744 research outputs found
Hamilton-Jacobi Diffieties
Diffieties formalize geometrically the concept of differential equations. We
introduce and study Hamilton-Jacobi diffieties. They are finite dimensional
subdiffieties of a given diffiety and appear to play a special role in the
field theoretic version of the geometric Hamilton-Jacobi theory.Comment: 31 pages, to appear in Journal of Geometry and Physics, slight
changes in the presentation to match the version accepted by the journa
Iterated Differential Forms III: Integral Calculus
Basic elements of integral calculus over algebras of iterated differential
forms, are presented. In particular, defining complexes for modules of integral
forms are described and the corresponding berezinians and complexes of integral
forms are computed. Various applications and the integral calculus over the
algebra will be discussed in subsequent notes.Comment: 7 pages, submitted to Math. Dok
Iterated Differential Forms VI: Differential Equations
We describe the first term of the --spectral
sequence (see math.DG/0610917) of the diffiety (E,C), E being the infinite
prolongation of an l-normal system of partial differential equations, and C the
Cartan distribution on it.Comment: 8 pages, to appear in Dokl. Mat
Iterated Differential Forms V: C-Spectral Sequence on Infinite Jet Spaces
In the preceding note math.DG/0610917 the
--spectral sequence, whose first term is composed of
\emph{secondary iterated differential forms}, was constructed for a generic
diffiety. In this note the zero and first terms of this spectral sequence are
explicitly computed for infinite jet spaces. In particular, this gives an
explicit description of secondary covariant tensors on these spaces and some
basic operations with them. On the basis of these results a description of the
--spectral sequence for infinitely prolonged PDE's
will be given in the subsequent note.Comment: 9 pages, to appear in Math. Dok
The Hamilton-Jacobi Formalism for Higher Order Field Theories
We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics
to higher order field theories with regular lagrangian density. We also
investigate the dependence of the formalism on the lagrangian density in the
class of those yelding the same Euler-Lagrange equations.Comment: 25 page
electron-positron-photon plasma around a collapsing star
We describe electron-positron pairs creation around an electrically charged
star core collapsing to an electromagnetic black hole (EMBH), as well as pairs
annihilation into photons. We use the kinetic Vlasov equation formalism for the
pairs and photons and show that a regime of plasma oscillations is established
around the core. As a byproduct of our analysis we can provide an estimate for
the thermalization time scale.Comment: 8 pages, 4 figures, to appear in the Proceedings of QABP200
Partial Differential Hamiltonian Systems
We define partial differential (PD in the following), i.e., field theoretic
analogues of Hamiltonian systems on abstract symplectic manifolds and study
their main properties, namely, PD Hamilton equations, PD Noether theorem, PD
Poisson bracket, etc.. Unlike in standard multisymplectic approach to
Hamiltonian field theory, in our formalism, the geometric structure
(kinematics) and the dynamical information on the "phase space" appear as just
different components of one single geometric object.Comment: 30 pages, the current version agrees with the published versio
Spin squeezing and entanglement for arbitrary spin
A complete set of generalized spin-squeezing inequalities is derived for an
ensemble of particles with an arbitrary spin. Our conditions are formulated
with the first and second moments of the collective angular momentum
coordinates. A method for mapping the spin-squeezing inequalities for spin-1/2
particles to entanglement conditions for spin-j particles is also presented. We
apply our mapping to obtain a generalization of the original spin-squeezing
inequality to higher spins. We show that, for large particle numbers, a
spin-squeezing parameter for entanglement detection based on one of our
inequalities is strictly stronger than the original spin-squeezing parameter
defined in [A. Sorensen et al., Nature 409, 63 (2001)]. We present a coordinate
system independent form of our inequalities that contains, besides the
correlation and covariance tensors of the collective angular momentum
operators, the nematic tensor appearing in the theory of spin nematics.
Finally, we discuss how to measure the quantities appearing in our inequalities
in experiments.Comment: 18 pages including 3 figures, revtex4; v2: references added, typos
corrected; v3: typos corrected, published versio
Domain modeling and grid generation for multi-block structured grids with application to aerodynamic and hydrodynamic configurations
About five years ago, a joint development was started of a flow simulation system for engine-airframe integration studies on propeller as well as jet aircraft. The initial system was based on the Euler equations and made operational for industrial aerodynamic design work. The system consists of three major components: a domain modeller, for the graphical interactive subdivision of flow domains into an unstructured collection of blocks; a grid generator, for the graphical interactive computation of structured grids in blocks; and a flow solver, for the computation of flows on multi-block grids. The industrial partners of the collaboration and NLR have demonstrated that the domain modeller, grid generator and flow solver can be applied to simulate Euler flows around complete aircraft, including propulsion system simulation. Extension to Navier-Stokes flows is in progress. Delft Hydraulics has shown that both the domain modeller and grid generator can also be applied successfully for hydrodynamic configurations. An overview is given about the main aspects of both domain modelling and grid generation
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