Galactic plane, which we estimate at approximately -20 km s(exp -1) kpc(exp -1). A similar vertical gradient of rotation velocity has been detected for more distant stars representing the thick disk (z greater than 1 kpc
2D Vector Field Simplification Based on Robustness
Skraba, Primoz
2014-03-01
Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. These geometric metrics do not consider the flow magnitude, an important physical property of the flow. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness, which provides a complementary view on flow structure compared to the traditional topological-skeleton-based approaches. Robustness enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory, has fewer boundary restrictions, and so can handle more general cases. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. © 2014 IEEE.
Multiresolution and Explicit Methods for Vector Field Analysis and Visualization
Nielson, Gregory M.
1997-01-01
This is a request for a second renewal (3d year of funding) of a research project on the topic of multiresolution and explicit methods for vector field analysis and visualization. In this report, we describe the progress made on this research project during the second year and give a statement of the planned research for the third year. There are two aspects to this research project. The first is concerned with the development of techniques for computing tangent curves for use in visualizing flow fields. The second aspect of the research project is concerned with the development of multiresolution methods for curvilinear grids and their use as tools for visualization, analysis and archiving of flow data. We report on our work on the development of numerical methods for tangent curve computation first.
International Nuclear Information System (INIS)
Dahmen, B.
1994-12-01
A recently proposed method for a strong coupling analysis of scattering phenomena in hamiltonian lattice field theories is applied to the SU(2) Yang-Mills model in (2 + 1) dimensions. The calculation is performed up to second order in the hopping parameter. All relevant quantities that characterize the collision between the lightest glueballs in the elastic region - cross section, phase shifts, resonance parameters - are determined. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Levi, Michele [Institut d' Astrophysique de Paris, Université Pierre et Marie Curie, CNRS-UMR 7095, 98 bis Boulevard Arago, 75014 Paris (France); Steinhoff, Jan, E-mail: michele.levi@upmc.fr, E-mail: jan.steinhoff@ist.utl.pt [Centro Multidisciplinar de Astrofisica, Instituto Superior Tecnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2014-12-01
The next-to-next-to-leading order spin1-spin2 potential for an inspiralling binary, that is essential for accuracy to fourth post-Newtonian order, if both components in the binary are spinning rapidly, has been recently derived independently via the ADM Hamiltonian and the Effective Field Theory approaches, using different gauges and variables. Here we show the complete physical equivalence of the two results, thereby we first prove the equivalence of the ADM Hamiltonian and the Effective Field Theory approaches at next-to-next-to-leading order with the inclusion of spins. The main difficulty in the spinning sectors, which also prescribes the manner in which the comparison of the two results is tackled here, is the existence of redundant unphysical spin degrees of freedom, associated with the spin gauge choice of a point within the extended spinning object for its representative worldline. After gauge fixing and eliminating the unphysical degrees of freedom of the spin and its conjugate at the level of the action, we arrive at curved spacetime generalizations of the Newton-Wigner variables in closed form, which can also be used to obtain further Hamiltonians, based on an Effective Field Theory formulation and computation. Finally, we make use of our validated result to provide gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to fourth post-Newtonian order, including all known sectors up to date.
Vector condensate and AdS soliton instability induced by a magnetic field
International Nuclear Information System (INIS)
Cai, Rong-Gen; Li, Li; Li, Li-Fang; Wu, You
2014-01-01
We continue to study the holographic p-wave superconductor model in the Einstein-Maxwell-complex vector field theory with a non-minimal coupling between the complex vector field and the Maxwell field. In this paper we work in the AdS soliton background which describes a conformal field theory in the confined phase and focus on the probe approximation. We find that an applied magnetic field can lead to the condensate of the vector field and the AdS soliton instability. As a result, a vortex lattice structure forms in the spatial directions perpendicular to the applied magnetic field. As a comparison, we also discuss the vector condensate in the Einstein-SU(2) Yang-Mills theory and find that in the setup of the present paper, the Einstein-Maxwell-complex vector field model is a generalization of the SU(2) model in the sense that the vector field has a general mass and gyromagnetic ratio
Noncanonical Hamiltonian mechanics
International Nuclear Information System (INIS)
Litteljohn, R.G.
1986-01-01
Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)
Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields
International Nuclear Information System (INIS)
Anco, Stephen C.
2003-01-01
A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here
Vector network analyzer ferromagnetic resonance spectrometer with field differential detection
Tamaru, S.; Tsunegi, S.; Kubota, H.; Yuasa, S.
2018-05-01
This work presents a vector network analyzer ferromagnetic resonance (VNA-FMR) spectrometer with field differential detection. This technique differentiates the S-parameter by applying a small binary modulation field in addition to the DC bias field to the sample. By setting the modulation frequency sufficiently high, slow sensitivity fluctuations of the VNA, i.e., low-frequency components of the trace noise, which limit the signal-to-noise ratio of the conventional VNA-FMR spectrometer, can be effectively removed, resulting in a very clean FMR signal. This paper presents the details of the hardware implementation and measurement sequence as well as the data processing and analysis algorithms tailored for the FMR spectrum obtained with this technique. Because the VNA measures a complex S-parameter, it is possible to estimate the Gilbert damping parameter from the slope of the phase variation of the S-parameter with respect to the bias field. We show that this algorithm is more robust against noise than the conventional algorithm based on the linewidth.
Derivative self-interactions for a massive vector field
Energy Technology Data Exchange (ETDEWEB)
Beltrán Jiménez, Jose, E-mail: jose.beltran@cpt.univ-mrs.fr [CPT, Aix Marseille Université, UMR 7332, 13288 Marseille (France); Heisenberg, Lavinia, E-mail: lavinia.heisenberg@eth-its.ethz.ch [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland)
2016-06-10
In this work we revisit the construction of theories for a massive vector field with derivative self-interactions such that only the 3 desired polarizations corresponding to a Proca field propagate. We start from the decoupling limit by constructing healthy interactions containing second derivatives of the Stueckelberg field with itself and also with the transverse modes. The resulting interactions can then be straightforwardly generalized beyond the decoupling limit. We then proceed to a systematic construction of the interactions by using the Levi–Civita tensors. Both approaches lead to a finite family of allowed derivative self-interactions for the Proca field. This construction allows us to show that some higher order terms recently introduced as new interactions trivialize in 4 dimensions by virtue of the Cayley–Hamilton theorem. Moreover, we discuss how the resulting derivative interactions can be written in a compact determinantal form, which can also be regarded as a generalization of the Born-Infeld lagrangian for electromagnetism. Finally, we generalize our results for a curved background and give the necessary non-minimal couplings guaranteeing that no additional polarizations propagate even in the presence of gravity.
On the non-Gaussian correlation of the primordial curvature perturbation with vector fields
DEFF Research Database (Denmark)
Kumar Jain, Rajeev; Sloth, Martin Snoager
2013-01-01
We compute the three-point cross-correlation function of the primordial curvature perturbation generated during inflation with two powers of a vector field in a model where conformal invariance is broken by a direct coupling of the vector field with the inflaton. If the vector field is identified...... with the electromagnetic field, this correlation would be a non-Gaussian signature of primordial magnetic fields generated during inflation. We find that the signal is maximized for the flattened configuration where the wave number of the curvature perturbation is twice that of the vector field and in this limit...
DEFF Research Database (Denmark)
Boeriis, Morten; van Leeuwen, Theo
2017-01-01
should be taken into account in discussing ‘reactions’, which Kress and van Leeuwen link only to eyeline vectors. Finally, the question can be raised as to whether actions are always realized by vectors. Drawing on a re-reading of Rudolf Arnheim’s account of vectors, these issues are outlined......This article revisits the concept of vectors, which, in Kress and van Leeuwen’s Reading Images (2006), plays a crucial role in distinguishing between ‘narrative’, action-oriented processes and ‘conceptual’, state-oriented processes. The use of this concept in image analysis has usually focused...
Non-gaussianity from the trispectrum and vector field perturbations
International Nuclear Information System (INIS)
Valenzuela-Toledo, Cesar A.; Rodriguez, Yeinzon
2010-01-01
We use the δN formalism to study the trispectrum T ζ of the primordial curvature perturbation ζ when the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, τ NL , is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f NL , and the level of statistical anisotropy in the power spectrum, g ζ . Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on τ NL from WMAP, for generic inflationary models, is done.
Non-gaussianity from the trispectrum and vector field perturbations
Energy Technology Data Exchange (ETDEWEB)
Valenzuela-Toledo, Cesar A., E-mail: cavalto@ciencias.uis.edu.c [Escuela de Fisica, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga (Colombia); Rodriguez, Yeinzon, E-mail: yeinzon.rodriguez@uan.edu.c [Escuela de Fisica, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga (Colombia); Centro de Investigaciones, Universidad Antonio Narino, Cra 3 Este 47A-15, Bogota D.C. (Colombia)
2010-03-01
We use the deltaN formalism to study the trispectrum T{sub z}eta of the primordial curvature perturbation zeta when the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, tau{sub NL}, is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f{sub NL}, and the level of statistical anisotropy in the power spectrum, g{sub z}eta. Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on tau{sub NL} from WMAP, for generic inflationary models, is done.
General projective relativity and the vector-tensor gravitational field
International Nuclear Information System (INIS)
Arcidiacono, G.
1986-01-01
In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation
Bountis, Tassos
2012-01-01
This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) res...
Lovelock vacua with a recurrent null vector field
Ortaggio, Marcello
2018-02-01
Vacuum solutions of Lovelock gravity in the presence of a recurrent null vector field (a subset of Kundt spacetimes) are studied. We first discuss the general field equations, which constrain both the base space and the profile functions. While choosing a "generic" base space puts stronger constraints on the profile, in special cases there also exist solutions containing arbitrary functions (at least for certain values of the coupling constants). These and other properties (such as the p p - waves subclass and the overlap with VSI, CSI and universal spacetimes) are subsequently analyzed in more detail in lower dimensions n =5 , 6 as well as for particular choices of the base manifold. The obtained solutions describe various classes of nonexpanding gravitational waves propagating, e.g., in Nariai-like backgrounds M2×Σn -2. An Appendix contains some results about general (i.e., not necessarily Kundt) Lovelock vacua of Riemann type III/N and of Weyl and traceless-Ricci type III/N. For example, it is pointed out that for theories admitting a triply degenerate maximally symmetric vacuum, all the (reduced) field equations are satisfied identically, giving rise to large classes of exact solutions.
Effective Hamiltonians for phosphorene and silicene
International Nuclear Information System (INIS)
Lew Yan Voon, L C; Lopez-Bezanilla, A; Wang, J; Zhang, Y; Willatzen, M
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene. We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector. We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k⋅p parameters. (paper)
On the existence of polynomial Lyapunov functions for rationally stable vector fields
DEFF Research Database (Denmark)
Leth, Tobias; Wisniewski, Rafal; Sloth, Christoffer
2018-01-01
This paper proves the existence of polynomial Lyapunov functions for rationally stable vector fields. For practical purposes the existence of polynomial Lyapunov functions plays a significant role since polynomial Lyapunov functions can be found algorithmically. The paper extents an existing result...... on exponentially stable vector fields to the case of rational stability. For asymptotically stable vector fields a known counter example is investigated to exhibit the mechanisms responsible for the inability to extend the result further....
Applications of the Local Algebras of Vector Fields to the Modelling of Physical Phenomena
Bayak, Igor V.
2015-01-01
In this paper we discuss the local algebras of linear vector fields that can be used in the mathematical modelling of physical space by building the dynamical flows of vector fields on eight-dimensional cylindrical or toroidal manifolds. It is shown that the topological features of the vector fields obey the Dirac equation when moving freely within the surface of a pseudo-sphere in the eight-dimensional pseudo-Euclidean space.
Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
Directory of Open Access Journals (Sweden)
Mitsuo Kato
2018-01-01
Full Text Available A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painlevé VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.
Gu, Bing; Xu, Danfeng; Rui, Guanghao; Lian, Meng; Cui, Yiping; Zhan, Qiwen
2015-09-20
Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in areas where exotic optical fields are desired. In this work, we experimentally demonstrate the versatile generation of linearly polarized vector fields, elliptically polarized vector fields, and circularly polarized vortex beams through introducing attenuators in a common-path interferometer. By means of Richards-Wolf vectorial diffraction method, the characteristics of the highly focused elliptically polarized vector fields are studied. The optical force and torque on a dielectric Rayleigh particle produced by these tightly focused vector fields are calculated and exploited for the stable trapping of dielectric Rayleigh particles. It is shown that the additional degree of freedom provided by the elliptically polarized vector field allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force and torque on a dielectric Rayleigh particle.
International Nuclear Information System (INIS)
Dai, H.L.; Wang, X.
2006-01-01
In this paper, an analytical method is introduced to solve the problem for the dynamic stress-focusing and centred-effect of perturbation of the magnetic field vector in orthotropic cylinders under thermal and mechanical shock loads. Analytical expressions for the dynamic stresses and the perturbation of the magnetic field vector are obtained by means of finite Hankel transforms and Laplace transforms. The response histories of dynamic stresses and the perturbation of the field vector are also obtained. In practical examples, the dynamic focusing effect on both magnetoelastic stress and perturbation of the axial magnetic field vector in an orthotropic cylinder subjected to various shock loads is presented and discussed
Energy Technology Data Exchange (ETDEWEB)
Rudowicz, Czesław, E-mail: crudowicz@zut.edu.pl [Institute of Physics, West Pomeranian University of Technology, Al. Piastów 17, 70-310 Szczecin (Poland); Karbowiak, Mirosław [Faculty of Chemistry, University of Wrocław, ul. F. Joliot-Curie 14, 50-383 Wrocław (Poland)
2014-10-15
The single transition ions in various crystals or molecules as well as the exchange coupled systems (ECS) of transition ions, especially the single molecule magnets (SMM) or molecular nanomagnets (MNM), have been extensively studied in recent decades using electron magnetic resonance (EMR), optical spectroscopy, and magnetic measurements. Interpretation of magnetic and spectroscopic properties of transition ions is based on two physically distinct types of Hamiltonians: the physical crystal field (CF), or equivalently ligand field (LF), Hamiltonians and the effective spin Hamiltonians (SH), which include the zero-field splitting (ZFS) Hamiltonians. Survey of recent literature has revealed a number of terminological confusions and specific problems occurring at the interface between these Hamiltonians (denoted CF (LF)↔SH (ZFS)). Elucidation of sloppy or incorrect usage of crucial notions, especially those describing or parameterizing crystal fields and zero field splittings, is a very challenging task that requires several reviews. Here we focus on the prevailing confusion between the CF (LF) and SH (ZFS) quantities, denoted as the CF=ZFS confusion, which consists in referring to the parameters (or Hamiltonians), which are the true ZFS (or SH) quantities, as purportedly the CF (LF) quantities. The inverse ZFS=CF confusion, which pertains to the cases of labeling the true CF (LF) quantities as purportedly the ZFS quantities, is considered in a follow-up paper. The two reviews prepare grounds for a systematization of nomenclature aimed at bringing order to the zoo of different Hamiltonians. Specific cases of the CF=ZFS confusion identified in the recent textbooks, review articles, and SMM (MNM)- and EMR-related papers are surveyed and the pertinent misconceptions are outlined. The consequences of the terminological confusions go far beyond simple semantic issues or misleading keyword classifications of papers in journals and scientific databases. Serious
ACHIEVING CONSISTENT DOPPLER MEASUREMENTS FROM SDO /HMI VECTOR FIELD INVERSIONS
International Nuclear Information System (INIS)
Schuck, Peter W.; Antiochos, S. K.; Leka, K. D.; Barnes, Graham
2016-01-01
NASA’s Solar Dynamics Observatory is delivering vector magnetic field observations of the full solar disk with unprecedented temporal and spatial resolution; however, the satellite is in a highly inclined geosynchronous orbit. The relative spacecraft–Sun velocity varies by ±3 km s −1 over a day, which introduces major orbital artifacts in the Helioseismic Magnetic Imager (HMI) data. We demonstrate that the orbital artifacts contaminate all spatial and temporal scales in the data. We describe a newly developed three-stage procedure for mitigating these artifacts in the Doppler data obtained from the Milne–Eddington inversions in the HMI pipeline. The procedure ultimately uses 32 velocity-dependent coefficients to adjust 10 million pixels—a remarkably sparse correction model given the complexity of the orbital artifacts. This procedure was applied to full-disk images of AR 11084 to produce consistent Dopplergrams. The data adjustments reduce the power in the orbital artifacts by 31 dB. Furthermore, we analyze in detail the corrected images and show that our procedure greatly improves the temporal and spectral properties of the data without adding any new artifacts. We conclude that this new procedure makes a dramatic improvement in the consistency of the HMI data and in its usefulness for precision scientific studies.
First principles of Hamiltonian medicine.
Crespi, Bernard; Foster, Kevin; Úbeda, Francisco
2014-05-19
We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.
Topological invariants and the dynamics of an axial vector torsion field
International Nuclear Information System (INIS)
Drechsler, W.
1983-01-01
A generalized throry of gravitation is discussed which is based on a Riemann-Cartan space-time, U 4 , with an axial vector torsion field. Besides Einstein's equations determining the metric of the U 4 a system of nonlinear field equations is established coupling an axial vector source current to the axial vector torsion field. The properties of the solutions of these equations are discussed assuming a London-type condition relating the axial current and torsion field. To characterize the solutions use is made of the Euler and Pontrjagin forms and the associated quadratic curvature invariants for the U 4 space-time. It is found that there exists for a Riemann-Cartan space-time a relation between the zeros of the axial vector torsion field and the singularities of the Pontrjagin invariant, which is analogous to the well-known Hopf relation between the zeros of vector fields and the Euler characteristic. (author)
ON A PROLONGATION CONSTRUCTION FOR LOCAL NON-DIVERGENT VECTOR FIELDS ON Rn
Directory of Open Access Journals (Sweden)
A. M. Lukatsky
2015-01-01
Full Text Available The problem of a prolongation of non-divergent vector field, defined in a vicinity of zero in Rn t, to a finite non-divergent vector field on Rn is considered. Explicit formulas for the elements of the simple Lie algebra of non-divergent vector from the well-known Cartan series are obtained. This construction allows to move from the Euler equations for the ideal incompressible fluid to the Euler equations on finite-dimensional Lie groups.
Enumeration of Combinatorial Classes of Single Variable Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
A vector field in the space of degree d monic, centered single variable complex polynomial vector fields has a combinatorial structure which can be fully described by a combinatorial data set consisting of an equivalence relation and a marked subset on the integers mod 2d-2, satisfying certain...
A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
Directory of Open Access Journals (Sweden)
Jaume Llibre
2012-06-01
Full Text Available We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields which are volume preserving and possess nontrivial normalizers. Our approach is geometric and coordinate-free and hence it works on any smooth orientable manifold.
Cobordism Obstructions to Vector Fields and a Generalization of Lin's Theorem
DEFF Research Database (Denmark)
Svane, Anne Marie
Atiyah and Dupont have studied the existence of linearly independent vector fields on manifolds by means of K-theory. They obtained the complete conditions for up to three independent vector fields. In the thesis, we try to copy their approach using certain spectra related to cobordism theory. We...
Limit sets and global dynamic for 2-D divergence-free vector fields
International Nuclear Information System (INIS)
Marzougui, H.
2004-08-01
T. Ma and S. Wang studied the global structure of regular divergence-free vector fields on compact surfaces with or without boundary. This paper extends their study to the general case of divergence-free vector fields (regular or not) on closed surfaces and gives as a consequence a simple proof of their results. (author)
Discovering and understanding the vector field using simulation in android app
Budi, A.; Muliyati, D.
2018-05-01
An understanding of vector field’s concepts are fundamental parts of the electrodynamics course. In this paper, we use a simple simulation that can be used to show qualitative imaging results as a variation of the vector field. Android application packages the simulation with consideration of the efficiency of use during the lecture. In addition, this simulation also trying to cover the divergences and curl concepts from the same conditions that students have a complete understanding and can distinguish concepts that have been described only mathematically. This simulation is designed to show the relationship between the field magnitude and its potential. This application can show vector field simulations in various conditions that help to improve students’ understanding of vector field concepts and their relation to particle existence around the field vector.
El-Nabulsi, Rami Ahmad
2018-03-01
Recently, the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations. Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties. One interesting form related to the inverse variational problem is the logarithmic Lagrangian, which has a number of motivating features related to the Liénard-type and Emden nonlinear differential equations. Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians. In this communication, we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians. One interesting consequence concerns the emergence of an extra pressure term, which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field. The case of the stellar halo of the Milky Way is considered.
Perspective: Quantum Hamiltonians for optical interactions
Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy
2018-01-01
The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.
Hamiltonian Algorithm Sound Synthesis
大矢, 健一
2013-01-01
Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.
Energy Technology Data Exchange (ETDEWEB)
Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)
2017-01-15
In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.
The Scalar, Vector and Tensor Fields in Theory of Elasticity and Plasticity
Directory of Open Access Journals (Sweden)
František FOJTÍK
2014-06-01
Full Text Available This article is devoted to an analysis of scalar, vector and tensor fields, which occur in the loaded and deformed bodies. The aim of this article is to clarify and simplify the creation of an understandable idea of some elementary concepts and quantities in field theories, such as, for example equiscalar levels, scalar field gradient, Hamilton operator, divergence, rotation and gradient of vector or tensor and others. Applications of those mathematical terms are shown in simple elasticity and plasticity tasks. We hope that content of our article might help technicians to make their studies of necessary mathematical chapters of vector and tensor analysis and field theories easier.
Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes
International Nuclear Information System (INIS)
Dias, Goncalo A. S.; Lemos, Jose P. S.
2008-01-01
The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free ω parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity (ω→±∞), a dimensionally reduced cylindrical four-dimensional general relativity theory (ω=0), and a theory representing a class of theories (ω=-3), all with a Maxwell term. The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P M ;Q,P Q ), where M is the mass parameter, which for ω M is the conjugate momenta of M, Q is the charge parameter, and P Q is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field φ. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.
Hamiltonian structure of linearly extended Virasoro algebra
International Nuclear Information System (INIS)
Arakelyan, T.A.; Savvidi, G.K.
1991-01-01
The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order
Hamiltonian Cycles on Random Eulerian Triangulations
DEFF Research Database (Denmark)
Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard
1998-01-01
. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...
Mesh-free Hamiltonian implementation of two dimensional Darwin model
Siddi, Lorenzo; Lapenta, Giovanni; Gibbon, Paul
2017-08-01
A new approach to Darwin or magnetoinductive plasma simulation is presented, which combines a mesh-free field solver with a robust time-integration scheme avoiding numerical divergence errors in the solenoidal field components. The mesh-free formulation employs an efficient parallel Barnes-Hut tree algorithm to speed up the computation of fields summed directly from the particles, avoiding the necessity of divergence cleaning procedures typically required by particle-in-cell methods. The time-integration scheme employs a Hamiltonian formulation of the Lorentz force, circumventing the development of violent numerical instabilities associated with time differentiation of the vector potential. It is shown that a semi-implicit scheme converges rapidly and is robust to further numerical instabilities which can develop from a dominant contribution of the vector potential to the canonical momenta. The model is validated by various static and dynamic benchmark tests, including a simulation of the Weibel-like filamentation instability in beam-plasma interactions.
Motion Vector field improvement for picture rate conversion with reduced Halo
Mertens, M.J.W.; Haan, de G.; Girod, B.; Bouman, C.A.; Steinbach, E.G.
2001-01-01
The quality of the interpolated images in picture rate upconversion is predominantly dependent on the accuracy of the motion vector fields. Block based MEs typically yield incorrect vectors in occlusion areas, which leads to an annoying halo in the upconverted video sequences. In the past we have
Correlation between topological structure and its properties in dynamic singular vector fields.
Vasilev, Vasyl; Soskin, Marat
2016-04-20
A new technique for establishment of topology measurements for static and dynamic singular vector fields is elaborated. It is based on precise measurement of the 3D landscape of ellipticity distribution for a checked singular optical field with C points on the tops of ellipticity hills. Vector fields possess three-component topology: areas with right-hand (RH) and left-hand (LH) ellipses, and delimiting those L lines as the singularities of handedness. The azimuth map of polarization ellipses is common for both RH and LH ellipses of vector fields and do not feel L lines. The strict rules were confirmed experimentally, which define the connection between the sign of underlying optical vortices and morphological parameters of upper-lying C points. Percolation phenomena explain their realization in-between singular vector fields and long duration of their chains of 103 s order.
Gu, Bing; Xu, Danfeng; Pan, Yang; Cui, Yiping
2014-07-01
Based on the vectorial Rayleigh-Sommerfeld integrals, the analytical expressions for azimuthal-variant vector fields diffracted by an annular aperture are presented. This helps us to investigate the propagation behaviors and the focusing properties of apertured azimuthal-variant vector fields under nonparaxial and paraxial approximations. The diffraction by a circular aperture, a circular disk, or propagation in free space can be treated as special cases of this general result. Simulation results show that the transverse intensity, longitudinal intensity, and far-field divergence angle of nonparaxially apertured azimuthal-variant vector fields depend strongly on the azimuthal index, the outer truncation parameter and the inner truncation parameter of the annular aperture, as well as the ratio of the waist width to the wavelength. Moreover, the multiple-ring-structured intensity pattern of the focused azimuthal-variant vector field, which originates from the diffraction effect caused by an annular aperture, is experimentally demonstrated.
Multi-Hamiltonian formulations and stability of higher-derivative extensions of 3d Chern-Simons
Energy Technology Data Exchange (ETDEWEB)
Abakumova, V.A.; Kaparulin, D.S.; Lyakhovich, S.L. [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)
2018-02-15
Most general third-order 3d linear gauge vector field theory is considered. The field equations involve, besides the mass, two dimensionless constant parameters. The theory admits two-parameter series of conserved tensors with the canonical energy-momentum being a particular representative of the series. For a certain range of the model parameters, the series of conserved tensors include bounded quantities. This makes the dynamics classically stable, though the canonical energy is unbounded in all the instances. The free third-order equations are shown to admit constrained multi-Hamiltonian form with the 00-components of conserved tensors playing the roles of corresponding Hamiltonians. The series of Hamiltonians includes the canonical Ostrogradski's one, which is unbounded. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. This means, the theory admits inequivalent quantizations at the free level. Covariant interactions are included with spinor fields such that the higher-derivative dynamics remains stable at interacting level if the bounded conserved quantity exists in the free theory. In the first-order formalism, the interacting theory remains Hamiltonian and therefore it admits quantization, though the vertices are not necessarily Lagrangian in the third-order field equations. (orig.)
VECTOR TOMOGRAPHY FOR THE CORONAL MAGNETIC FIELD. II. HANLE EFFECT MEASUREMENTS
International Nuclear Information System (INIS)
Kramar, M.; Inhester, B.; Lin, H.; Davila, J.
2013-01-01
In this paper, we investigate the feasibility of saturated coronal Hanle effect vector tomography or the application of vector tomographic inversion techniques to reconstruct the three-dimensional magnetic field configuration of the solar corona using linear polarization measurements of coronal emission lines. We applied Hanle effect vector tomographic inversion to artificial data produced from analytical coronal magnetic field models with equatorial and meridional currents and global coronal magnetic field models constructed by extrapolation of real photospheric magnetic field measurements. We tested tomographic inversion with only Stokes Q, U, electron density, and temperature inputs to simulate observations over large limb distances where the Stokes I parameters are difficult to obtain with ground-based coronagraphs. We synthesized the coronal linear polarization maps by inputting realistic noise appropriate for ground-based observations over a period of two weeks into the inversion algorithm. We found that our Hanle effect vector tomographic inversion can partially recover the coronal field with a poloidal field configuration, but that it is insensitive to a corona with a toroidal field. This result demonstrates that Hanle effect vector tomography is an effective tool for studying the solar corona and that it is complementary to Zeeman effect vector tomography for the reconstruction of the coronal magnetic field
Hamiltonian closures in fluid models for plasmas
Tassi, Emanuele
2017-11-01
This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and
Effective field theory and unitarity in vector boson scattering
International Nuclear Information System (INIS)
Sekulla, Marco; Kilian, Wolfgang; Ohl, Thorsten; Reuter, Juergen
2016-10-01
Weak vector boson scattering at high energies will be one of the key measurements in current and upcoming LHC runs. It is most sensitive to any new physics associated with electroweak symmetry breaking. However, a conventional EFT analysis will fail at high energies. To address this problem, we present a parameter-free prescription valid for arbitrary perturbative and non-perturbative models: the T-matrix unitarization. We describe its implementation as an asymptotically consistent reference model matched to the low-energy effective theory. We show examples of typical observables of vector-boson scattering at the LHC in our unitarized framework. For many strongly-coupled models like composite Higgs models, dimension-8 operators might be actually the leading operators. In addition to those longitudinal and transversal dimension eight EFT operators, the effects of generic tensor and scalar resonances within simplified models are considered.
A late time accelerated FRW model with scalar and vector fields via Noether symmetry
Directory of Open Access Journals (Sweden)
Babak Vakili
2014-11-01
Full Text Available We study the evolution of a three-dimensional minisuperspace cosmological model by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a flat Friedmann–Robertson–Walker (FRW model, a scalar field with potential function V(ϕ with which the gravity part of the action is minimally coupled and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f(ϕ. Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generator of the desired symmetry. We explicitly calculate the form of the coupling function between the scalar and the vector fields and also the scalar field potential function for which such symmetry exists. Finally, by means of the corresponding Noether current, we integrate the equations of motion and obtain exact solutions for the scale factor, scalar and vector fields. It is shown that the resulting cosmology is an accelerated expansion universe for which its expansion is due to the presence of the vector field in the early times, while the scalar field is responsible of its late time expansion. Keywords: Noether symmetry, Scalar field cosmology, Vector field cosmology
The principal part of plane vector fields with fixed Newton diagram
International Nuclear Information System (INIS)
Berezovskaya, F.
1991-09-01
Considering the main part of a plane vector field in a neighbourhood of a singular point 0(0,0) it is well known that if the singularity real parts of eigenvalues are non-zero, the linear part of the vector field provides the topological normal form and tangents of all the o-curves. The problem is to find the main part of a plane vector field which would provide the topological orbital normal form in a neighbourhood of singular point and asymptotics of all characteristics trajectories. In this work the solution to the problem for the generic ease of so-called nondegenerate vector fields, using Newton diagram is given. 13 refs, 5 figs
van Beurden, M.C.; Setija, Irwan
2017-01-01
We present two adapted formulations, one tailored to isotropic media and one for general anisotropic media, of the normal vector field framework previously introduced to improve convergence near arbitrarily shaped material interfaces in spectral simulation methods for periodic scattering geometries.
Spherical cap modelling of Orsted magnetic field vectors over southern Africa
CSIR Research Space (South Africa)
Kotze, PB
2001-01-01
Full Text Available Vector magnetic field observations by the Orsted satellite during geomagnetic quiet conditions around January 1, 2000, have been employed to derive a spherical cap harmonic model (Haines, 1985) over the southern African region between 10 degrees...
Realization of vector fields for quantum groups as pseudodifferential operators on quantum spaces
International Nuclear Information System (INIS)
Chu, Chong-Sun; Zumino, B.
1995-01-01
The vector fields of the quantum Lie algebra are described for the quantum groups GL q (n), SL q (N) and SO q (N) as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms SU q (N) and SO q (N,R) are discussed in detail
Theory of charged vector mesons interacting with the electromagnetic field
International Nuclear Information System (INIS)
Lee, T.D.; Yang, C.N.
1983-01-01
It is shown that starting from the usual canonical formalism for the electromagnetic interaction of a charged vector meson with arbitrary magnetic moment one is led to a set of rules for Feynman diagrams, which appears to contain terms that are both infinite and noncovariant. These difficulties, however, can be circumvented by introducing a xi-limiting process which depends on a dimensionless positive parameter xi → 0. Furthermore, by using the mathematical artifice of a negative metric the theory becomes renormalizable (for xi > 0)
On the use of the Kodama vector field in spherically symmetric dynamical problems
Energy Technology Data Exchange (ETDEWEB)
Racz, Istvan [MTA KFKI, Reszecske- es Magfizikai Kutatointezet, H-1121 Budapest, Konkoly Thege Miklos ut 29-33, (Hungary)
2006-01-07
It is shown that by making use of the Kodama vector field, as a preferred time evolution vector field, in spherically symmetric dynamical systems unexpected simplifications arise. In particular, the evolution equations relevant for the case of a massless scalar field minimally coupled to gravity are investigated. The simplest form of these equations in the 'canonical gauge' is known to possess the character of a mixed first-order elliptic-hyperbolic system. The advantages related to the use of the Kodama vector field are twofold although they show up simultaneously. First, it is found that the true degrees of freedom separate. Second, a subset of the field equations possessing the form of a first-order symmetric hyperbolic system for these preferred degrees of freedom is singled out. It is also demonstrated, in the appendix, that the above results generalize straightforwardly to the case of a generic self-interacting scalar field.
Metcalf, Thomas R.
1994-01-01
I present a robust algorithm that resolves the 180-deg ambiguity in measurements of the solar vector magnetic field. The technique simultaneously minimizes both the divergence of the magnetic field and the electric current density using a simulated annealing algorithm. This results in the field orientation with approximately minimum free energy. The technique is well-founded physically and is simple to implement.
Vector magnetic field microscopy using nitrogen vacancy centers in diamond
Maertz, B.J.; Wijnheijmer, A.P.; Fuchs, G.D.; Nowakowski, M.E.; Awschalom, D.D.
2010-01-01
The localized spin triplet ground state of a nitrogen vacancy (NV) center in diamond can be used in atomic-scale detection of local magnetic fields. Here we present a technique using ensembles of these defects in diamond to image fields around magnetic structures. We extract the local magnetic field
Collapse dynamics of a vector vortex optical field with inhomogeneous states of polarization
International Nuclear Information System (INIS)
Chen, Rui-Pin; Zhao, Ting-Yu; Zhang, Xiaobo; Zhong, Li-Xin; Chew, Khian-Hooi
2015-01-01
Based on a pair of coupled 2D nonlinear Schrödinger equations, the collapse dynamics of a vector field with hybrid states of polarization (SoP) in a Kerr medium is demonstrated. The critical power for an optical field to collapse is present, and the full vectorial numerical simulations provide detailed information about the evolution and partial collapse of the vector field in a Kerr medium. Our results reveal that the optical field prefers to collapse in linearly-polarization, as a result of the self-focusing effect difference in linearly, elliptically and circularly polarized components. The SoP in the field cross-section changes and propagates with a spiral trajectory when the vector beams are imposed with a vortex. The vectorial effect on the collapse of a vector optical field can prevail over the noise even though it reaches 10% amplitude of the optical field. The unique feature of these structured collapses of a vector optical field may lead to new phenomena in the interaction of light with matter. (paper)
Non-Gaussianity and statistical anisotropy from vector field populated inflationary models
Dimastrogiovanni, Emanuela; Matarrese, Sabino; Riotto, Antonio
2010-01-01
We present a review of vector field models of inflation and, in particular, of the statistical anisotropy and non-Gaussianity predictions of models with SU(2) vector multiplets. Non-Abelian gauge groups introduce a richer amount of predictions compared to the Abelian ones, mostly because of the presence of vector fields self-interactions. Primordial vector fields can violate isotropy leaving their imprint in the comoving curvature fluctuations zeta at late times. We provide the analytic expressions of the correlation functions of zeta up to fourth order and an analysis of their amplitudes and shapes. The statistical anisotropy signatures expected in these models are important and, potentially, the anisotropic contributions to the bispectrum and the trispectrum can overcome the isotropic parts.
Representation and display of vector field topology in fluid flow data sets
Helman, James; Hesselink, Lambertus
1989-01-01
The visualization of physical processes in general and of vector fields in particular is discussed. An approach to visualizing flow topology that is based on the physics and mathematics underlying the physical phenomenon is presented. It involves determining critical points in the flow where the velocity vector vanishes. The critical points, connected by principal lines or planes, determine the topology of the flow. The complexity of the data is reduced without sacrificing the quantitative nature of the data set. By reducing the original vector field to a set of critical points and their connections, a representation of the topology of a two-dimensional vector field that is much smaller than the original data set but retains with full precision the information pertinent to the flow topology is obtained. This representation can be displayed as a set of points and tangent curves or as a graph. Analysis (including algorithms), display, interaction, and implementation aspects are discussed.
A vector model for off-axis hysteresis loops using anisotropy field
International Nuclear Information System (INIS)
Jamali, Ali; Torre, Edward Della; Cardelli, Ermanno; ElBidweihy, Hatem; Bennett, Lawrence H.
2016-01-01
A model for the off-axis vector magnetization of a distribution of uniaxial particles is presented. Recent work by the authors decomposed the magnetization into two components and modeled the total vector magnetization as their vector sum. In this paper, to account for anisotropy, the direction of the reversible magnetization component is specified by the vector sum of the applied field and an effective anisotropy field. The formulation of the new anisotropy field (AF) model is derived and its results are discussed considering (i) oscillation and rotational modes, (ii) lag angle, and (iii) unitary magnetization. The advantages of the AF model are outlined by comparing its results to the results of the classical Stoner–Wohlfarth model.
A vector model for off-axis hysteresis loops using anisotropy field
Energy Technology Data Exchange (ETDEWEB)
Jamali, Ali, E-mail: alijamal@gwu.edu [Electrical and Computer Engineering Department, The George Washington University, Washington, D.C. 20052 (United States); Torre, Edward Della [Electrical and Computer Engineering Department, The George Washington University, Washington, D.C. 20052 (United States); Cardelli, Ermanno [Department of Engineering, University of Perugia, Perugia (Italy); ElBidweihy, Hatem [Electrical and Computer Engineering Department, United States Naval Academy, Annapolis, MD 21402 (United States); Bennett, Lawrence H. [Electrical and Computer Engineering Department, The George Washington University, Washington, D.C. 20052 (United States)
2016-11-15
A model for the off-axis vector magnetization of a distribution of uniaxial particles is presented. Recent work by the authors decomposed the magnetization into two components and modeled the total vector magnetization as their vector sum. In this paper, to account for anisotropy, the direction of the reversible magnetization component is specified by the vector sum of the applied field and an effective anisotropy field. The formulation of the new anisotropy field (AF) model is derived and its results are discussed considering (i) oscillation and rotational modes, (ii) lag angle, and (iii) unitary magnetization. The advantages of the AF model are outlined by comparing its results to the results of the classical Stoner–Wohlfarth model.
Solar monochromatic images in magneto-sensitive spectral lines and maps of vector magnetic fields
Shihui, Y.; Jiehai, J.; Minhan, J.
1985-01-01
A new method which allows by use of the monochromatic images in some magneto-sensitive spectra line to derive both the magnetic field strength as well as the angle between magnetic field lines and line of sight for various places in solar active regions is described. In this way two dimensional maps of vector magnetic fields may be constructed. This method was applied to some observational material and reasonable results were obtained. In addition, a project for constructing the three dimensional maps of vector magnetic fields was worked out.
International Nuclear Information System (INIS)
Rodríguez, Yeinzon; Navarro, Andrés A.
2017-01-01
An alternative for the construction of fundamental theories is the introduction of Galileons. These are fields whose action leads to non higher than second-order equations of motion. As this is a necessary but not sufficient condition to make the Hamiltonian bounded from below, as long as the action is not degenerate, the Galileon construction is a way to avoid pathologies both at the classical and quantum levels. Galileon actions are, therefore, of great interest in many branches of physics, specially in high energy physics and cosmology. This proceedings contribution presents the generalities of the construction of both scalar and vector Galileons following two different but complimentary routes. (paper)
DEFF Research Database (Denmark)
Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir
2007-01-01
The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...
Vector magnetic field changes associated with X-class flares
Wang, Haimin; Ewell, M. W., Jr.; Zirin, H.; Ai, Guoxiang
1994-01-01
We present high-resolution transverse and longitudinal magnetic field measurements bracketing five X-class solar flares. We show that the magnetic shear, defined as the angular difference between the measured field and calculated potential field, actually increases after all of these flares. In each case, the shear is shown to increase along a substantial portion of the magnetic neutral line. For two of the cases, we have excellent time resolution, on the order of several minutes, and we demonstrate that the shear increase is impulsive. We briefly discuss the theoretical implications of our results.
Inflationary buildup of a vector field condensate and its cosmological consequences
International Nuclear Information System (INIS)
Sanchez, Juan C. Bueno; Dimopoulos, Konstantinos
2014-01-01
Light vector fields during inflation obtain a superhorizon perturbation spectrum when their conformal invariance is appropriately broken. Such perturbations, by means of some suitable mechanism (e.g. the vector curvaton mechanism), can contribute to the curvatue perturbation in the Universe and produce characteristic signals, such as statistical anisotropy, on the microwave sky, most recently surveyed by the Planck satellite mission. The magnitude of such characteristic features crucially depends on the magnitude of the vector condensate generated during inflation. However, in the vast majority of the literature the expectation value of this condensate has so-far been taken as a free parameter, lacking a definite prediction or a physically motivated estimate. In this paper, we study the stochastic evolution of the vector condensate and obtain an estimate for its magnitude. Our study is mainly focused in the supergravity inspired case when the kinetic function and mass of the vector boson is time-varying during inflation, but other cases are also explored such as a parity violating axial theory or a non-minimal coupling between the vector field and gravity. As an example, we apply our findings in the context of the vector curvaton mechanism and contrast our results with current observations
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Garrido, L M; Pascual, P
1960-07-01
We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.
Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy
International Nuclear Information System (INIS)
Bogdanov, L V
2010-01-01
We consider two-component integrable generalizations of the dispersionless two-dimensional Toda lattice (2DTL) hierarchy connected with non-Hamiltonian vector fields, similar to the Manakov-Santini hierarchy generalizing the dKP hierarchy. They form a one-parametric family connected by hodograph-type transformations. Generating equations and Lax-Sato equations are introduced, and a dressing scheme based on the vector nonlinear Riemann problem is formulated. The simplest two-component generalization of the dispersionless 2DTL equation is derived, and its differential reduction analogous to the Dunajski interpolating system is presented. A symmetric two-component generalization of the dispersionless elliptic 2DTL equation is also constructed.
Investigation of optical currents in coherent and partially coherent vector fields
DEFF Research Database (Denmark)
Angelsky, O. V.; Gorsky, M. P.; Maksimyak, P. P.
2011-01-01
We present the computer simulation results of the spatial distri-bution of the Poynting vector and illustrate motion of micro and nanopar-ticles in spatially inhomogeneously polarized fields. The influence of phase relations and the degree of mutual coherence of superimposing waves...... by polarization characteristics of an optical field alone, using nanoscale me-tallic particles has been shown experimentally....
A median filter approach for correcting errors in a vector field
Schultz, H.
1985-01-01
Techniques are presented for detecting and correcting errors in a vector field. These methods employ median filters which are frequently used in image processing to enhance edges and remove noise. A detailed example is given for wind field maps produced by a spaceborne scatterometer. The error detection and replacement algorithm was tested with simulation data from the NASA Scatterometer (NSCAT) project.
Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion.
Skraba, Primoz; Rosen, Paul; Wang, Bei; Chen, Guoning; Bhatia, Harsh; Pascucci, Valerio
2016-02-29
Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. We apply our method to synthetic and simulation datasets to demonstrate its effectiveness.
Visualization of Morse connection graphs for topologically rich 2D vector fields.
Szymczak, Andrzej; Sipeki, Levente
2013-12-01
Recent advances in vector field topologymake it possible to compute its multi-scale graph representations for autonomous 2D vector fields in a robust and efficient manner. One of these representations is a Morse Connection Graph (MCG), a directed graph whose nodes correspond to Morse sets, generalizing stationary points and periodic trajectories, and arcs - to trajectories connecting them. While being useful for simple vector fields, the MCG can be hard to comprehend for topologically rich vector fields, containing a large number of features. This paper describes a visual representation of the MCG, inspired by previous work on graph visualization. Our approach aims to preserve the spatial relationships between the MCG arcs and nodes and highlight the coherent behavior of connecting trajectories. Using simulations of ocean flow, we show that it can provide useful information on the flow structure. This paper focuses specifically on MCGs computed for piecewise constant (PC) vector fields. In particular, we describe extensions of the PC framework that make it more flexible and better suited for analysis of data on complex shaped domains with a boundary. We also describe a topology simplification scheme that makes our MCG visualizations less ambiguous. Despite the focus on the PC framework, our approach could also be applied to graph representations or topological skeletons computed using different methods.
Relativistic theory of vector mesons in laser fields
Energy Technology Data Exchange (ETDEWEB)
Becker, W; Mitter, H [Tuebingen Univ. (F.R. Germany). Inst. fuer Theoretische Physik
1975-01-01
The relativistic wave equation for a particle with spin 1 and an anomalous magnetic moment ..mu.. in an external wave field is reduced to a set of coupled ordinary differential equations for three amplitudes, which multiply the exponential known from the spin 0 case. These amplitudes are constant for ..mu..=1 (and not ..mu..=0). Exact solutions are given for a linear polarized laser wave of finite pulse shape and for an infinitely extended plane wave with circular polarization. In contrast to the situation in a constant magnetic field there are no internal inconsistencies.
The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics
Estabrook, F. B.; Wahlquist, H. D.
1975-01-01
The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.
The Evolution of Vector Magnetic Field Associated with Major Flares ...
Indian Academy of Sciences (India)
great enhancement in the non-potential field several hours before an .... conclusion is similar with that from daily evolution view – no sudden change happened. ... Jain, R., Hanaoka, Y., Sakurai, T. et al., Solar flares with remote brightening as ...
Nanoscale electric and magnetic optical vector fields: mapping & injection
le Feber, Boris
2015-01-01
Nanophotonic structures, which offer a sub-wavelength control over light and nearby emitters, promise to advance, for example, our ability to harvest light, process information and detect (bio-) chemical compounds. In general, the optical field distributions near nanophotonic structures are much
Identification of cardiac rhythm features by mathematical analysis of vector fields.
Fitzgerald, Tamara N; Brooks, Dana H; Triedman, John K
2005-01-01
Automated techniques for locating cardiac arrhythmia features are limited, and cardiologists generally rely on isochronal maps to infer patterns in the cardiac activation sequence during an ablation procedure. Velocity vector mapping has been proposed as an alternative method to study cardiac activation in both clinical and research environments. In addition to the visual cues that vector maps can provide, vector fields can be analyzed using mathematical operators such as the divergence and curl. In the current study, conduction features were extracted from velocity vector fields computed from cardiac mapping data. The divergence was used to locate ectopic foci and wavefront collisions, and the curl to identify central obstacles in reentrant circuits. Both operators were applied to simulated rhythms created from a two-dimensional cellular automaton model, to measured data from an in situ experimental canine model, and to complex three-dimensional human cardiac mapping data sets. Analysis of simulated vector fields indicated that the divergence is useful in identifying ectopic foci, with a relatively small number of vectors and with errors of up to 30 degrees in the angle measurements. The curl was useful for identifying central obstacles in reentrant circuits, and the number of velocity vectors needed increased as the rhythm became more complex. The divergence was able to accurately identify canine in situ pacing sites, areas of breakthrough activation, and wavefront collisions. In data from human arrhythmias, the divergence reliably estimated origins of electrical activity and wavefront collisions, but the curl was less reliable at locating central obstacles in reentrant circuits, possibly due to the retrospective nature of data collection. The results indicate that the curl and divergence operators applied to velocity vector maps have the potential to add valuable information in cardiac mapping and can be used to supplement human pattern recognition.
Chen, Rui-Pin; Chen, Zhaozhong; Chew, Khian-Hooi; Li, Pei-Gang; Yu, Zhongliang; Ding, Jianping; He, Sailing
2015-05-29
A caustic vector vortex optical field is experimentally generated and demonstrated by a caustic-based approach. The desired caustic with arbitrary acceleration trajectories, as well as the structured states of polarization (SoP) and vortex orders located in different positions in the field cross-section, is generated by imposing the corresponding spatial phase function in a vector vortex optical field. Our study reveals that different spin and orbital angular momentum flux distributions (including opposite directions) in different positions in the cross-section of a caustic vector vortex optical field can be dynamically managed during propagation by intentionally choosing the initial polarization and vortex topological charges, as a result of the modulation of the caustic phase. We find that the SoP in the field cross-section rotates during propagation due to the existence of the vortex. The unique structured feature of the caustic vector vortex optical field opens the possibility of multi-manipulation of optical angular momentum fluxes and SoP, leading to more complex manipulation of the optical field scenarios. Thus this approach further expands the functionality of an optical system.
Derivatives, forms and vector fields on the κ-deformed Euclidean space
International Nuclear Information System (INIS)
Dimitrijevic, Marija; Moeller, Lutz; Tsouchnika, Efrossini
2004-01-01
The model of κ-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper, we present new results concerning different sets of derivatives on the coordinate algebra of κ-deformed Euclidean space. We introduce a differential calculus with two interesting sets of one-forms and higher-order forms. The transformation law of vector fields is constructed in accordance with the transformation behaviour of derivatives. The crucial property of the different derivatives, forms and vector fields is that in an n-dimensional spacetime there are always n of them. This is the key difference with respect to conventional approaches, in which the differential calculus is (n + 1)-dimensional. This work shows that derivative-valued quantities such as derivative-valued vector fields appear in a generic way on noncommutative spaces
A Hamiltonian approach to model and analyse networks of ...
Indian Academy of Sciences (India)
2015-09-24
Sep 24, 2015 ... Gyroscopes; energy harvesters; synchronization; Hamiltonian mechanics. ... ideas and methods from nonlinear dynamics system theory, in particular, ... deploy highly sensitive, lowpower, magnetic and electric field sensors.
Vector tomography for reconstructing electric fields with non-zero divergence in bounded domains
Koulouri, Alexandra; Brookes, Mike; Rimpiläinen, Ville
2017-01-01
In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are called the longitudinal and transverse measurements, respectively. In most cases, however, the transverse measurements cannot be physically acquired. Therefore, the VT methods are typically used to reconstruct divergence-free (or source-free) velocity and flow fields that can be reconstructed solely from the longitudinal measurements. In this paper, we show how vector fields with non-zero divergence in a bounded domain can also be reconstructed from the longitudinal measurements without the need of explicitly evaluating the transverse measurements. To the best of our knowledge, VT has not previously been used for this purpose. In particular, we study low-frequency, time-harmonic electric fields generated by dipole sources in convex bounded domains which arise, for example, in electroencephalography (EEG) source imaging. We explain in detail the theoretical background, the derivation of the electric field inverse problem and the numerical approximation of the line integrals. We show that fields with non-zero divergence can be reconstructed from the longitudinal measurements with the help of two sparsity constraints that are constructed from the transverse measurements and the vector Laplace operator. As a comparison to EEG source imaging, we note that VT does not require mathematical modeling of the sources. By numerical simulations, we show that the pattern of the electric field can be correctly estimated using VT and the location of the source activity can be determined accurately from the reconstructed magnitudes of the field.
International Nuclear Information System (INIS)
Gelinas, R.C.
1984-01-01
A system for transmission of information using a curl-free magnetic vector potential radiation field. The system includes current-carrying apparatus for generating a magnetic vector potential field with a curl-free component coupled to apparatus for modulating the current applied to the field generating apparatus. Receiving apparatus includes a detector with observable properties that vary with the application of an applied curl-free magnetic vector potential field. Analyzing apparatus for determining the information content of modulation imposed on the curl-free vector potential field can be established in materials that are not capable of transmitting more common electromagnetic radiation
Vector-field statistics for the analysis of time varying clinical gait data.
Donnelly, C J; Alexander, C; Pataky, T C; Stannage, K; Reid, S; Robinson, M A
2017-01-01
In clinical settings, the time varying analysis of gait data relies heavily on the experience of the individual(s) assessing these biological signals. Though three dimensional kinematics are recognised as time varying waveforms (1D), exploratory statistical analysis of these data are commonly carried out with multiple discrete or 0D dependent variables. In the absence of an a priori 0D hypothesis, clinicians are at risk of making type I and II errors in their analyis of time varying gait signatures in the event statistics are used in concert with prefered subjective clinical assesment methods. The aim of this communication was to determine if vector field waveform statistics were capable of providing quantitative corroboration to practically significant differences in time varying gait signatures as determined by two clinically trained gait experts. The case study was a left hemiplegic Cerebral Palsy (GMFCS I) gait patient following a botulinum toxin (BoNT-A) injection to their left gastrocnemius muscle. When comparing subjective clinical gait assessments between two testers, they were in agreement with each other for 61% of the joint degrees of freedom and phases of motion analysed. For tester 1 and tester 2, they were in agreement with the vector-field analysis for 78% and 53% of the kinematic variables analysed. When the subjective analyses of tester 1 and tester 2 were pooled together and then compared to the vector-field analysis, they were in agreement for 83% of the time varying kinematic variables analysed. These outcomes demonstrate that in principle, vector-field statistics corroborates with what a team of clinical gait experts would classify as practically meaningful pre- versus post time varying kinematic differences. The potential for vector-field statistics to be used as a useful clinical tool for the objective analysis of time varying clinical gait data is established. Future research is recommended to assess the usefulness of vector-field analyses
Vector magnetic field observations with the Haleakala polarimeter
Mickey, D. L.
1985-01-01
Several enhancements were recently made to the Haleakala polarimeter. Linear array detectors provide simultaneous resolution over a 3-A wavelength range, with spectral resolution of 40 mA. Optical fibers are now used to carry the intensity-modulated light from the rotating quarter-wave plate polarimeter to the echelle spectrometer, permitting its removal from the spar to a more stable environment. These changes, together with improved quarter-wave plates, reduced systematic errors to a few parts in 10,000 for routine observations. Examples of Stokes profiles and derived magnetic field maps are presented.
Lefschetz thimbles in fermionic effective models with repulsive vector-field
Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira
2018-06-01
We discuss two problems in complexified auxiliary fields in fermionic effective models, the auxiliary sign problem associated with the repulsive vector-field and the choice of the cut for the scalar field appearing from the logarithmic function. In the fermionic effective models with attractive scalar and repulsive vector-type interaction, the auxiliary scalar and vector fields appear in the path integral after the bosonization of fermion bilinears. When we make the path integral well-defined by the Wick rotation of the vector field, the oscillating Boltzmann weight appears in the partition function. This "auxiliary" sign problem can be solved by using the Lefschetz-thimble path-integral method, where the integration path is constructed in the complex plane. Another serious obstacle in the numerical construction of Lefschetz thimbles is caused by singular points and cuts induced by multivalued functions of the complexified scalar field in the momentum integration. We propose a new prescription which fixes gradient flow trajectories on the same Riemann sheet in the flow evolution by performing the momentum integration in the complex domain.
International Nuclear Information System (INIS)
Kramar, M.; Lin, H.; Tomczyk, S.
2016-01-01
We present the first direct “observation” of the global-scale, 3D coronal magnetic fields of Carrington Rotation (CR) Cycle 2112 using vector tomographic inversion techniques. The vector tomographic inversion uses measurements of the Fe xiii 10747 Å Hanle effect polarization signals by the Coronal Multichannel Polarimeter (CoMP) and 3D coronal density and temperature derived from scalar tomographic inversion of Solar Terrestrial Relations Observatory (STEREO)/Extreme Ultraviolet Imager (EUVI) coronal emission lines (CELs) intensity images as inputs to derive a coronal magnetic field model that best reproduces the observed polarization signals. While independent verifications of the vector tomography results cannot be performed, we compared the tomography inverted coronal magnetic fields with those constructed by magnetohydrodynamic (MHD) simulations based on observed photospheric magnetic fields of CR 2112 and 2113. We found that the MHD model for CR 2112 is qualitatively consistent with the tomography inverted result for most of the reconstruction domain except for several regions. Particularly, for one of the most noticeable regions, we found that the MHD simulation for CR 2113 predicted a model that more closely resembles the vector tomography inverted magnetic fields. In another case, our tomographic reconstruction predicted an open magnetic field at a region where a coronal hole can be seen directly from a STEREO-B/EUVI image. We discuss the utilities and limitations of the tomographic inversion technique, and present ideas for future developments
An improved exact inversion formula for solenoidal fields in cone beam vector tomography
Katsevich, Alexander; Rothermel, Dimitri; Schuster, Thomas
2017-06-01
In this paper we present an improved inversion formula for the 3D cone beam transform of vector fields supported in the unit ball which is exact for solenoidal fields. It is well known that only the solenoidal part of a vector field can be determined from the longitudinal ray transform of a vector field in cone beam geometry. The inversion formula, as it was developed in Katsevich and Schuster (2013 An exact inversion formula for cone beam vector tomography Inverse Problems 29 065013), consists of two parts. The first part is of the filtered backprojection type, whereas the second part is a costly 4D integration and very inefficient. In this article we tackle this second term and obtain an improved formula, which is easy to implement and saves one order of integration. We also show that the first part contains all information about the curl of the field, whereas the second part has information about the boundary values. More precisely, the second part vanishes if the solenoidal part of the original field is tangential at the boundary. A number of numerical tests presented in the paper confirm the theoretical results and the exactness of the formula. Also, we obtain an inversion algorithm that works for general convex domains.
Energy Technology Data Exchange (ETDEWEB)
Kubo, R; Takahashi, Y; Yokoyama, K
1975-01-01
In a wide class of neutral vector field theories, in which massive and massless fields are described in a unified way and a unique massless limit exists to quantum electrodynamics in covariant gauges, the commutability of the scale transformation and the massless limit is examined. It is shown that there occurs no anomaly with respect to the assignment for scale dimensions of relevant fields. Connection of scale transformation and gauge transformation is also discussed.
Signed zeros of Gaussian vector fields - density, correlation functions and curvature
Foltin, G
2003-01-01
We calculate correlation functions of the (signed) density of zeros of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann Cartan or Riemannian manifold. As an application, we discuss one- and two-point functions. The zeros of a two-dimensional Gaussian vector field model the distribution of topological defects in the high-temperature phase of two-dimensional systems with orientational degrees of freedom, such as superfluid films, thin superconductors and liquid crystals.
Hamiltonian description of bubble dynamics
International Nuclear Information System (INIS)
Maksimov, A. O.
2008-01-01
The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.
High-quality and interactive animations of 3D time-varying vector fields.
Helgeland, Anders; Elboth, Thomas
2006-01-01
In this paper, we present an interactive texture-based method for visualizing three-dimensional unsteady vector fields. The visualization method uses a sparse and global representation of the flow, such that it does not suffer from the same perceptual issues as is the case for visualizing dense representations. The animation is made by injecting a collection of particles evenly distributed throughout the physical domain. These particles are then tracked along their path lines. At each time step, these particles are used as seed points to generate field lines using any vector field such as the velocity field or vorticity field. In this way, the animation shows the advection of particles while each frame in the animation shows the instantaneous vector field. In order to maintain a coherent particle density and to avoid clustering as time passes, we have developed a novel particle advection strategy which produces approximately evenly-spaced field lines at each time step. To improve rendering performance, we decouple the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. The final display is rendered using texture-based direct volume rendering.
International Nuclear Information System (INIS)
Triyanta; Zen, F. P.; Supardi; Wardaya, A. Y.
2010-01-01
Gauge theory, under the framework of quantum field theory, has successfully described three fundamental interactions: electromagnetic, weak, and strong interactions. Problems of describing the gravitational interaction in a similar manner has not been satisfied yet until now. Teleparallel gravity (TG) is one proposal describing gravitational field as a gauge field. This theory is quite new and it is equivalent to Einstein's general relativity. But as gravitational field in TG is expressed by torsion, rather than curvature, it gives an alternative framework for solving problems on gravity. This paper will present solution of the dynamical equation of abelian vector fields under the framework of TG in the Bianchi type I spacetime.
Anomalous scaling of a passive vector advected by the Navier-Stokes velocity field
International Nuclear Information System (INIS)
Jurcisinova, E; Jurcisin, M; Remecky, R
2009-01-01
Using the field theoretic renormalization group and the operator-product expansion, the model of a passive vector field (a weak magnetic field in the framework of the kinematic MHD) advected by the velocity field which is governed by the stochastic Navier-Stokes equation with the Gaussian random stirring force δ-correlated in time and with the correlator proportional to k 4-d-2ε is investigated to the first order in ε (one-loop approximation). It is shown that the single-time correlation functions of the advected vector field have anomalous scaling behavior and the corresponding exponents are calculated in the isotropic case, as well as in the case with the presence of large-scale anisotropy. The hierarchy of the anisotropic critical dimensions is briefly discussed and the persistence of the anisotropy inside the inertial range is demonstrated on the behavior of the skewness and hyperskewness (dimensionless ratios of correlation functions) as functions of the Reynolds number Re. It is shown that even though the present model of a passive vector field advected by the realistic velocity field is mathematically more complicated than, on one hand, the corresponding models of a passive vector field advected by 'synthetic' Gaussian velocity fields and, on the other hand, than the corresponding model of a passive scalar quantity advected by the velocity field driven by the stochastic Navier-Stokes equation, the final one-loop approximate asymptotic scaling behavior of the single-time correlation or structure functions of the advected fields of all models are defined by the same anomalous dimensions (up to normalization)
Ouyang, J; Perrie, W; Allegre, O J; Heil, T; Jin, Y; Fearon, E; Eckford, D; Edwardson, S P; Dearden, G
2015-05-18
Precise tailoring of optical vector beams is demonstrated, shaping their focal electric fields and used to create complex laser micro-patterning on a metal surface. A Spatial Light Modulator (SLM) and a micro-structured S-waveplate were integrated with a picosecond laser system and employed to structure the vector fields into radial and azimuthal polarizations with and without a vortex phase wavefront as well as superposition states. Imprinting Laser Induced Periodic Surface Structures (LIPSS) elucidates the detailed vector fields around the focal region. In addition to clear azimuthal and radial plasmon surface structures, unique, variable logarithmic spiral micro-structures with a pitch Λ ∼1μm, not observed previously, were imprinted on the surface, confirming unambiguously the complex 2D focal electric fields. We show clearly also how the Orbital Angular Momentum(OAM) associated with a helical wavefront induces rotation of vector fields along the optic axis of a focusing lens and confirmed by the observed surface micro-structures.
Evolution of vector magnetic fields and the August 27 1990 X-3 flare
Wang, Haimin
1992-01-01
Vector magnetic fields in an active region of the sun are studied by means of continuous observations of magnetic-field evolution emphasizing magnetic shear build-up. The vector magnetograms are shown to measure magnetic fields correctly based on concurrent observations and a comparison of the transverse field with the H alpha fibril structure. The morphology and velocity pattern are examined, and these data and the shear build-up suggest that the active region's two major footprints are separated by a region with flows, new flux emergence, and several neutral lines. The magnetic shear appears to be caused by the collision and shear motion of two poles of opposite polarities. The transverse field is shown to turn from potential to sheared during the process of flux cancellation, and this effect can be incorporated into existing models of magnetic flux cancellation.
Achievement of needle-like focus by engineering radial-variant vector fields.
Gu, Bing; Wu, Jia-Lu; Pan, Yang; Cui, Yiping
2013-12-16
We present and demonstrate a novel method for engineering the radial-variant polarization on the incident field to achieve a needle of transversally polarized field without any pupil filters. We generate a new kind of localized linearly-polarized vector fields with distributions of states of polarization (SoPs) describing by the radius to the power p and explore its tight focusing, nonparaxial focusing, and paraxial focusing properties. By tuning the power p, we obtain the needle-like focal field with hybrid SoPs and give the formula for describing the length of the needle. Experimentally, we systematically investigate both the intensity distributions and the polarization evolution of the optical needle by paraxial focusing the generated vector field. Such an optical needle, which enhances the light-matter interaction, has intriguing applications in optical microma-chining and nonlinear optics.
Effect of a spiral phase on a vector optical field with hybrid polarization states
International Nuclear Information System (INIS)
Chen, Rui-Pin; Zhao, Tingyu; Zhong, Li-Xin; Chew, Khian-Hooi; Gu, Bing; Zhou, Guoquan
2015-01-01
The propagation dynamics of a vector field with inhomogeneous states of polarization (SoP) imposed a vortex is studied using the angular spectrum method. The evolution of SoP in the cross section of the field during propagation is analyzed numerically by the Stokes polarization parameters. The results indicate that SoP in the field cross section rotate along the propagation axis during propagation due to the existence of a vortex. In addition, the interaction between the phase singularity and the polarization singularity leads to the creation or annihilation of the optical field in the central region. In particular, the distributions of the transverse energy flow and both spin and orbital optical angular momentum fluxes in the cross section of the vortex vector optical field depend sensitively on both the vortex and polarization topology charges. (paper)
On the Lamb vector divergence as a momentum field diagnostic employed in turbulent channel flow
Hamman, Curtis W.; Kirby, Robert M.; Klewicki, Joseph C.
2006-11-01
Vorticity, enstrophy, helicity, and other derived field variables provide invaluable information about the kinematics and dynamics of fluids. However, whether or not derived field variables exist that intrinsically identify spatially localized motions having a distinct capacity to affect a time rate of change of linear momentum is seldom addressed in the literature. The purpose of the present study is to illustrate the unique attributes of the divergence of the Lamb vector in order to qualify its potential for characterizing such spatially localized motions. Toward this aim, we describe the mathematical properties, near-wall behavior, and scaling characteristics of the divergence of the Lamb vector for turbulent channel flow. When scaled by inner variables, the mean divergence of the Lamb vector merges to a single curve in the inner layer, and the fluctuating quantities exhibit a strong correlation with the Bernoulli function throughout much of the inner layer.
Migration transformation of two-dimensional magnetic vector and tensor fields
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2012-01-01
We introduce a new method of rapid interpretation of magnetic vector and tensor field data, based on ideas of potential field migration which extends the general principles of seismic and electromagnetic migration to potential fields. 2-D potential field migration represents a direct integral...... to the downward continuation of a well-behaved analytical function. We present case studies for imaging of SQUID-based magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from magnetic tensor field migration agree very well with both Euler deconvolution and the known...
Quantum Hamiltonian reduction in superspace formalism
International Nuclear Information System (INIS)
Madsen, J.O.; Ragoucy, E.
1994-02-01
Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs
Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature
International Nuclear Information System (INIS)
Himmetoglu, Burak; Peloso, Marco; Contaldi, Carlo R.
2009-01-01
We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill defined at the quantum level in the high energy/subhorizon regime (and create serious problems for finding a well-behaved UV completion), and (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without a vacuum expectation value in a Friedmann-Robertson-Walker geometry, and of a vector with a vacuum expectation value plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.
Tadesse, T.; Wiegelmann, T.; Gosain, S.; MacNeice, P.; Pevtsov, A. A.
2014-01-01
Context. The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently, there are several modelling techniques being used to calculate three-dimensional field lines into the solar atmosphere. Aims. For the first time, synoptic maps of a photospheric-vector magnetic field synthesized from the vector spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. Methods. We solve the nonlinear force-free field equations using an optimization principle in spherical geometry. The resulting threedimensional magnetic fields are used to estimate the magnetic free energy content E(sub free) = E(sub nlfff) - E(sub pot), which is the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the atmospheric imaging assembly (AIA) on board the Solar Dynamics Observatory (SDO). Results. For a single Carrington rotation 2121, we find that the global nonlinear force-free field (NLFFF) magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions.
Vector tomography for reconstructing electric fields with non-zero divergence in bounded domains
Energy Technology Data Exchange (ETDEWEB)
Koulouri, Alexandra, E-mail: koulouri@uni-muenster.de [Institute for Computational and Applied Mathematics, University of Münster, Einsteinstrasse 62, D-48149 Münster (Germany); Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, London SW7 2BT (United Kingdom); Brookes, Mike [Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, London SW7 2BT (United Kingdom); Rimpiläinen, Ville [Institute for Biomagnetism and Biosignalanalysis, University of Münster, Malmedyweg 15, D-48149 Münster (Germany); Department of Mathematics, University of Auckland, Private bag 92019, Auckland 1142 (New Zealand)
2017-01-15
In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are called the longitudinal and transverse measurements, respectively. In most cases, however, the transverse measurements cannot be physically acquired. Therefore, the VT methods are typically used to reconstruct divergence-free (or source-free) velocity and flow fields that can be reconstructed solely from the longitudinal measurements. In this paper, we show how vector fields with non-zero divergence in a bounded domain can also be reconstructed from the longitudinal measurements without the need of explicitly evaluating the transverse measurements. To the best of our knowledge, VT has not previously been used for this purpose. In particular, we study low-frequency, time-harmonic electric fields generated by dipole sources in convex bounded domains which arise, for example, in electroencephalography (EEG) source imaging. We explain in detail the theoretical background, the derivation of the electric field inverse problem and the numerical approximation of the line integrals. We show that fields with non-zero divergence can be reconstructed from the longitudinal measurements with the help of two sparsity constraints that are constructed from the transverse measurements and the vector Laplace operator. As a comparison to EEG source imaging, we note that VT does not require mathematical modeling of the sources. By numerical simulations, we show that the pattern of the electric field can be correctly estimated using VT and the location of the source activity can be determined accurately from the reconstructed magnitudes of the field. - Highlights: • Vector tomography is used to reconstruct electric fields generated by dipole
Involutive distributions of operator-valued evolutionary vector fields and their affine geometry
Kiselev, A.V.; van de Leur, J.W.
2010-01-01
We generalize the notion of a Lie algebroid over infinite jet bundle by replacing the variational anchor with an N-tuple of differential operators whose images in the Lie algebra of evolutionary vector fields of the jet space are subject to collective commutation closure. The linear space of such
Gravitational lensing due to dark matter modelled by a vector field
International Nuclear Information System (INIS)
Kiselev, V V; Yudin, D I
2006-01-01
The specified constant 4-vector field reproducing the spherically symmetric stationary metric of a cold dark matter halo in the region of flat rotation curves results in a constant angle of light deflection at small impact distances. The effective deflecting mass is a factor π/2 greater than the dark matter mass. The perturbation of deflection picture due to the halo edge is evaluated
International Nuclear Information System (INIS)
Wang Shikun; Xu Kaiwen.
1989-12-01
The superconformal algebras of meromorphic vector fields with multipoles, the central extension and the relevant abelian differential of the third kind on super Riemann sphere were constructed. The background of our theory is concerned with the interaction of closed superstrings. (author). 9 refs
Superconformal algebra on meromorphic vector fields with three poles on super-Riemann sphere
International Nuclear Information System (INIS)
Wang Shikun; Xu Kaiwen.
1989-07-01
Based upon the Riemann-Roch theorem, we construct superconformal algebra of meromorphic vector fields with three poles and the relevant abelian differential of the third kind on super Riemann sphere. The algebra includes two Ramond sectors as subalgebra, and implies a picture of interaction of three superstrings. (author). 14 refs
Flavor-singlet axial-vector current in quark model within background field
International Nuclear Information System (INIS)
Chen Kun; Yan Mulin
1993-01-01
The flavor-singlet axial-vector current is calculated in a quark model within pseudoscalar background-field through the Seeley-DeWitt coefficients. This current is responsible for the quark spin content of proton and is of O(1) in the large-N e expansion
Normal forms of invariant vector fields under a finite group action
International Nuclear Information System (INIS)
Sanchez Bringas, F.
1992-07-01
Let Γ be a finite subgroup of GL(n,C). This subgroup acts on the space of germs of holomorphic vector fields vanishing at the origin in C n . We prove a theorem of invariant conjugation to a normal form and linearization for the subspace of invariant elements and we give a description of these normal forms in dimension n=2. (author)
Codimension-one tangency bifurcations of global Poincare maps of four-dimensional vector fields
Krauskopf, B.; Lee, C.M.; Osinga, H.M.
2009-01-01
When one considers a Poincarreturn map on a general unbounded (n - 1)-dimensional section for a vector field in R-n there are typically points where the flow is tangent to the section. The only notable exception is when the system is (equivalent to) a periodically forced system. The tangencies can
Cryogenic STM in 3D vector magnetic fields realized through a rotatable insert.
Trainer, C; Yim, C M; McLaren, M; Wahl, P
2017-09-01
Spin-polarized scanning tunneling microscopy (SP-STM) performed in vector magnetic fields promises atomic scale imaging of magnetic structure, providing complete information on the local spin texture of a sample in three dimensions. Here, we have designed and constructed a turntable system for a low temperature STM which in combination with a 2D vector magnet provides magnetic fields of up to 5 T in any direction relative to the tip-sample geometry. This enables STM imaging and spectroscopy to be performed at the same atomic-scale location and field-of-view on the sample, and most importantly, without experiencing any change on the tip apex before and after field switching. Combined with a ferromagnetic tip, this enables us to study the magnetization of complex magnetic orders in all three spatial directions.
In-Flight spacecraft magnetic field monitoring using scalar/vector gradiometry
DEFF Research Database (Denmark)
Primdahl, Fritz; Risbo, Torben; Merayo, José M.G.
2006-01-01
Earth magnetic field mapping from planetary orbiting satellites requires a spacecraft magnetic field environment control program combined with the deployment of the magnetic sensors on a boom in order to reduce the measurement error caused by the local spacecraft field. Magnetic mapping missions...... (Magsat, Oersted, CHAMP, SAC-C MMP and the planned ESA Swarm project) carry a vector magnetometer and an absolute scalar magnetometer for in-flight calibration of the vector magnetometer scale values and for monitoring of the inter-axes angles and offsets over time intervals from months to years...... sensors onboard the Oersted satellite. For Oersted, a large difference between the pre-flight determined spacecraft magnetic field and the in-flight estimate exists causing some concern about the general applicability of the dual sensors technique....
International Nuclear Information System (INIS)
Vasconcelos Dos Santos, R.J.; Coutinho, S.
1995-01-01
The effect of a local field acting on decorating classical D-vector bond spins of an antiferromagnetic Ising model on the square lattice is studied for both the annealed isotropic and the axial decorated cases. In both models the effect on the phase diagrams of the transversal and the longitudinal components of the local field acting on the decorating spins are fully analyzed and discussed
International Nuclear Information System (INIS)
Gnutek, P; Rudowicz, C; Yang, Z Y
2009-01-01
The local structure and the spin Hamiltonian (SH) parameters, including the zero-field-splitting (ZFS) parameters D and (a+2F/3), and the Zeeman g factors g || and g perpendicular , are theoretically investigated for the Fe K 3+ -O I 2- center in KTaO 3 crystal. The microscopic SH (MSH) parameters are modeled within the framework of the crystal field (CF) theory employing the CF analysis (CFA) package, which also incorporates the MSH modules. Our approach takes into account the spin-orbit interaction as well as the spin-spin and spin-other-orbit interactions omitted in previous studies. The superposition model (SPM) calculations are carried out to provide input CF parameters for the CFA/MSH package. The combined SPM-CFA/MSH approach is used to consider various structural models for the Fe K 3+ -O I 2- defect center in KTaO 3 . This modeling reveals that the off-center displacement of the Fe 3+ ions, Δ 1 (Fe 3+ ), combined with an inward relaxation of the nearest oxygen ligands, Δ 2 (O 2- ), and the existence of the interstitial oxygen O I 2- give rise to a strong tetragonal crystal field. This finding may explain the large ZFS experimentally observed for the Fe K 3+ -O I 2- center in KTaO 3 . Matching the theoretical MSH predictions with the available structural data as well as electron magnetic resonance (EMR) and optical spectroscopy data enables predicting reasonable ranges of values of Δ 1 (Fe 3+ ) and Δ 2 (O 2- ) as well as the possible location of O I 2- ligands around Fe 3+ ions in KTaO 3 . The defect structure model obtained using the SPM-CFA/MSH approach reproduces very well the ranges of the experimental SH parameters D, g || and g perpendicular and importantly yields not only the correct magnitude of D but also the sign, unlike previous studies. More reliable predictions may be achieved when experimental data on (a+2F/3) and/or crystal field energy levels become available. Comparison of our results with those arising from alternative models existing
Energy Technology Data Exchange (ETDEWEB)
Bhatia, Harsh [Univ. of Utah, Salt Lake City, UT (United States)
2015-05-01
This dissertation presents research on addressing some of the contemporary challenges in the analysis of vector fields—an important type of scientific data useful for representing a multitude of physical phenomena, such as wind flow and ocean currents. In particular, new theories and computational frameworks to enable consistent feature extraction from vector fields are presented. One of the most fundamental challenges in the analysis of vector fields is that their features are defined with respect to reference frames. Unfortunately, there is no single “correct” reference frame for analysis, and an unsuitable frame may cause features of interest to remain undetected, thus creating serious physical consequences. This work develops new reference frames that enable extraction of localized features that other techniques and frames fail to detect. As a result, these reference frames objectify the notion of “correctness” of features for certain goals by revealing the phenomena of importance from the underlying data. An important consequence of using these local frames is that the analysis of unsteady (time-varying) vector fields can be reduced to the analysis of sequences of steady (timeindependent) vector fields, which can be performed using simpler and scalable techniques that allow better data management by accessing the data on a per-time-step basis. Nevertheless, the state-of-the-art analysis of steady vector fields is not robust, as most techniques are numerical in nature. The residing numerical errors can violate consistency with the underlying theory by breaching important fundamental laws, which may lead to serious physical consequences. This dissertation considers consistency as the most fundamental characteristic of computational analysis that must always be preserved, and presents a new discrete theory that uses combinatorial representations and algorithms to provide consistency guarantees during vector field analysis along with the uncertainty
Stokes profile analysis and vector magnetic fields. I. Inversion of photospheric lines
International Nuclear Information System (INIS)
Skumanich, A.; Lites, B.W.
1987-01-01
Improvements are proposed for the Auer et al. (1977) method for the analytic inversion of Stokes profiles via nonlinear least squares. The introduction of additional physics into the Mueller absorption matrix (by including damping wings and magnetooptical birefringence, and by decoupling the intensity profile from the three-vector polarization profile in the analysis) is found to result in a more robust inversion method, providing more reliable and accurate estimates of sunspot vector magnetic fields without significant loss of economy. The method is applied to sunspot observations obtained with the High Altitude Observatory polarimeter. 29 references
Theory of collective Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Zhang Qingying
1982-02-01
Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.
Ding, Zi'ang
2016-01-01
Both vector and tensor fields are important mathematical tools used to describe the physics of many phenomena in science and engineering. Effective vector and tensor field visualization techniques are therefore needed to interpret and analyze the corresponding data and achieve new insight into the considered problem. This dissertation is concerned with the extraction of important structural properties from vector and tensor datasets. Specifically, we present a unified approach for the charact...
Balasubramaniam, K. S.; West, E. A.
1991-01-01
The Marshall Space Flight Center (MSFC) vector magnetograph is a tunable filter magnetograph with a bandpass of 125 mA. Results are presented of the inversion of Stokes polarization profiles observed with the MSFC vector magnetograph centered on a sunspot to recover the vector magnetic field parameters and thermodynamic parameters of the spectral line forming region using the Fe I 5250.2 A spectral line using a nonlinear least-squares fitting technique. As a preliminary investigation, it is also shown that the recovered thermodynamic parameters could be better understood if the fitted parameters like Doppler width, opacity ratio, and damping constant were broken down into more basic quantities like temperature, microturbulent velocity, or density parameter.
Geometric Representations of Condition Queries on Three-Dimensional Vector Fields
Henze, Chris
1999-01-01
Condition queries on distributed data ask where particular conditions are satisfied. It is possible to represent condition queries as geometric objects by plotting field data in various spaces derived from the data, and by selecting loci within these derived spaces which signify the desired conditions. Rather simple geometric partitions of derived spaces can represent complex condition queries because much complexity can be encapsulated in the derived space mapping itself A geometric view of condition queries provides a useful conceptual unification, allowing one to intuitively understand many existing vector field feature detection algorithms -- and to design new ones -- as variations on a common theme. A geometric representation of condition queries also provides a simple and coherent basis for computer implementation, reducing a wide variety of existing and potential vector field feature detection techniques to a few simple geometric operations.
Ronan, R. S.; Mickey, D. L.; Orrall, F. Q.
1987-01-01
The results of two methods for deriving photospheric vector magnetic fields from the Zeeman effect, as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA), are compared. The first method does not take magnetooptical effects into account, but determines the vector magnetic field from the integral properties of the Stokes profiles. The second method is an iterative least-squares fitting technique which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. For sunspot fields above about 1500 gauss, the two methods are found to agree in derived azimuthal and inclination angles to within about + or - 20 deg.
Lee, Wen-Li; Chang, Koyin; Hsieh, Kai-Sheng
2016-09-01
Segmenting lung fields in a chest radiograph is essential for automatically analyzing an image. We present an unsupervised method based on multiresolution fractal feature vector. The feature vector characterizes the lung field region effectively. A fuzzy c-means clustering algorithm is then applied to obtain a satisfactory initial contour. The final contour is obtained by deformable models. The results show the feasibility and high performance of the proposed method. Furthermore, based on the segmentation of lung fields, the cardiothoracic ratio (CTR) can be measured. The CTR is a simple index for evaluating cardiac hypertrophy. After identifying a suspicious symptom based on the estimated CTR, a physician can suggest that the patient undergoes additional extensive tests before a treatment plan is finalized.
Hamiltonians and variational principles for Alfvén simple waves
International Nuclear Information System (INIS)
Webb, G M; Hu, Q; Roux, J A le; Dasgupta, B; Zank, G P
2012-01-01
The evolution equations for the magnetic field induction B with the wave phase for Alfvén simple waves are expressed as variational principles and in the Hamiltonian form. The evolution of B with the phase (which is a function of the space and time variables) depends on the generalized Frenet–Serret equations, in which the wave normal n (which is a function of the phase) is taken to be tangent to a curve X, in a 3D Cartesian geometry vector space. The physical variables (the gas density, fluid velocity, gas pressure and magnetic field induction) in the wave depend only on the phase. Three approaches are developed. One approach exploits the fact that the Frenet equations may be written as a 3D Hamiltonian system, which can be described using the Nambu bracket. It is shown that B as a function of the phase satisfies a modified version of the Frenet equations, and hence the magnetic field evolution equations can be expressed in the Hamiltonian form. A second approach develops an Euler–Poincaré variational formulation. A third approach uses the Frenet frame formulation, in which the hodograph of B moves on a sphere of constant radius and uses a stereographic projection transformation due to Darboux. The equations for the projected field components reduce to a complex Riccati equation. By using a Cole–Hopf transformation, the Riccati equation reduces to a linear second order differential equation for the new variable. A Hamiltonian formulation of the second order differential equation then allows the system to be written in the Hamiltonian form. Alignment dynamics equations for Alfvén simple waves give rise to a complex Riccati equation or, equivalently, to a quaternionic Riccati equation, which can be mapped onto the Riccati equation obtained by stereographic projection. (paper)
Bommier, V.
1986-01-01
The Hanle effect is the modification of the linear polarization parameters of a spectral line due to the effect of the magnetic field. It has been successfully applied to the magnetic field vector diagnostic in solar prominences. The magnetic field vector is determined by comparing the measured polarization to the polarization computed, taking into account all the polarizing and depolarizing processes in line formation and the depolarizing effect of the magnetic field. The method was applied to simultaneous polarization measurements in the Helium D3 line and in the hydrogen beta line in 14 prominences. Four polarization parameters are measured, which lead to the determination of the three coordinates of the magnetic field vector and the electron density, owing to the sensitivity of the hydrogen beta line to the non-negligible effect of depolarizing collisions with electrons and protons of the medium. A mean value of 1.3 x 10 to the 10th power cu. cm. is derived in 14 prominences.
Hamiltonian formulation of reduced magnetohydrodynamics
International Nuclear Information System (INIS)
Morrison, P.J.; Hazeltine, R.D.
1983-07-01
Reduced magnetohydrodynamics (RMHD) has become a principal tool for understanding nonlinear processes, including disruptions, in tokamak plasmas. Although analytical studies of RMHD turbulence have been useful, the model's impressive ability to simulate tokamak fluid behavior has been revealed primarily by numerical solution. The present work describes a new analytical approach, not restricted to turbulent regimes, based on Hamiltonian field theory. It is shown that the nonlinear (ideal) RMHD system, in both its high-beta and low-beta versions, can be expressed in Hanmiltonian form. Thus a Poisson bracket, [ , ], is constructed such that each RMHD field quantitity, xi/sub i/, evolves according to xi/sub i/ = [xi/sub i/,H], where H is the total field energy. The new formulation makes RMHD accessible to the methodology of Hamiltonian mechanics; it has lead, in particular, to the recognition of new RMHD invariants and even exact, nonlinear RMHD solutions. A canonical version of the Poisson bracket, which requires the introduction of additional fields, leads to a nonlinear variational principle for time-dependent RMHD
International Nuclear Information System (INIS)
Cairo, Laurent; Llibre, Jaume
2007-01-01
We classify all the global phase portraits of the cubic polynomial vector fields of Lotka-Volterra type having a rational first integral of degree 2. For such vector fields there are exactly 28 different global phase portraits in the Poincare disc up to a reversal of sense of all orbits
Near-field/far-field array manifold of an acoustic vector-sensor near a reflecting boundary.
Wu, Yue Ivan; Lau, Siu-Kit; Wong, Kainam Thomas
2016-06-01
The acoustic vector-sensor (a.k.a. the vector hydrophone) is a practical and versatile sound-measurement device, with applications in-room, open-air, or underwater. It consists of three identical uni-axial velocity-sensors in orthogonal orientations, plus a pressure-sensor-all in spatial collocation. Its far-field array manifold [Nehorai and Paldi (1994). IEEE Trans. Signal Process. 42, 2481-2491; Hawkes and Nehorai (2000). IEEE Trans. Signal Process. 48, 2981-2993] has been introduced into the technical field of signal processing about 2 decades ago, and many direction-finding algorithms have since been developed for this acoustic vector-sensor. The above array manifold is subsequently generalized for outside the far field in Wu, Wong, and Lau [(2010). IEEE Trans. Signal Process. 58, 3946-3951], but only if no reflection-boundary is to lie near the acoustic vector-sensor. As for the near-boundary array manifold for the general case of an emitter in the geometric near field, the far field, or anywhere in between-this paper derives and presents that array manifold in terms of signal-processing mathematics. Also derived here is the corresponding Cramér-Rao bound for azimuth-elevation-distance localization of an incident emitter, with the reflected wave shown to play a critical role on account of its constructive or destructive summation with the line-of-sight wave. The implications on source localization are explored, especially with respect to measurement model mismatch in maximum-likelihood direction finding and with regard to the spatial resolution between coexisting emitters.
Introduction to thermodynamics of spin models in the Hamiltonian limit
Energy Technology Data Exchange (ETDEWEB)
Berche, Bertrand [Groupe M, Laboratoire de Physique des Materiaux, UMR CNRS No 7556, Universite Henri Poincare, Nancy 1, BP 239, F-54506 Vandoeuvre les Nancy, (France); Lopez, Alexander [Instituto Venezolano de Investigaciones CientIficas, Centro de Fisica, Carr. Panamericana, km 11, Altos de Pipe, Aptdo 21827, 1020-A Caracas, (Venezuela)
2006-01-01
A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices. The targeted students are those of a graduate statistical physics course.
Infrared Dual-Line Hanle Diagnostic of the Coronal Vector Magnetic Field
Energy Technology Data Exchange (ETDEWEB)
Dima, Gabriel I.; Kuhn, Jeffrey R. [Institute for Astronomy, University of Hawaii, Pukalani, HI (United States); Berdyugina, Svetlana V., E-mail: gdima@hawaii.edu [Institute for Astronomy, University of Hawaii, Pukalani, HI (United States); Kiepenheuer Institut fuer Sonnenphysik, Freiburg (Germany); Predictive Science Inc., San Diego, CA (United States)
2016-04-20
Measuring the coronal vector magnetic field is still a major challenge in solar physics. This is due to the intrinsic weakness of the field (e.g., ~4G at a height of 0.1R⊙ above an active region) and the large thermal broadening of coronal emission lines. We propose using concurrent linear polarization measurements of near-infrared forbidden and permitted lines together with Hanle effect models to calculate the coronal vector magnetic field. In the unsaturated Hanle regime both the direction and strength of the magnetic field affect the linear polarization, while in the saturated regime the polarization is insensitive to the strength of the field. The relatively long radiative lifetimes of coronal forbidden atomic transitions implies that the emission lines are formed in the saturated Hanle regime and the linear polarization is insensitive to the strength of the field. By combining measurements of both forbidden and permitted lines, the direction and strength of the field can be obtained. For example, the SiX 1.4301 μm line shows strong linear polarization and has been observed in emission over a large field-of-view (out to elongations of 0.5 R⊙). Here we describe an algorithm that combines linear polarization measurements of the SiX 1.4301 μm forbidden line with linear polarization observations of the HeI 1.0830 μm permitted coronal line to obtain the vector magnetic field. To illustrate the concept we assume that the emitting gas for both atomic transitions is located in the plane of the sky. The further development of this method and associated tools will be a critical step toward interpreting the high spectral, spatial and temporal infrared spectro-polarimetric measurements that will be possible when the Daniel K. Inouye Solar Telescope (DKIST) is completed in 2019.
International Nuclear Information System (INIS)
Shabbir, Ghulam; Khan, Suhail
2010-01-01
In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times. (general)
Rotations with Rodrigues' vector
International Nuclear Information System (INIS)
Pina, E
2011-01-01
The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears to be a fundamental matrix that is used to express the components of the angular velocity, the rotation matrix and the angular momentum vector. The Hamiltonian formalism of rotational dynamics in terms of this vector uses the same matrix. The quantization of the rotational dynamics is performed with simple rules if one uses Rodrigues' vector and similar formal expressions for the quantum operators that mimic the Hamiltonian classical dynamics.
Strong-field non-sequential ionization: The vector momentum distribution of multiply charged Ne ions
International Nuclear Information System (INIS)
Rottke, H.; Trump, C.; Wittmann, M.; Korn, G.; Becker, W.; Hoffmann, K.; Sandner, W.; Moshammer, R.; Feuerstein, B.; Dorn, A.; Schroeter, C.D.; Ullrich, J.; Schmitt, W.
2000-01-01
COLTRIMS (COLd Target Recoil-Ion Momentum Spectroscopy) was used to measure the vector momentum distribution of Ne n+ (n=1,2,3) ions formed in ultrashort (30 fsec) high-intensity (≅10 15 W/cm 2 ) laser pulses with center wavelength at 795 nm. To a high degree of accuracy the length of the Ne n+ ion momentum vector is equal to the length of the total momentum vector of the n photoelectrons released, with both vectors pointing into opposite directions. At a light intensity where non-sequential ionization of the atom dominates the Ne 2+ and Ne 3+ momentum distributions show distinct maxima at 4.0 a.u. and 7.5 a.u. along the polarization axis of the linearly polarized light beam. First, this is a clear signature of non-sequential multiple ionization. Second, it indicates that instantaneous emission of two (or more) electrons at electric field strength maxima of the light wave can be ruled out as main mechanism of non-sequential strong-field multiple ionization. In contrast, this experimental result is in accordance with the kinematical constraints of the 'rescattering model'
Bray, D P; Bandi, K K; Brazil, R P; Oliveira, A G; Hamilton, J G C
2009-05-01
Improving vector control remains a key goal in reducing the world's burden of infectious diseases. More cost-effective approaches to vector control are urgently needed, particularly because vaccines are unavailable and treatment is prohibitively expensive. The causative agent of American visceral leishmaniasis (AVL), Leishmania chagasi, Cunha and Chagas (Kinetoplastida: Trypanosomatidae), is transmitted between animal and human hosts by blood-feeding female sand flies attracted to mating aggregations formed on or above host animals by male-produced sex pheromones. Our results show the potential of using synthetic pheromones to control populations of Lutzomyia longipalpis Lutz and Neiva (Diptera: Psychodidae), the sand fly vector of one of the world's most important neglected diseases, AVL. We showed that a synthetic pheromone, (+/-)-9-methylgermacrene-B, produced from a low-cost plant intermediate, attracted females in the laboratory. By formulating dispensers that released this pheromone at a rate similar to that released by aggregating males, we were able to attract flies of both sexes to traps in the field. These dispensers worked equally well when deployed with mechanical light traps and inexpensive sticky traps. If deployed effectively, pheromone-based traps could be used to decrease AVL transmission rates through specific targeting and reduction of L. longipalpis populations. This is the first study to show attraction of a human disease-transmitting insect to a synthetic pheromone in the field, showing the general applicability of this novel approach for developing new tools for use in vector control.
Bray, D. P.; Bandi, K. K.; Brazil, R. P.; Oliveira, A. G.; Hamilton, J.G.C.
2011-01-01
Improving vector control remains a key goal in reducing the world’s burden of infectious diseases. More cost-effective approaches to vector control are urgently needed, particularly as vaccines are unavailable and treatment is prohibitively expensive. The causative agent of AVL, Leishmania chagasi, Cunha and Chagas (Kinetoplastida: Trypanosomatidae) is transmitted between animal and human hosts by blood-feeding female sand flies, attracted to mating aggregations formed on or above host animals by male-produced sex pheromones. Our results demonstrate the potential of using synthetic pheromones to control populations of Lutzomyia longipalpis Lutz and Neiva (Diptera: Psychodidae), the sand fly vector of one of the world’s most important neglected diseases, American visceral leishmaniasis (AVL). We showed that a synthetic pheromone, (±)-9-methylgermacrene-B, produced from a low-cost plant intermediate, attracted females in the laboratory. Then by formulating dispensers that released this pheromone at a rate similar to that released by aggregating males, we were able to attract flies of both sexes to traps in the field. These dispensers worked equally well when deployed with mechanical light traps and inexpensive sticky traps. If deployed effectively, pheromone-based traps could be used to decrease AVL transmission rates through specific targeting and reduction of L. longipalpis populations. This is the first study to show attraction of a human disease-transmitting insect to a synthetic pheromone in the field, demonstrating the general applicability of this novel approach for developing new tools for use in vector control. PMID:19496409
Boundary conditions and dualities: vector fields in AdS/CFT
International Nuclear Information System (INIS)
Marolf, Donald; Ross, Simo F.
2006-01-01
In AdS, scalar fields with masses slightly above the Breitenlohner-Freedman bound admit a variety of possible boundary conditions which are reflected in the Lagrangian of the dual field theory. Generic small changes in the AdS boundary conditions correspond to deformations of the dual field theory by multi-trace operators. Here we extend this discussion to the case of vector gauge fields in the bulk spacetime using the results of Ishibashi and Wald [hep-th/0402184]. As in the context of scalar fields, general boundary conditions for vector fields involve multi-trace deformations which lead to renormalization-group flows. Such flows originate in ultra-violet CFTs which give new gauge/gravity dualities. At least for AdS 4 /CFT 3 , the dual of the bulk photon appears to be a propagating gauge field instead of the usual R-charge current. Applying similar reasoning to tensor fields suggests the existence of a duality between string theory on AdS 4 and a quantum gravity theory in three dimensions
Optimization of Transverse Oscillating Fields for Vector Velocity Estimation with Convex Arrays
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt
2013-01-01
A method for making Vector Flow Images using the transverse oscillation (TO) approach on a convex array is presented. The paper presents optimization schemes for TO fields for convex probes and evaluates their performance using Field II simulations and measurements using the SARUS experimental...... from 90 to 45 degrees in steps of 15 degrees. The optimization routine changes the lateral oscillation period lx to yield the best possible estimates based on the energy ratio between positive and negative spatial frequencies in the ultrasound field. The basic equation for lx gives 1.14 mm at 40 mm...
Effective magnetic Hamiltonians
Czech Academy of Sciences Publication Activity Database
Drchal, Václav; Kudrnovský, Josef; Turek, I.
2013-01-01
Roč. 26, č. 5 (2013), s. 1997-2000 ISSN 1557-1939 R&D Projects: GA ČR GA202/09/0775 Institutional support: RVO:68378271 Keywords : effective magnetic Hamiltonian * ab initio * magnetic structure Subject RIV: BE - Theoretical Physics Impact factor: 0.930, year: 2013
Vector electric field measurement via position-modulated Kelvin probe force microscopy
Dwyer, Ryan P.; Smieska, Louisa M.; Tirmzi, Ali Moeed; Marohn, John A.
2017-10-01
High-quality spatially resolved measurements of electric fields are critical to understanding charge injection, charge transport, and charge trapping in semiconducting materials. Here, we report a variation of frequency-modulated Kelvin probe force microscopy that enables spatially resolved measurements of the electric field. We measure electric field components along multiple directions simultaneously by employing position modulation and lock-in detection in addition to numeric differentiation of the surface potential. We demonstrate the technique by recording linescans of the in-plane electric field vector in the vicinity of a patch of trapped charge in a 2,7-diphenyl[1]benzothieno[3,2-b][1]benzothiophene (DPh-BTBT) organic field-effect transistor. This technique is simple to implement and should be especially useful for studying electric fields in spatially inhomogeneous samples like organic transistors and photovoltaic blends.
Combined tangential-normal vector elements for computing electric and magnetic fields
International Nuclear Information System (INIS)
Sachdev, S.; Cendes, Z.J.
1993-01-01
A direct method for computing electric and magnetic fields in two dimensions is developed. This method determines both the fields and fluxes directly from Maxwell's curl and divergence equations without introducing potential functions. This allows both the curl and the divergence of the field to be set independently in all elements. The technique is based on a new type of vector finite element that simultaneously interpolates to the tangential component of the electric or the magnetic field and the normal component of the electric or magnetic flux. Continuity conditions are imposed across element edges simply by setting like variables to be the same across element edges. This guarantees the continuity of the field and flux at the mid-point of each edge and that for all edges the average value of the tangential component of the field and of the normal component of the flux is identical
A Genealogy of Convex Solids Via Local and Global Bifurcations of Gradient Vector Fields
Domokos, Gábor; Holmes, Philip; Lángi, Zsolt
2016-12-01
Three-dimensional convex bodies can be classified in terms of the number and stability types of critical points on which they can balance at rest on a horizontal plane. For typical bodies, these are non-degenerate maxima, minima, and saddle points, the numbers of which provide a primary classification. Secondary and tertiary classifications use graphs to describe orbits connecting these critical points in the gradient vector field associated with each body. In previous work, it was shown that these classifications are complete in that no class is empty. Here, we construct 1- and 2-parameter families of convex bodies connecting members of adjacent primary and secondary classes and show that transitions between them can be realized by codimension 1 saddle-node and saddle-saddle (heteroclinic) bifurcations in the gradient vector fields. Our results indicate that all combinatorially possible transitions can be realized in physical shape evolution processes, e.g., by abrasion of sedimentary particles.
On the electromagnetic fields, Poynting vector, and peak power radiated by lightning return strokes
Krider, E. P.
1992-01-01
The initial radiation fields, Poynting vector, and total electromagnetic power that a vertical return stroke radiates into the upper half space have been computed when the speed of the stroke, nu, is a significant fraction of the speed of light, c, assuming that at large distances and early times the source is an infinitesimal dipole. The initial current is also assumed to satisfy the transmission-line model with a constant nu and to be perpendicular to an infinite, perfectly conducting ground. The effect of a large nu is to increase the radiation fields by a factor of (1-beta-sq cos-sq theta) exp -1, where beta = nu/c and theta is measured from the vertical, and the Poynting vector by a factor of (1-beta-sq cos-sq theta) exp -2.
Algebras of Complete Hörmander Vector Fields, and Lie-Group Construction
Directory of Open Access Journals (Sweden)
Andrea Bonfiglioli
2014-12-01
Full Text Available The aim of this note is to characterize the Lie algebras g of the analytic vector fields in RN which coincide with the Lie algebras of the (analytic Lie groups defined on RN (with its usual differentiable structure. We show that such a characterization amounts to asking that: (i g is N-dimensional; (ii g admits a set of Lie generators which are complete vector fields; (iii g satisfies Hörmander’s rank condition. These conditions are necessary, sufficient and mutually independent. Our approach is constructive, in that for any such g we show how to construct a Lie group G = (RN, * whose Lie algebra is g. We do not make use of Lie’s Third Theorem, but we only exploit the Campbell-Baker-Hausdorff-Dynkin Theorem for ODE’s.
Deformation structure analysis of material at fatigue on the basis of the vector field
Kibitkin, Vladimir V.; Solodushkin, Andrey I.; Pleshanov, Vasily S.
2017-12-01
In the paper, spatial distributions of deformation, circulation, and shear amplitudes and shear angles are obtained from the displacement vector field measured by the DIC technique. This vector field and its characteristics of shears and vortices are given as an example of such approach. The basic formulae are also given. The experiment shows that honeycomb deformation structures can arise in the center of a macrovortex at developed plastic flow. The spatial distribution of local circulation and shears is discovered, which coincides with the deformation structure but their amplitudes are different. The analysis proves that the spatial distribution of shear angles is a result of maximum tangential and normal stresses. The anticlockwise circulation of most local vortices obeys the normal Gaussian law in the area of interest.
Foliated vector fields, the Godbillon-Vey invariant and the invariant I(F)
International Nuclear Information System (INIS)
Banyaga, A.; Landa, Alain Musesa
2004-03-01
We prove that if the invariant I(F) constructed in 'An invariant of contact structures and transversally oriented foliations', Ann. Global Analysis and Geom. 14(1996) 427-441 (A. Banyaga), through the Lie algebra of infinitesimal automorphisms of transversally oriented foliations F is trivial, then the Godbillon-Vey invariant GV (F) of F is also trivial, but that the converse is not true. For codimension one foliations, the restrictions I τ , (F) of I(F) to the Lie subalgebra of vector fields tangent to the leaves is the Reeb class R(F) of F. We also prove that if there exists a foliated vector field which is everywhere transverse to a codimension one foliation, then the Reeb class R(F) is trivial, hence so is the GV(F) invariant. (author)
Double gauge invariance and covariantly-constant vector fields in Weyl geometry
Kassandrov, Vladimir V.; Rizcallah, Joseph A.
2014-08-01
The wave equation and equations of covariantly-constant vector fields (CCVF) in spaces with Weyl nonmetricity turn out to possess, in addition to the canonical conformal-gauge, a gauge invariance of another type. On a Minkowski metric background, the CCVF system alone allows us to pin down the Weyl 4-metricity vector, identified herein with the electromagnetic potential. The fundamental solution is given by the ordinary Lienard-Wiechert field, in particular, by the Coulomb distribution for a charge at rest. Unlike the latter, however, the magnitude of charge is necessarily unity, "elementary", and charges of opposite signs correspond to retarded and advanced potentials respectively, thus establishing a direct connection between the particle/antiparticle asymmetry and the "arrow of time".
Non-Gaussianity at tree and one-loop levels from vector field perturbations
International Nuclear Information System (INIS)
Valenzuela-Toledo, Cesar A.; Rodriguez, Yeinzon; Lyth, David H.
2009-01-01
We study the spectrum P ζ and bispectrum B ζ of the primordial curvature perturbation ζ when the latter is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree-level terms [both (either) in P ζ and (or) in B ζ ] and vice versa. The level of non-Gaussianity in the bispectrum, f NL , is calculated and related to the level of statistical anisotropy in the power spectrum, g ζ . For very small amounts of statistical anisotropy in the power spectrum, the level of non-Gaussianity may be very high, in some cases exceeding the current observational limit.
Comparative Visualization of Vector Field Ensembles Based on Longest Common Subsequence
Energy Technology Data Exchange (ETDEWEB)
Liu, Richen; Guo, Hanqi; Zhang, Jiang; Yuan, Xiaoru
2016-04-19
We propose a longest common subsequence (LCS) based approach to compute the distance among vector field ensembles. By measuring how many common blocks the ensemble pathlines passing through, the LCS distance defines the similarity among vector field ensembles by counting the number of sharing domain data blocks. Compared to the traditional methods (e.g. point-wise Euclidean distance or dynamic time warping distance), the proposed approach is robust to outlier, data missing, and sampling rate of pathline timestep. Taking the advantages of smaller and reusable intermediate output, visualization based on the proposed LCS approach revealing temporal trends in the data at low storage cost, and avoiding tracing pathlines repeatedly. Finally, we evaluate our method on both synthetic data and simulation data, which demonstrate the robustness of the proposed approach.
Plattner, Alain; Simons, Frederik J.
2017-10-01
When modelling satellite data to recover a global planetary magnetic or gravitational potential field, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are available, or when data quality varies strongly with geographic location, the inversion problem becomes severely ill-posed. In those cases, adopting explicitly local methods is to be preferred over adapting global ones (e.g. by regularization). Here, we develop the theory behind a procedure to invert for planetary potential fields from vector observations collected within a spatially bounded region at varying satellite altitude. Our method relies on the construction of spatiospectrally localized bases of functions that mitigate the noise amplification caused by downward continuation (from the satellite altitude to the source) while balancing the conflicting demands for spatial concentration and spectral limitation. The `altitude-cognizant' gradient vector Slepian functions (AC-GVSF) enjoy a noise tolerance under downward continuation that is much improved relative to the `classical' gradient vector Slepian functions (CL-GVSF), which do not factor satellite altitude into their construction. Furthermore, venturing beyond the realm of their first application, published in a preceding paper, in the present article we extend the theory to being able to handle both internal and external potential-field estimation. Solving simultaneously for internal and external fields under the limitation of regional data availability reduces internal-field artefacts introduced by downward-continuing unmodelled external fields, as we show with numerical examples. We explain our solution strategies on the basis of analytic expressions for the behaviour of the estimation bias and variance of models for which signal and noise are uncorrelated, (essentially) space- and band-limited, and spectrally (almost) white. The AC-GVSF are optimal linear combinations of vector spherical harmonics
On parasupersymmetric oscillators and relativistic vector mesons in constant magnetic fields
Debergh, Nathalie; Beckers, Jules
1995-01-01
Johnson-Lippmann considerations on oscillators and their connection with the minimal coupling schemes are visited in order to introduce a new Sakata-Taketani equation describing vector mesons in interaction with a constant magnetic field. This new proposal, based on a specific parasupersymmetric oscillator-like system, is characterized by real energies as opposed to previously pointed out relativistic equations corresponding to this interacting context.
Localization of periodic orbits of polynomial vector fields of even degree by linear functions
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E. [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)] e-mail: konst@citedi.mx
2005-08-01
This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered.
Localization of periodic orbits of polynomial vector fields of even degree by linear functions
International Nuclear Information System (INIS)
Starkov, Konstantin E.
2005-01-01
This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered
Dissipative systems and Bateman's Hamiltonian
International Nuclear Information System (INIS)
Pedrosa, I.A.; Baseia, B.
1983-01-01
It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt
Visualizing Robustness of Critical Points for 2D Time-Varying Vector Fields
Wang, B.
2013-06-01
Analyzing critical points and their temporal evolutions plays a crucial role in understanding the behavior of vector fields. A key challenge is to quantify the stability of critical points: more stable points may represent more important phenomena or vice versa. The topological notion of robustness is a tool which allows us to quantify rigorously the stability of each critical point. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it within a local neighborhood, measured under an appropriate metric. In this paper, we introduce a new analysis and visualization framework which enables interactive exploration of robustness of critical points for both stationary and time-varying 2D vector fields. This framework allows the end-users, for the first time, to investigate how the stability of a critical point evolves over time. We show that this depends heavily on the global properties of the vector field and that structural changes can correspond to interesting behavior. We demonstrate the practicality of our theories and techniques on several datasets involving combustion and oceanic eddy simulations and obtain some key insights regarding their stable and unstable features. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd.
Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields.
Skraba, Primoz; Bei Wang; Guoning Chen; Rosen, Paul
2015-08-01
Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.
Visualizing Robustness of Critical Points for 2D Time-Varying Vector Fields
Wang, B.; Rosen, P.; Skraba, P.; Bhatia, H.; Pascucci, V.
2013-01-01
Analyzing critical points and their temporal evolutions plays a crucial role in understanding the behavior of vector fields. A key challenge is to quantify the stability of critical points: more stable points may represent more important phenomena or vice versa. The topological notion of robustness is a tool which allows us to quantify rigorously the stability of each critical point. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it within a local neighborhood, measured under an appropriate metric. In this paper, we introduce a new analysis and visualization framework which enables interactive exploration of robustness of critical points for both stationary and time-varying 2D vector fields. This framework allows the end-users, for the first time, to investigate how the stability of a critical point evolves over time. We show that this depends heavily on the global properties of the vector field and that structural changes can correspond to interesting behavior. We demonstrate the practicality of our theories and techniques on several datasets involving combustion and oceanic eddy simulations and obtain some key insights regarding their stable and unstable features. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd.
Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields
Skraba, Primoz
2015-08-01
© 2015 IEEE. Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.
Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields
Skraba, Primoz; Wang, Bei; Chen, Guoning; Rosen, Paul
2015-01-01
© 2015 IEEE. Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.
Hamiltonian Evolution of Monokinetic Measures with Rough Momentum Profile
Bardos, Claude W.
2014-12-27
Consider a monokinetic probability measure on the phase space (Formula presented.) , i.e. (Formula presented.) where Uin is a vector field on RN and ρin a probability density on RN. Let Φt be a Hamiltonian flow on RN × RN. In this paper, we study the structure of the transported measure (Formula presented.) and of its integral in the ξ variable denoted ρ(t). In particular, we give estimates on the number of folds in (Formula presented.) , on which μ(t) is concentrated. We explain how our results can be applied to investigate the classical limit of the Schrödinger equation by using the formalism of Wigner measures. Our formalism includes initial momentum profiles Uin with much lower regularity than required by the WKB method. Finally, we discuss a few examples showing that our results are sharp.
Hamiltonian Evolution of Monokinetic Measures with Rough Momentum Profile
Bardos, Claude W.; Golse, Franç ois; Markowich, Peter A.; Paul, Thierry A.
2014-01-01
Consider a monokinetic probability measure on the phase space (Formula presented.) , i.e. (Formula presented.) where Uin is a vector field on RN and ρin a probability density on RN. Let Φt be a Hamiltonian flow on RN × RN. In this paper, we study the structure of the transported measure (Formula presented.) and of its integral in the ξ variable denoted ρ(t). In particular, we give estimates on the number of folds in (Formula presented.) , on which μ(t) is concentrated. We explain how our results can be applied to investigate the classical limit of the Schrödinger equation by using the formalism of Wigner measures. Our formalism includes initial momentum profiles Uin with much lower regularity than required by the WKB method. Finally, we discuss a few examples showing that our results are sharp.
The Vector Electric Field Instrument on the C/NOFS Satellite
Pfaff, R.; Kujawski, J.; Uribe, P.; Bromund, K.; Fourre, R.; Acuna, M.; Le, G.; Farrell, W.; Holzworth, R.; McCarthy, M.;
2008-01-01
We provide an overview of the Vector Electric Field Instrument (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite, a mission designed to understand, model, and forecast the presence of equatorial ionospheric irregularities. VEFI is a NASA GSFC instrument designed 1) to investigate the role of the ambient electric fields in initiating nighttime ionospheric density depletions and turbulence; 2) to determine the electric fields associated with abrupt, large amplitude, density depletions and 3) to quantify the spectrum of the wave electric fields and plasma densities (irregularities) associated with density depletions or Equatorial Spread-F. The VEFI instrument includes a vector electric field double probe detector, a Langmuir trigger probe, a flux gate magnetometer, a lightning detector and associated electronics. The heart of the instrument is the set of double probe detectors designed to measure DC and AC electric fields using 6 identical, mutually orthogonal, deployable 9.5 m booms tipped with 10 cm diameter spheres containing embedded preamplifiers. A description of the instrument and its sensors will be presented. If available, representative measurements will be provided.
Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field
International Nuclear Information System (INIS)
Mandal, Anirban; Hunt, Katharine L. C.
2016-01-01
In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gauge dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels identically with a gauge-dependent term in the usual form of the field Hamiltonian. We treat the electromagnetic field classically and treat the molecule quantum mechanically, but nonrelativistically. Our derivation starts from the Lagrangian for a set of charged particles and an electromagnetic field, with the particle coordinates, the vector potential, the scalar potential, and their time derivatives treated as the variables in the Lagrangian. We construct the full Hamiltonian using a Lagrange multiplier method originally suggested by Dirac, partition this Hamiltonian into a molecular term H m and a field term H f , and show that both H m and H f have gauge-independent expectation values. Any gauge may be chosen for the calculations; but
On the (1 + 3) threading of spacetime with respect to an arbitrary timelike vector field
Energy Technology Data Exchange (ETDEWEB)
Bejancu, Aurel [Kuwait University, Department of Mathematics, P.O.Box 5969, Safat (Kuwait); Calin, Constantin [Technical University ' ' Gh.Asachi' ' , Department of Mathematics, Iasi (Romania)
2015-04-15
We develop a newapproach on the (1 + 3) threading of spacetime (M, g) with respect to a congruence of curves defined by an arbitrary timelike vector field. The study is based on spatial tensor fields and on theRiemannian spatial connection ∇*, which behave as 3D geometric objects. We obtain new formulas for local components of the Ricci tensor field of (M, g) with respect to the threading frame field, in terms of the Ricci tensor field of ∇* and of kinematic quantities. Also, new expressions for time covariant derivatives of kinematic quantities are stated. In particular, a new form of Raychaudhuri's equation enables us to prove Lemma 6.3, which completes a well-known lemma used in the proof of the Penrose-Hawking singularity theorems. Finally, we apply the new (1 + 3) formalism to the study of the dynamics of a Kerr-Newman black hole. (orig.)
Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes.
Frolov, Valeri P; Krtouš, Pavel; Kubizňák, David; Santos, Jorge E
2018-06-08
We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-AdS black-hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in an excellent agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.
Quantization of the minimal and non-minimal vector field in curved space
Toms, David J.
2015-01-01
The local momentum space method is used to study the quantized massive vector field (the Proca field) with the possible addition of non-minimal terms. Heat kernel coefficients are calculated and used to evaluate the divergent part of the one-loop effective action. It is shown that the naive expression for the effective action that one would write down based on the minimal coupling case needs modification. We adopt a Faddeev-Jackiw method of quantization and consider the case of an ultrastatic...
Development of Techniques for Visualization of Scalar and Vector Fields in the Immersive Environment
Bidasaria, Hari B.; Wilson, John W.; Nealy, John E.
2005-01-01
Visualization of scalar and vector fields in the immersive environment (CAVE - Cave Automated Virtual Environment) is important for its application to radiation shielding research at NASA Langley Research Center. A complete methodology and the underlying software for this purpose have been developed. The developed software has been put to use for the visualization of the earth s magnetic field, and in particular for the study of the South Atlantic Anomaly. The methodology has also been put to use for the visualization of geomagnetically trapped protons and electrons within Earth's magnetosphere.
Topological events on the lines of circular polarization in nonparaxial vector optical fields.
Freund, Isaac
2017-02-01
In nonparaxial vector optical fields, the following topological events are shown to occur in apparent violation of charge conservation: as one translates the observation plane along a line of circular polarization (a C line), the points on the line (C points) are seen to change not only the signs of their topological charges, but also their handedness, and, at turning points on the line, paired C points with the same topological charge and opposite handedness are seen to nucleate. These counter-intuitive events cannot occur in paraxial fields.
Energy Technology Data Exchange (ETDEWEB)
Bagrov, V G; Dorofeev, O F; Sokolov, A A; Ternov, I M; Khalilov, V R [Moskovskij Gosudarstvennyj Univ. (USSR)
1975-03-11
When electrons move in a magnetic field, synchrotron radiation gives rise to transitions accompanied by the electron spin reorientation. In this case, it is essential that the transition probability depends on the spin orientation; as a result electron polarization takes place with the spin orientation being predominantly opposite to the direction of the magnetic field. This effect has been called ''radiative self-polarization of electrons''. The present work is concerned with the question how the choice of the spin operator will affect the self-polarization degree and relaxation time. The problem has been solved for a vector spin operator.
Changes in measured vector magnetic fields when transformed into heliographic coordinates
Hagyard, M. J.
1987-01-01
The changes that occur in measured magnetic fields when they are transformed into a heliographic coordinate system are investigated. To carry out this investigation, measurements of the vector magnetic field of an active region that was observed at 1/3 the solar radius from disk center are taken, and the observed field is transformed into heliographic coordinates. Differences in the calculated potential field that occur when the heliographic normal component of the field is used as the boundary condition rather than the observed line-of-sight component are also examined. The results of this analysis show: (1) that the observed fields of sunspots more closely resemble the generally accepted picture of the distribution of umbral fields if they are displayed in heliographic coordinates; (2) that the differences in the potential calculations are less than 200 G in field strength and 20 deg in field azimuth outside sunspots; and (3) that differences in the two potential calculations in the sunspot areas are no more than 400 G in field strength but range from 60 to 80 deg in field azimuth in localized umbral areas.
On scalar and vector fields coupled to the energy-momentum tensor
Jiménez, Jose Beltrán; Cembranos, Jose A. R.; Sánchez Velázquez, Jose M.
2018-05-01
We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity theories, we build the action by means of an iterative process that leads to an infinite series, which can be resumed as the solution of a set of differential equations. We show that, in some particular cases, the equations become algebraic and that is also possible to find solutions in the form of polynomials. We briefly review the case of the scalar field that has already been studied in the literature and extend the analysis to the case of derivative (disformal) couplings. We then explore theories with vector fields, distinguishing between gauge-and non-gauge-invariant couplings. Interactions with matter are also considered, taking a scalar field as a proxy for the matter sector. We also discuss the ambiguity introduced by superpotential (boundary) terms in the definition of the energy-momentum tensor and use them to show that it is also possible to generate Galileon-like interactions with this procedure. We finally use collider and astrophysical observations to set constraints on the dimensionful coupling which characterises the phenomenology of these models.
Hamiltonian formulation for the Martin-Taylor model
International Nuclear Information System (INIS)
Vasconcelos, D.B.; Viana, R.L.
1993-01-01
Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)
Initial Results from the Vector Electric Field Investigation on the C/NOFS Satellite
Pfaff, R.; Rowland, D.; Acuna, M.; Le, G.; Farrell, W.; Holzworth, R.; Wilson, G.; Burke, W.; Freudenreich, H.; Bromund, K.;
2009-01-01
Initial results are presented from the Vector Electric Field Investigation (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite, a mission designed to understand, model, and forecast the presence of equatorial ionospheric irregularities. The VEFI instrument includes a vector DC electric field detector, a fixed-bias Langmuir probe operating in the ion saturation regime, a flux gate magnetometer, an optical lightning detector, and associated electronics including a burst memory. The DC electric field detector has revealed zonal and meridional electric fields that undergo a diurnal variation, typically displaying eastward and outward-directed fields during the day and westward and downward-directed fields at night. In general, the measured DC electric field amplitudes are in the 0.5-2 mV/m range, corresponding to I3 x B drifts of the order of 30-150 m/s. What is surprising is the high degree of large-scale (10's to 100's of km) structure in the DC electric field, particularly at night, regardless of whether well-defined spread-F plasma density depletions are present. The spread-F density depletions and corresponding electric fields that have been detected thus far have displayed a preponderance to appear between midnight and dawn. Associated with the narrow plasma depletions that are detected are broad spectra of electric field and plasma density irregularities for which a full vector set of measurements is available for detailed study. On some occasions, localized regions of low frequency (field broadband irregularities have been detected, suggestive of filamentary currents, although there is no one-to-one correspondence of these waves with the observed plasma density depletions, at least within the data examined thus far. Finally, the data set includes a wide range of ELF/VLF/HF waves corresponding to a variety of plasma waves, in particular banded ELF hiss, whistlers, and lower hybrid wave turbulence triggered by lightning
Estimation of 3-D conduction velocity vector fields from cardiac mapping data.
Barnette, A R; Bayly, P V; Zhang, S; Walcott, G P; Ideker, R E; Smith, W M
2000-08-01
A method to estimate three-dimensional (3-D) conduction velocity vector fields in cardiac tissue is presented. The speed and direction of propagation are found from polynomial "surfaces" fitted to space-time (x, y, z, t) coordinates of cardiac activity. The technique is applied to sinus rhythm and paced rhythm mapped with plunge needles at 396-466 sites in the canine myocardium. The method was validated on simulated 3-D plane and spherical waves. For simulated data, conduction velocities were estimated with an accuracy of 1%-2%. In experimental data, estimates of conduction speeds during paced rhythm were slower than those found during normal sinus rhythm. Vector directions were also found to differ between different types of beats. The technique was able to distinguish between premature ventricular contractions and sinus beats and between sinus and paced beats. The proposed approach to computing velocity vector fields provides an automated, physiological, and quantitative description of local electrical activity in 3-D tissue. This method may provide insight into abnormal conduction associated with fatal ventricular arrhythmias.
Instability in Hamiltonian systems
Directory of Open Access Journals (Sweden)
A. Pumarino
2005-11-01
Besides proving the existence of Arnold diffusion for a new family of three degrees of freedom Hamiltonian systems, another goal of this book is not only to show how Arnold-like results can be extended to substantially larger sets of parameters, but also how to obtain effective estimates on the splitting of separatrices size when the frequency of the perturbation belongs to open real sets.
Discrete variational Hamiltonian mechanics
International Nuclear Information System (INIS)
Lall, S; West, M
2006-01-01
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
Ostrogradski Hamiltonian approach for geodetic brane gravity
International Nuclear Information System (INIS)
Cordero, Ruben; Molgado, Alberto; Rojas, Efrain
2010-01-01
We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.
Chen, D. W.; Sengupta, S. K.; Welch, R. M.
1989-01-01
This paper compares the results of cloud-field classification derived from two simplified vector approaches, the Sum and Difference Histogram (SADH) and the Gray Level Difference Vector (GLDV), with the results produced by the Gray Level Cooccurrence Matrix (GLCM) approach described by Welch et al. (1988). It is shown that the SADH method produces accuracies equivalent to those obtained using the GLCM method, while the GLDV method fails to resolve error clusters. Compared to the GLCM method, the SADH method leads to a 31 percent saving in run time and a 50 percent saving in storage requirements, while the GLVD approach leads to a 40 percent saving in run time and an 87 percent saving in storage requirements.
Superradiant Instability and Backreaction of Massive Vector Fields around Kerr Black Holes.
East, William E; Pretorius, Frans
2017-07-28
We study the growth and saturation of the superradiant instability of a complex, massive vector (Proca) field as it extracts energy and angular momentum from a spinning black hole, using numerical solutions of the full Einstein-Proca equations. We concentrate on a rapidly spinning black hole (a=0.99) and the dominant m=1 azimuthal mode of the Proca field, with real and imaginary components of the field chosen to yield an axisymmetric stress-energy tensor and, hence, spacetime. We find that in excess of 9% of the black hole's mass can be transferred into the field. In all cases studied, the superradiant instability smoothly saturates when the black hole's horizon frequency decreases to match the frequency of the Proca cloud that spontaneously forms around the black hole.
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Gauge theories of infinite dimensional Hamiltonian superalgebras
International Nuclear Information System (INIS)
Sezgin, E.
1989-05-01
Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)
Hairy Slices: Evaluating the Perceptual Effectiveness of Cutting Plane Glyphs for 3D Vector Fields.
Stevens, Andrew H; Butkiewicz, Thomas; Ware, Colin
2017-01-01
Three-dimensional vector fields are common datasets throughout the sciences. Visualizing these fields is inherently difficult due to issues such as visual clutter and self-occlusion. Cutting planes are often used to overcome these issues by presenting more manageable slices of data. The existing literature provides many techniques for visualizing the flow through these cutting planes; however, there is a lack of empirical studies focused on the underlying perceptual cues that make popular techniques successful. This paper presents a quantitative human factors study that evaluates static monoscopic depth and orientation cues in the context of cutting plane glyph designs for exploring and analyzing 3D flow fields. The goal of the study was to ascertain the relative effectiveness of various techniques for portraying the direction of flow through a cutting plane at a given point, and to identify the visual cues and combinations of cues involved, and how they contribute to accurate performance. It was found that increasing the dimensionality of line-based glyphs into tubular structures enhances their ability to convey orientation through shading, and that increasing their diameter intensifies this effect. These tube-based glyphs were also less sensitive to visual clutter issues at higher densities. Adding shadows to lines was also found to increase perception of flow direction. Implications of the experimental results are discussed and extrapolated into a number of guidelines for designing more perceptually effective glyphs for 3D vector field visualizations.
Arrows as anchors: An analysis of the material features of electric field vector arrows
Gire, Elizabeth; Price, Edward
2014-12-01
Representations in physics possess both physical and conceptual aspects that are fundamentally intertwined and can interact to support or hinder sense making and computation. We use distributed cognition and the theory of conceptual blending with material anchors to interpret the roles of conceptual and material features of representations in students' use of representations for computation. We focus on the vector-arrows representation of electric fields and describe this representation as a conceptual blend of electric field concepts, physical space, and the material features of the representation (i.e., the physical writing and the surface upon which it is drawn). In this representation, spatial extent (e.g., distance on paper) is used to represent both distances in coordinate space and magnitudes of electric field vectors. In conceptual blending theory, this conflation is described as a clash between the input spaces in the blend. We explore the benefits and drawbacks of this clash, as well as other features of this representation. This analysis is illustrated with examples from clinical problem-solving interviews with upper-division physics majors. We see that while these intermediate physics students make a variety of errors using this representation, they also use the geometric features of the representation to add electric field contributions and to organize the problem situation productively.
Arrows as anchors: An analysis of the material features of electric field vector arrows
Directory of Open Access Journals (Sweden)
Elizabeth Gire
2014-08-01
Full Text Available Representations in physics possess both physical and conceptual aspects that are fundamentally intertwined and can interact to support or hinder sense making and computation. We use distributed cognition and the theory of conceptual blending with material anchors to interpret the roles of conceptual and material features of representations in students’ use of representations for computation. We focus on the vector-arrows representation of electric fields and describe this representation as a conceptual blend of electric field concepts, physical space, and the material features of the representation (i.e., the physical writing and the surface upon which it is drawn. In this representation, spatial extent (e.g., distance on paper is used to represent both distances in coordinate space and magnitudes of electric field vectors. In conceptual blending theory, this conflation is described as a clash between the input spaces in the blend. We explore the benefits and drawbacks of this clash, as well as other features of this representation. This analysis is illustrated with examples from clinical problem-solving interviews with upper-division physics majors. We see that while these intermediate physics students make a variety of errors using this representation, they also use the geometric features of the representation to add electric field contributions and to organize the problem situation productively.
On the Reduction of Vector and Axial-Vector Fields in a Meson Effective Action at O(p4)
International Nuclear Information System (INIS)
Bel'kov, A.A.; Lanev, A.V.; Schaale, A.
1994-01-01
Starting from an effective NJL-type quark interaction we have derived an effective meson action for the pseudoscalar sector. The vector and axial-vector degrees of freedom have been integrated out, applying the static equations of motion. As the results we have found a (reduced) pseudoscalar meson Lagrangian of the Gasser-Leutwyler type with modified structure coefficients L i . This method has been also used to construct the reduced weak and electromagnetic-weak currents. The application of the reduced Lagrangian and currents has been considered in physical processes. 36 refs., 1 fig., 1 tab
The Vector Electric Field Investigation on the C/NOFS Satellite
Pfaff, R.; Acuna, M.; Kujawski, J.; Fourre, R.; Uribe, P.; Hunsaker, F.; Rowland, D.; Le, G.; Farrell, W.; Maynard, N.;
2008-01-01
We provide an overview of the Vector Electric Field Investigation (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite, a mission designed to understand, model, and forecast the presence of equatorial ionospheric irregularities. VEFI is a NASA/GSFC instrument funded by the Air Force Research Laboratory whose main objectives are to: 1) investigate the role of the ambient electric fields in initiating nighttime ionospheric density depletions and turbulence; 2) determine the quasi-DC electric fields associated with abrupt, large amplitude, density depletions, and 3) quantify the spectrum of the wave electric fields and plasma densities (irregularities) associated with density depletions typically referred to as equatorial spread-F. The VEFI instrument includes a vector electric field double probe detector, a fixed-bias Langmuir probe operating in the ion saturation regime, a flux-gate magnetometer, an optical lightning detector, and associated electronics. The heart of the instrument is the set of detectors designed to measure DC and AC electric fields using 6 identical booms that provide 3 axis, 20-m tip-to-tip orthogonal double probes. Each probe extends a 10 cm diameter sphere containing an embedded preamplifier. VEFI also includes a burst memory that enables snapshots of data from 1-8 channels of selected instruments to be sampled at rates of up to 32 kHz each. The bursts may be triggered by the detection of density depletions, intense electric field wave activity in a given band, lightning detector pulses, or an event at a pre-determined time or location. All VEFI instrument components are working exceptionally well. A description of the instrument, its sensors, and their sampling frequencies and sensitivities will be presented. Representative measurements will be shown.
Establishment of a large semi-field system for experimental study of African malaria vector ecology and control in Tanzania
Ferguson, H.M.; Ng'habi, K.R.; Walder, T.; Kadungula, D.; Moore, S.J.; Lyimo, I.; Russell, T.L.; Urassa, H.; Mshinda, H.; Killeen, G.F.; Knols, B.G.J.
2008-01-01
Background - Medical entomologists increasingly recognize that the ability to make inferences between laboratory experiments of vector biology and epidemiological trends observed in the field is hindered by a conceptual and methodological gap occurring between these approaches which prevents
3D vector distribution of the electro-magnetic fields on a random gold film
Canneson, Damien; Berini, Bruno; Buil, Stéphanie; Hermier, Jean-Pierre; Quélin, Xavier
2018-05-01
The 3D vector distribution of the electro-magnetic fields at the very close vicinity of the surface of a random gold film is studied. Such films are well known for their properties of light confinement and large fluctuations of local density of optical states. Using Finite-Difference Time-Domain simulations, we show that it is possible to determine the local orientation of the electro-magnetic fields. This allows us to obtain a complete characterization of the fields. Large fluctuations of their amplitude are observed as previously shown. Here, we demonstrate large variations of their direction depending both on the position on the random gold film, and on the distance to it. Such characterization could be useful for a better understanding of applications like the coupling of point-like dipoles to such films.
Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.
Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2018-01-22
We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.
Z3 model of Saturns magnetic field and the Pioneer 11 vector helium magnetometer observations
International Nuclear Information System (INIS)
Connerney, J.E.P.; Acuna, M.H.; Ness, N.F.
1984-05-01
Magnetic field observations obtained by the Pioneer 11 vector helium magnetometer are compared with the Z(sub 3) model magnetic field. These Pioneer 11 observations, obtained at close-in radial distances, constitute an important and independent test of the Z(sub 3) zonal harmonic model, which was derived from Voyager 1 and Voyager 2 fluxgate magnetometer observations. Differences between the Pioneer 11 magnetometer and the Z(sub 3) model field are found to be small (approximately 1%) and quantitatively consistent with the expected instrumental accuracy. A detailed examination of these differences in spacecraft payload coordinates shows that they are uniquely associated with the instrument frame of reference and operation. A much improved fit to the Pioneer 11 observations is obtained by rotation of the instrument coordinate system about the spacecraft spin axis by 1.4 degree. With this adjustment, possibly associated with an instrumental phase lag or roll attitude error, the Pioneer 11 vector helium magnetometer observations are fully consistent with the Voyager Z(sub 3) model
Vector-like fields, messenger mixing and the Higgs mass in gauge mediation
Energy Technology Data Exchange (ETDEWEB)
Fischler, Willy; Tangarife, Walter [Department of Physics and Texas Cosmology Center,The University of Texas at Austin,TX 78712 (United States)
2014-05-30
In order to generate, in the context of gauge mediation, a Higgs mass around 126 GeV that avoids the little hierarchy problem, we explore a set of models where the messengers are directly coupled to new vector-like fields at the TeV scale in addition to the usual low energy degrees of freedom. We find that in this context, stop masses lighter than 2 TeV and large A-terms are generated, thereby improving issues of fine tuning.
A program for computing cohomology of Lie superalgebras of vector fields
International Nuclear Information System (INIS)
Kornyak, V.V.
1998-01-01
An algorithm and its C implementation for computing the cohomology of Lie algebras and superalgebras is described. When elaborating the algorithm we paid primary attention to cohomology in trivial, adjoint and coadjoint modules for Lie algebras and superalgebras of the formal vector fields. These algebras have found many applications to modern supersymmetric models of theoretical and mathematical physics. As an example, we present 3- and 5-cocycles from the cohomology in the trivial module for the Poisson algebra Po (2), as found by computer
Lites, B. W.; Skumanich, A.
1985-01-01
A method is presented for recovery of the vector magnetic field and thermodynamic parameters from polarization measurement of photospheric line profiles measured with filtergraphs. The method includes magneto-optic effects and may be utilized on data sampled at arbitrary wavelengths within the line profile. The accuracy of this method is explored through inversion of synthetic Stokes profiles subjected to varying levels of random noise, instrumental wave-length resolution, and line profile sampling. The level of error introduced by the systematic effect of profile sampling over a finite fraction of the 5 minute oscillation cycle is also investigated. The results presented here are intended to guide instrumental design and observational procedure.
Involutive co-distributions preserved by transitive families of vector fields
International Nuclear Information System (INIS)
Ayala Bravo, V.
1994-06-01
This paper leads with integrability conditions of involutive co-distributions defined on co-tangent bundle of a differentiable manifold M. Via Frobenius's integrability theorem, the analysis is aimed at the search for conditions so that this type of co-distributions preserved by transitive families of vector fields in M. We rely on the work of Lobry, Sussmann, Matsuda and Stefan. The type of situation studies comes up naturally in weak-observability problems and weakly-minimal realizations of arbitrary control systems. (author). 10 refs
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms
Equivalence of Lagrangian and Hamiltonian BRST quantizations
International Nuclear Information System (INIS)
Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.
1992-01-01
Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme
New techniques for the scientific visualization of three-dimensional multi-variate and vector fields
Energy Technology Data Exchange (ETDEWEB)
Crawfis, Roger A. [Univ. of California, Davis, CA (United States)
1995-10-01
Volume rendering allows us to represent a density cloud with ideal properties (single scattering, no self-shadowing, etc.). Scientific visualization utilizes this technique by mapping an abstract variable or property in a computer simulation to a synthetic density cloud. This thesis extends volume rendering from its limitation of isotropic density clouds to anisotropic and/or noisy density clouds. Design aspects of these techniques are discussed that aid in the comprehension of scientific information. Anisotropic volume rendering is used to represent vector based quantities in scientific visualization. Velocity and vorticity in a fluid flow, electric and magnetic waves in an electromagnetic simulation, and blood flow within the body are examples of vector based information within a computer simulation or gathered from instrumentation. Understand these fields can be crucial to understanding the overall physics or physiology. Three techniques for representing three-dimensional vector fields are presented: Line Bundles, Textured Splats and Hair Splats. These techniques are aimed at providing a high-level (qualitative) overview of the flows, offering the user a substantial amount of information with a single image or animation. Non-homogenous volume rendering is used to represent multiple variables. Computer simulations can typically have over thirty variables, which describe properties whose understanding are useful to the scientist. Trying to understand each of these separately can be time consuming. Trying to understand any cause and effect relationships between different variables can be impossible. NoiseSplats is introduced to represent two or more properties in a single volume rendering of the data. This technique is also aimed at providing a qualitative overview of the flows.
Statistical properties of the nuclear shell-model Hamiltonian
International Nuclear Information System (INIS)
Dias, H.; Hussein, M.S.; Oliveira, N.A. de
1986-01-01
The statistical properties of realistic nuclear shell-model Hamiltonian are investigated in sd-shell nuclei. The probability distribution of the basic-vector amplitude is calculated and compared with the Porter-Thomas distribution. Relevance of the results to the calculation of the giant resonance mixing parameter is pointed out. (Author) [pt
A vector field method on the distorted Fourier side and decay for wave equations with potentials
Donninger, Roland
2016-01-01
The authors study the Cauchy problem for the one-dimensional wave equation \\partial_t^2 u(t,x)-\\partial_x^2 u(t,x)+V(x)u(t,x)=0. The potential V is assumed to be smooth with asymptotic behavior V(x)\\sim -\\tfrac14 |x|^{-2}\\mbox{ as } |x|\\to \\infty. They derive dispersive estimates, energy estimates, and estimates involving the scaling vector field t\\partial_t+x\\partial_x, where the latter are obtained by employing a vector field method on the âeoedistortedâe Fourier side. In addition, they prove local energy decay estimates. Their results have immediate applications in the context of geometric evolution problems. The theory developed in this paper is fundamental for the proof of the co-dimension 1 stability of the catenoid under the vanishing mean curvature flow in Minkowski space; see Donninger, Krieger, Szeftel, and Wong, âeoeCodimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski spaceâe, preprint arXiv:1310.5606 (2013).
Integrable couplings of the multi-component Dirac hierarchy and its Hamiltonian structure
International Nuclear Information System (INIS)
Li Zhu; Dong Huanhe
2008-01-01
Integrable couplings of the multi-component Dirac hierarchy is obtained by use of the vector loop algebra G ∼ M , then the Hamiltonian structure of the above system is given by the quadratic-form identity
Local modular Hamiltonians from the quantum null energy condition
Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin
2018-03-01
The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .
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.)
Integrable Hamiltonian systems and interactions through quadratic constraints
International Nuclear Information System (INIS)
Pohlmeyer, K.
1975-08-01
Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de
Experimental Hamiltonian identification for controlled two-level systems
International Nuclear Information System (INIS)
Schirmer, S.G.; Kolli, A.; Oi, D.K.L.
2004-01-01
We present a strategy to empirically determine the internal and control Hamiltonians for an unknown two-level system (black box) subject to various (piecewise constant) control fields when direct readout by measurement is limited to a single, fixed observable
On the physical applications of hyper-Hamiltonian dynamics
International Nuclear Information System (INIS)
Gaeta, Giuseppe; Rodriguez, Miguel A
2008-01-01
An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin
Energy Technology Data Exchange (ETDEWEB)
Kubo, R; Yokoyama, K
1974-11-01
The purpose of this work is to study the structure of c-number gauge transformation in connection with renormalization problem. In the wide theory of neutral vector fields, there is the gauge structure described essentially by free Lagrangian density. The c-number gauge transformation makes the Lagrangian invariant correspondingly to the usual case of quantum electrodynamics. The c-number transformation can be used to derive relationships among all relevant renormalization constants in the case of interacting fields. In the presence of interaction, total Lagrangian density L is written as L=L/sub 0/+L/sub 1/+L/sub 2/, where L/sub 1/ is given from matter-field Lagrangian density, and L/sub 2/ denotes necessary additional counter terms. In order to conserve the gauge structure, the form of L is invariant under the gauge transformation. Since L matter is self-adjoining, L/sub 1/ remains invariant by itself under the transformation. The form of L/sub 2/ is finally given from the observation that L/sub 3/ cannot contain wave-function renormalization constants. Since L/sub 2/ is invariant under q-number gauge transformation, this transformation in unrenormalized form makes the present L form-invariant. Therefore, together with the above results, auxiliary fields produce the q-number gauge transformation for renormalized fields.
Directory of Open Access Journals (Sweden)
Hoyeon Kim
Full Text Available In order to broaden the use of microrobots in practical fields, autonomous control algorithms such as obstacle avoidance must be further developed. However, most previous studies of microrobots used manual motion control to navigate past tight spaces and obstacles while very few studies demonstrated the use of autonomous motion. In this paper, we demonstrated a dynamic obstacle avoidance algorithm for bacteria-powered microrobots (BPMs using electric field in fluidic environments. A BPM consists of an artificial body, which is made of SU-8, and a high dense layer of harnessed bacteria. BPMs can be controlled using externally applied electric fields due to the electrokinetic property of bacteria. For developing dynamic obstacle avoidance for BPMs, a kinematic model of BPMs was utilized to prevent collision and a finite element model was used to characteristic the deformation of an electric field near the obstacle walls. In order to avoid fast moving obstacles, we modified our previously static obstacle avoidance approach using a modified vector field histogram (VFH method. To validate the advanced algorithm in experiments, magnetically controlled moving obstacles were used to intercept the BPMs as the BPMs move from the initial position to final position. The algorithm was able to successfully guide the BPMs to reach their respective goal positions while avoiding the dynamic obstacles.
Kim, Hoyeon; Cheang, U Kei; Kim, Min Jun
2017-01-01
In order to broaden the use of microrobots in practical fields, autonomous control algorithms such as obstacle avoidance must be further developed. However, most previous studies of microrobots used manual motion control to navigate past tight spaces and obstacles while very few studies demonstrated the use of autonomous motion. In this paper, we demonstrated a dynamic obstacle avoidance algorithm for bacteria-powered microrobots (BPMs) using electric field in fluidic environments. A BPM consists of an artificial body, which is made of SU-8, and a high dense layer of harnessed bacteria. BPMs can be controlled using externally applied electric fields due to the electrokinetic property of bacteria. For developing dynamic obstacle avoidance for BPMs, a kinematic model of BPMs was utilized to prevent collision and a finite element model was used to characteristic the deformation of an electric field near the obstacle walls. In order to avoid fast moving obstacles, we modified our previously static obstacle avoidance approach using a modified vector field histogram (VFH) method. To validate the advanced algorithm in experiments, magnetically controlled moving obstacles were used to intercept the BPMs as the BPMs move from the initial position to final position. The algorithm was able to successfully guide the BPMs to reach their respective goal positions while avoiding the dynamic obstacles.
Hamiltonian reduction of Kac-Moody algebras
International Nuclear Information System (INIS)
Kimura, Kazuhiro
1991-01-01
Feigin-Fucks construction provides us methods to treat rational conformal theories in terms of free fields. This formulation enables us to describe partition functions and correlation functions in the Fock space of free fields. There are several attempt extending to supersymmetric theories. In this report authors present an explicit calculation of the Hamiltonian reduction based on the free field realization. In spite of the results being well-known, the relations can be clearly understood in the language of bosons. Authors perform the hamiltonian reduction by imposing a constraint with appropriate gauge transformations which preserve the constraint. This approaches enables us to gives the geometric interpretation of super Virasoro algebras and relations of the super gravity. In addition, author discuss the properties of quantum groups by using the explicit form of the group element. It is also interesting to extend to super Kac-Moody algebras. (M.N.)
Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.
Risser, Steven Michael
This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb
Energy Technology Data Exchange (ETDEWEB)
Walstrom, Peter Lowell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-08-07
A numerical algorithm for computing the field components B_{r} and B_{z} and their r and z derivatives with open boundaries in cylindrical coordinates for radially thin solenoids with uniform current density is described in this note. An algorithm for computing the vector potential A_{θ} is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. The (apparently) new feature of the algorithms described in this note applies to cases where the field point is outside of the bore of the solenoid and the field-point radius approaches the solenoid radius. Since the elliptic integrals of the third kind normally used in computing B_{z} and A_{θ} become infinite in this region of parameter space, fields for points with the axial coordinate z outside of the ends of the solenoid and near the solenoid radius are treated by use of elliptic integrals of the third kind of modified argument, derived by use of an addition theorem. Also, the algorithms also avoid the numerical difficulties the textbook solutions have for points near the axis arising from explicit factors of 1/r or 1/r^{2} in the some of the expressions.
Naz, Rehana; Naeem, Imran
2018-03-01
The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.
Directory of Open Access Journals (Sweden)
Shi-Xiong Zhang
2014-02-01
Full Text Available Permanent Magnet Synchronous motor (PMSM has received widespread acceptance in recent years. In this paper, a new rotor and stator Magnetic Fields Direct-Orthogonalized Vector Control (MFDOVC scheme is proposed for PMSM servo system. This method simplified the complex calculation of traditional vector control, a part of the system resource is economized. At the same time, through the simulation illustration validation, the performance of PMSM servo system with the proposed MFDOVC scheme can achieve the same with the complex traditional vector control method, but much simpler calculation is implemented using the proposed method.
Robust online Hamiltonian learning
International Nuclear Information System (INIS)
Granade, Christopher E; Ferrie, Christopher; Wiebe, Nathan; Cory, D G
2012-01-01
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer–Rao lower bound, certifying its own performance. (paper)
Chromatic roots and hamiltonian paths
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...
Gauge fixing and the Hamiltonian for cylindrical spacetimes
Mena Marugán, Guillermo A.
2001-01-01
We introduce a complete gauge fixing for cylindrical spacetimes in vacuo that, in principle, do not contain the axis of symmetry. By cylindrically symmetric we understand spacetimes that possess two commuting spacelike Killing vectors, one of them rotational and the other one translational. The result of our gauge fixing is a constraint-free model whose phase space has four field-like degrees of freedom and that depends on three constant parameters. Two of these constants determine the global angular momentum and the linear momentum in the axis direction, while the third parameter is related with the behavior of the metric around the axis. We derive the explicit expression of the metric in terms of the physical degrees of freedom, calculate the reduced equations of motion and obtain the Hamiltonian that generates the reduced dynamics. We also find upper and lower bounds for this reduced Hamiltonian that provides the energy per unit length contained in the system. In addition, we show that the reduced formalism constructed is well defined and consistent at least when the linear momentum in the axis direction vanishes. Furthermore, in that case we prove that there exists an infinite number of solutions in which all physical fields are constant both in the surroundings of the axis and at sufficiently large distances from it. If the global angular momentum is different from zero, the isometry group of these solutions is generally not orthogonally transitive. Such solutions generalize the metric of a spinning cosmic string in the region where no closed timelike curves are present.
SOLAR FLARE PREDICTION USING SDO/HMI VECTOR MAGNETIC FIELD DATA WITH A MACHINE-LEARNING ALGORITHM
International Nuclear Information System (INIS)
Bobra, M. G.; Couvidat, S.
2015-01-01
We attempt to forecast M- and X-class solar flares using a machine-learning algorithm, called support vector machine (SVM), and four years of data from the Solar Dynamics Observatory's Helioseismic and Magnetic Imager, the first instrument to continuously map the full-disk photospheric vector magnetic field from space. Most flare forecasting efforts described in the literature use either line-of-sight magnetograms or a relatively small number of ground-based vector magnetograms. This is the first time a large data set of vector magnetograms has been used to forecast solar flares. We build a catalog of flaring and non-flaring active regions sampled from a database of 2071 active regions, comprised of 1.5 million active region patches of vector magnetic field data, and characterize each active region by 25 parameters. We then train and test the machine-learning algorithm and we estimate its performances using forecast verification metrics with an emphasis on the true skill statistic (TSS). We obtain relatively high TSS scores and overall predictive abilities. We surmise that this is partly due to fine-tuning the SVM for this purpose and also to an advantageous set of features that can only be calculated from vector magnetic field data. We also apply a feature selection algorithm to determine which of our 25 features are useful for discriminating between flaring and non-flaring active regions and conclude that only a handful are needed for good predictive abilities
Velocity Vector Field Visualization of Flow in Liquid Acquisition Device Channel
McQuillen, John B.; Chao, David F.; Hall, Nancy R.; Zhang, Nengli
2012-01-01
A capillary flow liquid acquisition device (LAD) for cryogenic propellants has been developed and tested in NASA Glenn Research Center to meet the requirements of transferring cryogenic liquid propellants from storage tanks to an engine in reduced gravity environments. The prototypical mesh screen channel LAD was fabricated with a mesh screen, covering a rectangular flow channel with a cylindrical outlet tube, and was tested with liquid oxygen (LOX). In order to better understand the performance in various gravity environments and orientations at different liquid submersion depths of the screen channel LAD, a series of computational fluid dynamics (CFD) simulations of LOX flow through the LAD screen channel was undertaken. The resulting velocity vector field visualization for the flow in the channel has been used to reveal the gravity effects on the flow in the screen channel.
Differential Galois theory and non-integrability of planar polynomial vector fields
Acosta-Humánez, Primitivo B.; Lázaro, J. Tomás; Morales-Ruiz, Juan J.; Pantazi, Chara
2018-06-01
We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular solution it is obtained a necessary condition for the existence of a rational first integral. The method is systematic starting with the first order variational equation. We illustrate this result with several families of examples. A key point is to check whether a suitable primitive is elementary or not. Using a theorem by Liouville, the problem is equivalent to the existence of a rational solution of a certain first order linear equation, the Risch equation. This is a classical problem studied by Risch in 1969, and the solution is given by the "Risch algorithm". In this way we point out the connection of the non integrability with some higher transcendent functions, like the error function.
The Casimir interaction of a massive vector field between concentric spherical bodies
International Nuclear Information System (INIS)
Teo, L.P.
2011-01-01
The Casimir interaction energy due to the vacuum fluctuations of a massive vector field between two perfectly conducting concentric spherical bodies is computed. The TE contribution to the Casimir interaction energy is a direct generalization of the massless case but the TM contribution is much more complicated. Each TM mode is a linear combination of a transverse mode which is the generalization of a TM mode in the massless case and a longitudinal mode that does not appear in the massless case. In contrast to the case of two parallel perfectly conducting plates, there are no TM discrete modes that vanish identically in the perfectly conducting spherical bodies. Numerical simulations show that the Casimir interaction force between the two bodies is always attractive.
Regularity results for the minimum time function with Hörmander vector fields
Albano, Paolo; Cannarsa, Piermarco; Scarinci, Teresa
2018-03-01
In a bounded domain of Rn with boundary given by a smooth (n - 1)-dimensional manifold, we consider the homogeneous Dirichlet problem for the eikonal equation associated with a family of smooth vector fields {X1 , … ,XN } subject to Hörmander's bracket generating condition. We investigate the regularity of the viscosity solution T of such problem. Due to the presence of characteristic boundary points, singular trajectories may occur. First, we characterize these trajectories as the closed set of all points at which the solution loses point-wise Lipschitz continuity. Then, we prove that the local Lipschitz continuity of T, the local semiconcavity of T, and the absence of singular trajectories are equivalent properties. Finally, we show that the last condition is satisfied whenever the characteristic set of {X1 , … ,XN } is a symplectic manifold. We apply our results to several examples.
Simplest bifurcation diagrams for monotone families of vector fields on a torus
Baesens, C.; MacKay, R. S.
2018-06-01
In part 1, we prove that the bifurcation diagram for a monotone two-parameter family of vector fields on a torus has to be at least as complicated as the conjectured simplest one proposed in Baesens et al (1991 Physica D 49 387–475). To achieve this, we define ‘simplest’ by sequentially minimising the numbers of equilibria, Bogdanov–Takens points, closed curves of centre and of neutral saddle, intersections of curves of centre and neutral saddle, Reeb components, other invariant annuli, arcs of rotational homoclinic bifurcation of horizontal homotopy type, necklace points, contractible periodic orbits, points of neutral horizontal homoclinic bifurcation and half-plane fan points. We obtain two types of simplest case, including that initially proposed. In part 2, we analyse the bifurcation diagram for an explicit monotone family of vector fields on a torus and prove that it has at most two equilibria, precisely four Bogdanov–Takens points, no closed curves of centre nor closed curves of neutral saddle, at most two Reeb components, precisely four arcs of rotational homoclinic connection of ‘horizontal’ homotopy type, eight horizontal saddle-node loop points, two necklace points, four points of neutral horizontal homoclinic connection, and two half-plane fan points, and there is no simultaneous existence of centre and neutral saddle, nor contractible homoclinic connection to a neutral saddle. Furthermore, we prove that all saddle-nodes, Bogdanov–Takens points, non-neutral and neutral horizontal homoclinic bifurcations are non-degenerate and the Hopf condition is satisfied for all centres. We also find it has four points of degenerate Hopf bifurcation. It thus provides an example of a family satisfying all the assumptions of part 1 except the one of at most one contractible periodic orbit.
Hamiltonian theory of guiding-center motion
International Nuclear Information System (INIS)
Littlejohn, R.G.
1980-05-01
A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion
Symplectic Geometric Algorithms for Hamiltonian Systems
Feng, Kang
2010-01-01
"Symplectic Geometry Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development
The Effective Hamiltonian in the Scalar Electrodynamics
Dineykhan, M D; Zhaugasheva, S A; Sakhyev, S K
2002-01-01
On the basis of an investigation of the asymptotic behaviour of the polarization loop for the scalar particles in the external electromagnetic field the relativistic corrections to the Hamiltonian are determined. The constituent mass of the particles in the bound state is analytically derived. It is shown that the constituent mass of the particles differs from the mass of the particles in the free state. The corrections connected with the Thomas precession have been calculated.
Hamiltonian theory of guiding-center motion
Energy Technology Data Exchange (ETDEWEB)
Littlejohn, R.G.
1980-05-01
A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.
On the 4D generalized Proca action for an Abelian vector field
Energy Technology Data Exchange (ETDEWEB)
Allys, Erwan [Institut d’Astrophysique de Paris, UMR 7095, UPMC Université Paris 6 et CNRS,98 bis boulevard Arago, 75014 Paris (France); Almeida, Juan P. Beltrán [Departamento de Física, Universidad Antonio Nariño,Cra 3 Este # 47A-15, Bogotá D.C. 110231 (Colombia); Peter, Patrick [Institut d’Astrophysique de Paris, UMR 7095, UPMC Université Paris 6 et CNRS,98 bis boulevard Arago, 75014 Paris (France); Institut Lagrange de Paris,UPMC Université Paris 6 et CNRS,Sorbonne Universités, Paris (France); Rodríguez, Yeinzon [Centro de Investigaciones en Ciencias Básicas y Aplicadas, Universidad Antonio Nariño, Cra 3 Este # 47A-15, Bogotá D.C. 110231 (Colombia); Escuela de Física, Universidad Industrial de Santander,Ciudad Universitaria, Bucaramanga 680002 (Colombia); Simons Associate at The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151, Trieste (Italy)
2016-09-19
We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated StÃ¼ckelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the StÃ¼ckelberg field describing the longitudinal mode, which is in agreement with the results of http://dx.doi.org/10.1088/1475-7516/2014/05/015 and http://dx.doi.org/10.1016/j.physletb.2016.04.017 and complements those of http://dx.doi.org/10.1088/1475-7516/2016/02/004. We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field A{sub μ}, the Faraday tensor F{sub μν} and its Hodge dual F-tilde{sub μν}.
Darabi, H; Vatandoost, H; Abaei, M R; Gharibi, O; Pakbaz, F
2011-01-01
Methoprene, an insect growth regulator, was evaluated under field conditions against the main malaria vectors in the Islamic Republic of Iran. The effect of 5, 10 and 20 kg ha(-1) concentration ofmethoprene granule formulation and 100 and 200 mL ha(-1) concentration of EC formulation was measured to determine any changes in Anophelini larval abundance and IE ratio in both rice fields and artificial ponds. In artificial ponds, granular methoprene at a dose of 20 kg ha(-1) inhibited adult emergence by 77.1% after 1 day and 65.9% after 3 days. The emulsifiable concentrate formulation of methoprene at 200 mL ha(-1) inhibited adult emergence by 83.7% after 1 day and 32.2% after 3 days. In rice fields, inhibition of emergence was 44.3% at 20 kg ha(-1) granule and 35.8% for emulsifiable concentrate at 200 mL ha(-1) after 3 days. The results vary depending on the mosquito species, treatment methods, breeding places and type of formulation.
On the 4D generalized Proca action for an Abelian vector field
International Nuclear Information System (INIS)
Allys, Erwan; Almeida, Juan P. Beltrán; Peter, Patrick; Rodríguez, Yeinzon
2016-01-01
We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated StÃ¼ckelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the StÃ¼ckelberg field describing the longitudinal mode, which is in agreement with the results of http://dx.doi.org/10.1088/1475-7516/2014/05/015 and http://dx.doi.org/10.1016/j.physletb.2016.04.017 and complements those of http://dx.doi.org/10.1088/1475-7516/2016/02/004. We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field A_μ, the Faraday tensor F_μ_ν and its Hodge dual F-tilde_μ_ν.
Remarks on Hamiltonian structures in G2-geometry
International Nuclear Information System (INIS)
Cho, Hyunjoo; Salur, Sema; Todd, A. J.
2013-01-01
In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen
2006-01-01
We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out
Energy Technology Data Exchange (ETDEWEB)
Walstrom, Peter Lowell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-08-24
A numerical algorithm for computing the field components B_{r} and B_{z} and their r and z derivatives with open boundaries in cylindrical coordinates for circular current loops is described. An algorithm for computing the vector potential is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations (especially for the field derivatives) are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. Since cel can evaluate complete elliptic integrals of a fairly general type, in some cases the elliptic integrals can be evaluated without first reducing them to forms containing standard Legendre forms. The algorithms avoid the numerical difficulties that many of the textbook solutions have for points near the axis because of explicit factors of 1=r or 1=r^{2} in the some of the expressions.
A partial Hamiltonian approach for current value Hamiltonian systems
Naz, R.; Mahomed, F. M.; Chaudhry, Azam
2014-10-01
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.
Directory of Open Access Journals (Sweden)
Karel Van Roey
2014-12-01
Full Text Available Scaling up of insecticide treated nets has contributed to a substantial malaria decline. However, some malaria vectors, and most arbovirus vectors, bite outdoors and in the early evening. Therefore, topically applied insect repellents may provide crucial additional protection against mosquito-borne pathogens. Among topical repellents, DEET is the most commonly used, followed by others such as picaridin. The protective efficacy of two formulated picaridin repellents against mosquito bites, including arbovirus and malaria vectors, was evaluated in a field study in Cambodia. Over a period of two years, human landing collections were performed on repellent treated persons, with rotation to account for the effect of collection place, time and individual collector. Based on a total of 4996 mosquitoes collected on negative control persons, the overall five hour protection rate was 97.4% [95%CI: 97.1-97.8%], not decreasing over time. Picaridin 20% performed equally well as DEET 20% and better than picaridin 10%. Repellents performed better against Mansonia and Culex spp. as compared to aedines and anophelines. A lower performance was observed against Aedes albopictus as compared to Aedes aegypti, and against Anopheles barbirostris as compared to several vector species. Parity rates were higher in vectors collected on repellent treated person as compared to control persons. As such, field evaluation shows that repellents can provide additional personal protection against early and outdoor biting malaria and arbovirus vectors, with excellent protection up to five hours after application. The heterogeneity in repellent sensitivity between mosquito genera and vector species could however impact the efficacy of repellents in public health programs. Considering its excellent performance and potential to protect against early and outdoor biting vectors, as well as its higher acceptability as compared to DEET, picaridin is an appropriate product to evaluate the
Van Roey, Karel; Sokny, Mao; Denis, Leen; Van den Broeck, Nick; Heng, Somony; Siv, Sovannaroth; Sluydts, Vincent; Sochantha, Tho; Coosemans, Marc; Durnez, Lies
2014-12-01
Scaling up of insecticide treated nets has contributed to a substantial malaria decline. However, some malaria vectors, and most arbovirus vectors, bite outdoors and in the early evening. Therefore, topically applied insect repellents may provide crucial additional protection against mosquito-borne pathogens. Among topical repellents, DEET is the most commonly used, followed by others such as picaridin. The protective efficacy of two formulated picaridin repellents against mosquito bites, including arbovirus and malaria vectors, was evaluated in a field study in Cambodia. Over a period of two years, human landing collections were performed on repellent treated persons, with rotation to account for the effect of collection place, time and individual collector. Based on a total of 4996 mosquitoes collected on negative control persons, the overall five hour protection rate was 97.4% [95%CI: 97.1-97.8%], not decreasing over time. Picaridin 20% performed equally well as DEET 20% and better than picaridin 10%. Repellents performed better against Mansonia and Culex spp. as compared to aedines and anophelines. A lower performance was observed against Aedes albopictus as compared to Aedes aegypti, and against Anopheles barbirostris as compared to several vector species. Parity rates were higher in vectors collected on repellent treated person as compared to control persons. As such, field evaluation shows that repellents can provide additional personal protection against early and outdoor biting malaria and arbovirus vectors, with excellent protection up to five hours after application. The heterogeneity in repellent sensitivity between mosquito genera and vector species could however impact the efficacy of repellents in public health programs. Considering its excellent performance and potential to protect against early and outdoor biting vectors, as well as its higher acceptability as compared to DEET, picaridin is an appropriate product to evaluate the epidemiological
International Nuclear Information System (INIS)
Shabbir, Ghulam; Khan, Suhail; Ali, Amjad
2011-01-01
In this paper we classify spatially homogeneous rotating space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields is 5 or 10. In the case of 10 teleparallel Killing vector fields the space-time becomes Minkowski and all the torsion components are zero. Teleparallel Killing vector fields in this case are exactly the same as in general relativity. In the cases of 5 teleparallel Killing vector fields we get two more conservation laws in the teleparallel theory of gravitation. Here we also discuss some well-known examples of spatially homogeneous rotating space-times according to their teleparallel Killing vector fields. (general)
International Nuclear Information System (INIS)
Shabbir, Ghulam; Khan, Suhail
2010-01-01
In this paper we classify Kantowski-Sachs and Bianchi type III space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields are 4 or 6, which are the same in numbers as in general relativity. In case of 4 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of t. In the case of 6 Killing vector fields the metric functions become constants and the Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case. (general)
Time and a physical Hamiltonian for quantum gravity.
Husain, Viqar; Pawłowski, Tomasz
2012-04-06
We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society
Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD
International Nuclear Information System (INIS)
Morrison, P.J.; Greene, J.M.
1980-04-01
A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables
Trochoidal X-ray Vector Radiography: Directional dark-field without grating stepping
Sharma, Y.; Bachche, S.; Kageyama, M.; Kuribayashi, M.; Pfeiffer, F.; Lasser, T.; Momose, A.
2018-03-01
X-ray Vector Radiography (XVR) is an imaging technique that reveals the orientations of sub-pixel sized structures within a sample. Several dark-field radiographs are acquired by rotating the sample around the beam propagation direction and stepping one of the gratings to several positions for every pose of the sample in an X-ray grating interferometry setup. In this letter, we present a method of performing XVR of a continuously moving sample without the need of any grating motion. We reconstruct the orientations within a sample by analyzing the change in the background moire fringes caused by the sample moving and simultaneously rotating in plane (trochoidal trajectory) across the detector field-of-view. Avoiding the motion of gratings provides significant advantages in terms of stability and repeatability, while the continuous motion of the sample makes this kind of system adaptable for industrial applications such as the scanning of samples on a conveyor belt. Being the first step in the direction of utilizing advanced sample trajectories to replace grating motion, this work also lays the foundations for a full three dimensional reconstruction of scattering function without grating motion.
Transient rotation of photospheric vector magnetic fields associated with a solar flare.
Xu, Yan; Cao, Wenda; Ahn, Kwangsu; Jing, Ju; Liu, Chang; Chae, Jongchul; Huang, Nengyi; Deng, Na; Gary, Dale E; Wang, Haimin
2018-01-03
As one of the most violent eruptions on the Sun, flares are believed to be powered by magnetic reconnection. The fundamental physics involving the release, transfer, and deposition of energy have been studied extensively. Taking advantage of the unprecedented resolution provided by the 1.6 m Goode Solar Telescope, here, we show a sudden rotation of vector magnetic fields, about 12-20° counterclockwise, associated with a flare. Unlike the permanent changes reported previously, the azimuth-angle change is transient and cospatial/temporal with Hα emission. The measured azimuth angle becomes closer to that in potential fields suggesting untwist of flare loops. The magnetograms were obtained in the near infrared at 1.56 μm, which is minimally affected by flare emission and no intensity profile change was detected. We believe that these transient changes are real and discuss the possible explanations in which the high-energy electron beams or Alfve'n waves play a crucial role.
Layeghi, Azam; Latifi, Hamid
2018-06-01
A magnetic field vector sensor based on super-paramagnetic fluid and tapered Hi-Bi fiber (THB) in fiber loop mirror (FLM) is proposed. A two-dimensional detection of external magnetic field (EMF) is experimentally demonstrated and theoretically simulated by Jones matrix to analyze the physical operation in detail. A birefringence is obtained due to magnetic fluid (MF) in applied EMF. By surrounding the THB with MF, a tunable birefringence of MF affect the transmission of the sensor. Slow and fast axes of this obtained birefringence are determined by the direction of applied EMF. In this way, the transmission response of the sensor is depended on the angle between the EMF orientation and the main axes of polarization maintaining fiber (PMF) in FLM. The wavelength shift and intensity shift versus EMF orientation show a sinusoidal behavior, while the applied EMF is constant. Also, the changes in the intensity of EMF in a certain direction results in wavelength shift in the sensor spectrum. The maximum wavelength sensitivity of 214 pm/mT is observed.
Hamiltonian Monte Carlo study of the N=1 Wess-Zumino model on the lattice in 1+1 dimensions
International Nuclear Information System (INIS)
Schiller, A.
1984-01-01
1+1 dimensional models with restricted supersymmetry are studied. The problems of formulating supersymmetric models on the lattice are overcome by working in the Hamiltonian lattice formulation and using restricted supersymmetry algebra involving only the Hamiltonian. For the two-dimensional Wess-Zumino model a lattice Hamiltonian suitable for the local Hamiltonian method is obtained. Using this method field theoretical models with fermions and scalar Higgs fields are investigated. Emphasis is laid on supersymmetry breaking and soliton formation
Scattering theory for Stark Hamiltonians
International Nuclear Information System (INIS)
Jensen, Arne
1994-01-01
An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1998-01-01
The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. copyright 1998 The American Physical Society
Robot Training With Vector Fields Based on Stroke Survivors' Individual Movement Statistics.
Wright, Zachary A; Lazzaro, Emily; Thielbar, Kelly O; Patton, James L; Huang, Felix C
2018-02-01
The wide variation in upper extremity motor impairments among stroke survivors necessitates more intelligent methods of customized therapy. However, current strategies for characterizing individual motor impairments are limited by the use of traditional clinical assessments (e.g., Fugl-Meyer) and simple engineering metrics (e.g., goal-directed performance). Our overall approach is to statistically identify the range of volitional movement capabilities, and then apply a robot-applied force vector field intervention that encourages under-expressed movements. We investigated whether explorative training with such customized force fields would improve stroke survivors' (n = 11) movement patterns in comparison to a control group that trained without forces (n = 11). Force and control groups increased Fugl-Meyer UE scores (average of 1.0 and 1.1, respectively), which is not considered clinically meaningful. Interestingly, participants from both groups demonstrated dramatic increases in their range of velocity during exploration following only six days of training (average increase of 166.4% and 153.7% for the Force and Control group, respectively). While both groups showed evidence of improvement, we also found evidence that customized forces affected learning in a systematic way. When customized forces were active, we observed broader distributions of velocity that were not present in the controls. Second, we found that these changes led to specific changes in unassisted motion. In addition, while the shape of movement distributions changed significantly for both groups, detailed analysis of the velocity distributions revealed that customized forces promoted a greater proportion of favorable changes. Taken together, these results provide encouraging evidence that patient-specific force fields based on individuals' movement statistics can be used to create new movement patterns and shape them in a customized manner. To the best of our knowledge, this paper is the first
Quantum Hamiltonian Physics with Supercomputers
International Nuclear Information System (INIS)
Vary, James P.
2014-01-01
The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed
Quantum Hamiltonian Physics with Supercomputers
Energy Technology Data Exchange (ETDEWEB)
Vary, James P.
2014-06-15
The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.
Directory of Open Access Journals (Sweden)
Ricardo Castillo-Neyra
2015-01-01
Full Text Available Chagas disease affects millions of people in Latin America. The control of this vector-borne disease focuses on halting transmission by reducing or eliminating insect vector populations. Most transmission of Trypanosoma cruzi, the causative agent of Chagas disease, involves insects living within or very close to households and feeding mostly on domestic animals. As animal hosts can be intermittently present it is important to understand how host availability can modify transmission risk to humans and to characterize the host-seeking dispersal of triatomine vectors on a very fine scale. We used a semi-field system with motion-detection cameras to characterize the dispersal of Triatoma infestans, and compare the behavior of vector populations in the constant presence of hosts (guinea pigs, and after the removal of the hosts. The emigration rate - net insect population decline in original refuge - following host removal was on average 19.7% of insects per 10 days compared to 10.2% in constant host populations (p = 0.029. However, dispersal of T. infestans occurred in both directions, towards and away from the initial location of the hosts. The majority of insects that moved towards the original location of guinea pigs remained there for 4 weeks. Oviposition and mortality were observed and analyzed in the context of insect dispersal, but only mortality was higher in the group where animal hosts were removed (p-value <0.01. We discuss different survival strategies associated with the observed behavior and its implications for vector control. Removing domestic animals in infested areas increases vector dispersal from the first day of host removal. The implications of these patterns of vector dispersal in a field setting are not yet known but could result in movement towards human rooms.
DEFF Research Database (Denmark)
Dridi, Kim; Bjarklev, Anders Overgaard
1999-01-01
An electromagnetic vector-field modle for design of optical components based on the finite-difference-time-domain method and radiation integrals in presented. Its ability to predict the optical electromagnetic dynamics in structures with complex material distribution is demonstrated. Theoretical...
Park, Kyoung-Duck; Raschke, Markus B.
2018-05-01
Controlling the propagation and polarization vectors in linear and nonlinear optical spectroscopy enables to probe the anisotropy of optical responses providing structural symmetry selective contrast in optical imaging. Here we present a novel tilted antenna-tip approach to control the optical vector-field by breaking the axial symmetry of the nano-probe in tip-enhanced near-field microscopy. This gives rise to a localized plasmonic antenna effect with significantly enhanced optical field vectors with control of both \\textit{in-plane} and \\textit{out-of-plane} components. We use the resulting vector-field specificity in the symmetry selective nonlinear optical response of second-harmonic generation (SHG) for a generalized approach to optical nano-crystallography and -imaging. In tip-enhanced SHG imaging of monolayer MoS$_2$ films and single-crystalline ferroelectric YMnO$_3$, we reveal nano-crystallographic details of domain boundaries and domain topology with enhanced sensitivity and nanoscale spatial resolution. The approach is applicable to any anisotropic linear and nonlinear optical response, and provides for optical nano-crystallographic imaging of molecular or quantum materials.
International Nuclear Information System (INIS)
Meyer, R.-L.
1975-01-01
The evolution of the scattering cross section maximas of an electromagnetic wave by a magnetoplasma, the angle between the wave vector and the confining magnetic field approaching π/2 were computed. It is shown that the maximas are shifted toward the roots of the electrostatic dispersion relation in perpendicular propagation. These roots are not exactly the electron cyclotron harmonics [fr
A Class of Quasi-exact Solutions of Rabi Hamiltonian
International Nuclear Information System (INIS)
Pan Feng; Yao Youkun; Xie Mingxia; Han Wenjuan; Draayer, J.P.
2007-01-01
A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems
Homogeneous collapsing star: Tensor and vector harmonics for matter and field asymmetries
International Nuclear Information System (INIS)
Gerlach, U.H.; Sengupta, U.K.
1978-01-01
For the space-time of the interior of a homogeneous collapsing star complete sets of orthogonal vector and tensor harmonics are presented. Their relationship to the set of vector and tensor harmonics for a generic spherically symmetric space-time is exhibited
An adaptive radiotherapy planning strategy for bladder cancer using deformation vector fields
International Nuclear Information System (INIS)
Vestergaard, Anne; Kallehauge, Jesper Folsted; Petersen, Jørgen Breede Baltzer; Høyer, Morten; Søndergaard, Jimmi; Muren, Ludvig Paul
2014-01-01
Purpose: Adaptive radiotherapy (ART) has considerable potential in treatment of bladder cancer due to large inter-fractional changes in shape and size of the target. The aim of this study was to compare our clinically applied method for plan library creation that involves manual bladder delineations (Clin-ART) with a method using the deformation vector fields (DVFs) resulting from intensity-based deformable image registrations (DVF-based ART). Materials and methods: The study included thirteen patients with urinary bladder cancer who had daily cone beam CTs (CBCTs) acquired for set-up. In both ART strategies investigated, three plan selection volumes were generated using the CBCTs from the first four fractions; in Clin-ART boolean combinations of delineated bladders were used, while the DVF-based strategy applied combinations of the mean and standard deviation of patient-specific DVFs. The volume ratios (VRs) of the course-averaged PTV for the two ART strategies relative the non-adaptive PTV were calculated. Results: Both Clin-ART and DVF-based ART considerably reduced the course-averaged PTV, compared to non-adaptive RT. The VR for DVF-based ART was lower than for Clin-ART (0.65 vs. 0.73; p < 0.01). Conclusions: DVF-based ART for bladder irradiation has a considerable normal tissue sparing potential surpassing our already highly conformal clinically applied ART strategy