28,262 research outputs found
One Controller at a Time (1-CAT): A mimo design methodology
The One Controller at a Time (1-CAT) methodology for designing digital controllers for Large Space Structures (LSS's) is introduced and illustrated. The flexible mode problem is first discussed. Next, desirable features of a LSS control system design methodology are delineated. The 1-CAT approach is presented, along with an analytical technique for carrying out the 1-CAT process. Next, 1-CAT is used to design digital controllers for the proposed Space Based Laser (SBL). Finally, the SBL design is evaluated for dynamical performance, noise rejection, and robustness
Dirac--Lie systems and Schwarzian equations
A Lie system is a system of differential equations admitting a superposition
rule, i.e., a function describing its general solution in terms of any generic
set of particular solutions and some constants. Following ideas going back to
the Dirac's description of constrained systems, we introduce and analyse a
particular class of Lie systems on Dirac manifolds, called Dirac--Lie systems,
which are associated with `Dirac--Lie Hamiltonians'. Our results enable us to
investigate constants of the motion, superposition rules, and other general
properties of such systems in a more effective way. Several concepts of the
theory of Lie systems are adapted to this `Dirac setting' and new applications
of Dirac geometry in differential equations are presented. As an application,
we analyze traveling wave solutions of Schwarzian equations, but our methods
can be applied also to other classes of differential equations important for
Physics.Comment: 41 page
Injection locking of two frequency-doubled lasers with 3.2 GHz offset for driving Raman transitions with low photon scattering in Ca
We describe the injection locking of two infrared (794 nm) laser diodes which
are each part of a frequency-doubled laser system. An acousto-optic modulator
(AOM) in the injection path gives an offset of 1.6 GHz between the lasers for
driving Raman transitions between states in the hyperfine split (by 3.2 GHz)
ground level of Ca. The offset can be disabled for use in
Ca. We measure the relative linewidth of the frequency-doubled beams
to be 42 mHz in an optical heterodyne measurement. The use of both injection
locking and frequency doubling combines spectral purity with high optical
power. Our scheme is applicable for providing Raman beams across other ion
species and neutral atoms where coherent optical manipulation is required.Comment: 3 pages, 3 figure
Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
The momentum distribution in a Fermi gas with two spin states and a large
scattering length has a tail that falls off like 1/k^4 at large momentum k, as
pointed out by Shina Tan. He used novel methods to derive exact relations
between the coefficient of the tail in the momentum distribution and various
other properties of the system. We present simple derivations of these
relations using the operator product expansion for quantum fields. We identify
the coefficient as the integral over space of the expectation value of a local
operator that measures the density of pairs.Comment: 4 pages, 2 figure
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