15,091 research outputs found
Analytical Approximation Methods for the Stabilizing Solution of the Hamilton–Jacobi Equation
In this paper, two methods for approximating the stabilizing solution of the Hamilton–Jacobi equation are proposed using symplectic geometry and a Hamiltonian perturbation technique as well as stable manifold theory. The first method uses the fact that the Hamiltonian lifted system of an integrable system is also integrable and regards the corresponding Hamiltonian system of the Hamilton–Jacobi equation as an integrable Hamiltonian system with a perturbation caused by control. The second method directly approximates the stable flow of the Hamiltonian systems using a modification of stable manifold theory. Both methods provide analytical approximations of the stable Lagrangian submanifold from which the stabilizing solution is derived. Two examples illustrate the effectiveness of the methods.
Spacecraft telecommunications system mass estimates
Mass is the most important limiting parameter for present-day planetary spacecraft design, In fact, the entire design can be characterized by mass. The more efficient the design of the spacecraft, the less mass will be required. The communications system is an essential and integral part of planetary spacecraft. A study is presented of the mass attributable to the communications system for spacecraft designs used in recent missions in an attempt to help guide future design considerations and research and development efforts. The basic approach is to examine the spacecraft by subsystem and allocate a portion of each subsystem to telecommunications. Conceptually, this is to divide the spacecraft into two parts, telecommunications and nontelecommunications. In this way, it is clear what the mass attributable to the communications system is. The percentage of mass is calculated using the actual masses of the spacecraft parts, except in the case of CRAF. In that case, estimated masses are used since the spacecraft was not yet built. The results show that the portion of the spacecraft attributable to telecommunications is substantial. The mass fraction for Voyager, Galileo, and CRAF (Mariner Mark 2) is 34, 19, and 18 percent, respectively. The large reduction of telecommunications mass from Voyager to Galileo is mainly due to the use of a deployable antenna instead of the solid antenna on Voyager
An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian
We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic
field in the n-dimensional torus. We obtained a complete set of solutions for a
broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a
quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice
{\Lambda}. The lattice is not necessary either cubic or rectangular. The
magnetic field is also arbitrary. However, we restrict ourselves within
potential-free problems; the Schr{\"o}dinger operator is assumed to be the
Laplace operator defined with the covariant derivative. We defined an algebra
that characterizes the symmetry of the Laplacian and named it the magnetic
algebra. We proved that the space of functions on which the Laplacian acts is
an irreducible representation space of the magnetic algebra. In this sense the
magnetic algebra completely characterizes the quantum mechanics in the magnetic
torus. We developed a new method for Fourier analysis for the magnetic torus
and used it to solve the eigenvalue problem of the Laplacian. All the
eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad
Quantum Scattering in Two Black Hole Moduli Space
We discuss the quantum scattering process in the moduli space consisting of
two maximally charged dilaton black holes. The black hole moduli space geometry
has different structures for arbitrary dimensions and various values of dilaton
coupling. We study the quantum effects of the different moduli space geometries
with scattering process. Then, it is found that there is a resonance state on
certain moduli spaces.Comment: 15 pages, 19 figures, RevTeX 3.
Microwave radiometric studies and ground truth measurements of the NASA/USGS Southern California test site
The field measurement program conducted at the NASA/USGS Southern California Test Site is discussed. Ground truth data and multifrequency microwave brightness data were acquired by a mobile field laboratory operating in conjunction with airborne instruments. The ground based investigations were performed at a number of locales representing a variety of terrains including open desert, cultivated fields, barren fields, portions of the San Andreas Fault Zone, and the Salton Sea. The measurements acquired ground truth data and microwave brightness data at wavelengths of 0.8 cm, 2.2 cm, and 21 cm
Magnetic translation groups in an n-dimensional torus
A charged particle in a uniform magnetic field in a two-dimensional torus has
a discrete noncommutative translation symmetry instead of a continuous
commutative translation symmetry. We study topology and symmetry of a particle
in a magnetic field in a torus of arbitrary dimensions. The magnetic
translation group (MTG) is defined as a group of translations that leave the
gauge field invariant. We show that the MTG on an n-dimensional torus is
isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x
Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible
unitary representations of the MTG on a three-torus and apply the
representation theory to three examples. We shortly describe a representation
theory for a general n-torus. The MTG on an n-torus can be regarded as a
generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in
Journal of Mathematical Physic
-folds from Yang-Baxter deformations
Yang-Baxter (YB) deformations of type IIB string theory have been well
studied from the viewpoint of classical integrability. Most of the works,
however, are focused upon the local structure of the deformed geometries and
the global structure still remains unclear. In this work, we reveal a
non-geometric aspect of YB-deformed backgrounds as -fold by explicitly
showing the associated -duality monodromy. In
particular, the appearance of an extra vector field in the generalized
supergravity equations (GSE) leads to the non-geometric -flux. In addition,
we study a particular solution of GSE that is obtained by a non-Abelian
-duality but cannot be expressed as a homogeneous YB deformation, and show
that it can also be regarded as a -fold. This result indicates that
solutions of GSE should be non-geometric quite in general beyond the YB
deformation.Comment: 47 page
Supersymmetry in gauge theories with extra dimensions
We show that a quantum-mechanical N=2 supersymmetry is hidden in 4d mass
spectrum of any gauge invariant theories with extra dimensions. The N=2
supercharges are explicitly constructed in terms of differential forms. The
analysis can be extended to extra dimensions with boundaries, and for a single
extra dimension we clarify a possible set of boundary conditions consistent
with 5d gauge invariance, although some of the boundary conditions break 4d
gauge symmetries.Comment: 18 page
- …