2,060 research outputs found
Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic Field
In this paper we consider the minimum time population transfer problem for
the -component of the spin of a (spin 1/2) particle driven by a magnetic
field, controlled along the x axis, with bounded amplitude. On the Bloch sphere
(i.e. after a suitable Hopf projection), this problem can be attacked with
techniques of optimal syntheses on 2-D manifolds. Let be the two
energy levels, and the bound on the field amplitude. For
each couple of values and , we determine the time optimal synthesis
starting from the level and we provide the explicit expression of the time
optimal trajectories steering the state one to the state two, in terms of a
parameter that can be computed solving numerically a suitable equation. For
, every time optimal trajectory is bang-bang and in particular the
corresponding control is periodic with frequency of the order of the resonance
frequency . On the other side, for , the time optimal
trajectory steering the state one to the state two is bang-bang with exactly
one switching. Fixed we also prove that for the time needed to
reach the state two tends to zero. In the case there are time optimal
trajectories containing a singular arc. Finally we compare these results with
some known results of Khaneja, Brockett and Glaser and with those obtained by
controlling the magnetic field both on the and directions (or with one
external field, but in the rotating wave approximation). As byproduct we prove
that the qualitative shape of the time optimal synthesis presents different
patterns, that cyclically alternate as , giving a partial proof of a
conjecture formulated in a previous paper.Comment: 31 pages, 10 figures, typos correcte
Quantum control of molecular rotation
The angular momentum of molecules, or, equivalently, their rotation in
three-dimensional space, is ideally suited for quantum control. Molecular
angular momentum is naturally quantized, time evolution is governed by a
well-known Hamiltonian with only a few accurately known parameters, and
transitions between rotational levels can be driven by external fields from
various parts of the electromagnetic spectrum. Control over the rotational
motion can be exerted in one-, two- and many-body scenarios, thereby allowing
to probe Anderson localization, target stereoselectivity of bimolecular
reactions, or encode quantum information, to name just a few examples. The
corresponding approaches to quantum control are pursued within separate, and
typically disjoint, subfields of physics, including ultrafast science, cold
collisions, ultracold gases, quantum information science, and condensed matter
physics. It is the purpose of this review to present the various control
phenomena, which all rely on the same underlying physics, within a unified
framework. To this end, we recall the Hamiltonian for free rotations, assuming
the rigid rotor approximation to be valid, and summarize the different ways for
a rotor to interact with external electromagnetic fields. These interactions
can be exploited for control --- from achieving alignment, orientation, or
laser cooling in a one-body framework, steering bimolecular collisions, or
realizing a quantum computer or quantum simulator in the many-body setting.Comment: 52 pages, 11 figures, 607 reference
Magnetic bearings-state of the art
Magnetic bearings have existed for many years, at least in theory. Earnshaw's theorem, formulated in 1842, concerns stability of magnetic suspensions, and states that not all axes of a bearing can be stable without some means of active control. In Beam's widely referenced experiments, a tiny (1/64 in diameter) rotor was rotated to the astonishing speed of 800,000 rps while it was suspended in a magnetic field. Despite a long history, magnetic bearings have only begun to see practical application since about 1980. The development that finally made magnetic bearings practical was solid state electronics, enabling power supplies and controls to be reduced in size to where they are now comparable in volume to the bearings themselves. An attempt is made to document the current (1991) state of the art of magnetic bearings. The referenced papers are large drawn from two conferences publications published in 1988 and 1990 respectively
On the Eigenvalue Distribution for a Beam with Attached Masses
We study a mathematical model of a hinged flexible beam with piezoelectric
actuators and electromagnetic shaker in this paper. The shaker is modelled as a
mass and spring system attached to the beam. To analyze free vibrations of this
mechanical system, we consider the corresponding spectral problem for a
fourth-order differential operator with interface conditions that characterize
the shaker dynamics. The characteristic equation is studied analytically, and
asymptotic estimates of eigenvalues are obtained. The eigenvalue distribution
is also illustrated by numerical simulations under a realistic choice of
mechanical parameters.Comment: Accepted for publication in the special issue "Stabilization of
Distributed Parameter Systems: Design Methods and Applications", SEMA SIMAI
Springer Serie
Some components of safety and comfort of a car
This paper addresses the need to minimize of vibration levels of unsprung weight of elements of vehicles suspension are considered. In the study design, some methods of parametric optimization with dynamic vibration absorbers (DVA) in elements of a nonlinear suspension with dynamic mechanical properties have been applied. To determine the low frequency components of vibration of laminated composite plates with the DVA system numerical estimates of the vibration of the equivalent plate of Timoshenko used. One structural version for ensuring the preservation of the residual space of the passenger cabin of the bus during the rollover according to norms 66 is considered. The energy-absorbing structure of the roof of the bus is made in the form of tubular space-frame made of composite materials
Technology for large space systems: A special bibliography with indexes (supplement 06)
This bibliography lists 220 reports, articles and other documents introduced into the NASA scientific and technical information system between July 1, 1981 and December 31, 1981. Its purpose is to provide helpful information to the researcher, manager, and designer in technology development and mission design in the area of the Large Space Systems Technology (LSST) Program. Subject matter is grouped according to systems, interactive analysis and design, structural concepts, control systems, electronics, advanced materials, assembly concepts, propulsion, solar power satellite systems, and flight experiments
Nonisotropic 3-level Quantum Systems: Complete Solutions for Minimum Time and Minimum Energy
We apply techniques of subriemannian geometry on Lie groups and of optimal
synthesis on 2-D manifolds to the population transfer problem in a three-level
quantum system driven by two laser pulses, of arbitrary shape and frequency. In
the rotating wave approximation, we consider a nonisotropic model i.e. a model
in which the two coupling constants of the lasers are different. The aim is to
induce transitions from the first to the third level, minimizing 1) the time of
the transition (with bounded laser amplitudes),
2) the energy of lasers (with fixed final time). After reducing the problem
to real variables, for the purpose 1) we develop a theory of time optimal
syntheses for distributional problem on 2-D-manifolds, while for the purpose 2)
we use techniques of subriemannian geometry on 3-D Lie groups. The complete
optimal syntheses are computed.Comment: 29 pages, 6 figure
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