29,499 research outputs found
Composite oscillator systems for meeting user needs for time and frequency
Frequency standards are used in most navigation and telecommunications systems to provide a long term memory of either frequency, phase, or time epoch. From a systems point of view, the performance aspects of the frequency standard are weighed against other systems characteristics, such as overall performance, cost, size, and accessibility; a number of examples are very briefly reviewed. The theory of phase lock and frequency lock systems is outlined in sufficient detail that total oscillator system performance can be predicted from measurements on the individual components. As an example, details of the performance of a high spectral purity oscillator phase locked to a long term stable oscillator are given. Results for several systems, including the best system stability that can be obtained from present commercially available 5-MHz sources, are shown
The Effects of Weak Spatiotemporal Noise on a Bistable One-Dimensional System
We treat analytically a model that captures several features of the
phenomenon of spatially inhomogeneous reversal of an order parameter. The model
is a classical Ginzburg-Landau field theory restricted to a bounded
one-dimensional spatial domain, perturbed by weak spatiotemporal noise having a
flat power spectrum in time and space. Our analysis extends the Kramers theory
of noise-induced transitions to the case when the system acted on by the noise
has nonzero spatial extent, and the noise itself is spatially dependent. By
extending the Langer-Coleman theory of the noise-induced decay of a metastable
state, we determine the dependence of the activation barrier and the Kramers
reversal rate prefactor on the size of the spatial domain. As this is increased
from zero and passes through a certain critical value, a transition between
activation regimes occurs, at which the rate prefactor diverges. Beyond the
transition, reversal preferentially takes place in a spatially inhomogeneous
rather than in a homogeneous way. Transitions of this sort were not discovered
by Langer or Coleman, since they treated only the infinite-volume limit. Our
analysis uses higher transcendental functions to handle the case of finite
volume. Similar transitions between activation regimes should occur in other
models of metastable systems with nonzero spatial extent, perturbed by weak
noise, as the size of the spatial domain is varied.Comment: 16 page
Digital adaptive controllers for VTOL vehicles. Volume 1: Concept evaluation
A digital self-adaptive flight control system was developed for flight test in the VTOL approach and landing technology (VALT) research aircraft (a modified CH-47 helicopter). The control laws accept commands from an automatic on-board guidance system. The primary objective of the control laws is to provide good command-following with a minimum cross-axis response. Three attitudes and vertical velocity are separately commanded. Adaptation of the control laws is based on information from rate and attitude gyros and a vertical velocity measurement. The final design resulted from a comparison of two different adaptive concepts--one based on explicit parameter estimates from a real-time maximum-likelihood estimation algorithm, the other based on an implicit model reference adaptive system. The two designs were compared on the basis of performance and complexity
Digital adaptive controllers for VTOL vehicles. Volume 2: Software documentation
The VTOL approach and landing test (VALT) adaptive software is documented. Two self-adaptive algorithms, one based on an implicit model reference design and the other on an explicit parameter estimation technique were evaluated. The organization of the software, user options, and a nominal set of input data are presented along with a flow chart and program listing of each algorithm
Noisy Classical Field Theories with Two Coupled Fields: Dependence of Escape Rates on Relative Field Stiffnesses
Exit times for stochastic Ginzburg-Landau classical field theories with two
or more coupled classical fields depend on the interval length on which the
fields are defined, the potential in which the fields deterministically evolve,
and the relative stiffness of the fields themselves. The latter is of
particular importance in that physical applications will generally require
different relative stiffnesses, but the effect of varying field stiffnesses has
not heretofore been studied. In this paper, we explore the complete phase
diagram of escape times as they depend on the various problem parameters. In
addition to finding a transition in escape rates as the relative stiffness
varies, we also observe a critical slowing down of the string method algorithm
as criticality is approached.Comment: 16 pages, 10 figure
Asymptotic Exit Location Distributions in the Stochastic Exit Problem
Consider a two-dimensional continuous-time dynamical system, with an
attracting fixed point . If the deterministic dynamics are perturbed by
white noise (random perturbations) of strength , the system state
will eventually leave the domain of attraction of . We analyse the
case when, as , the exit location on the boundary
is increasingly concentrated near a saddle point of the
deterministic dynamics. We show that the asymptotic form of the exit location
distribution on is generically non-Gaussian and asymmetric,
and classify the possible limiting distributions. A key role is played by a
parameter , equal to the ratio of the stable
and unstable eigenvalues of the linearized deterministic flow at . If
then the exit location distribution is generically asymptotic as
to a Weibull distribution with shape parameter , on the
length scale near . If it is generically
asymptotic to a distribution on the length scale, whose
moments we compute. The asymmetry of the asymptotic exit location distribution
is attributable to the generic presence of a `classically forbidden' region: a
wedge-shaped subset of with as vertex, which is reached from ,
in the limit, only via `bent' (non-smooth) fluctuational paths
that first pass through the vicinity of . We deduce from the presence of
this forbidden region that the classical Eyring formula for the
small- exponential asymptotics of the mean first exit time is
generically inapplicable.Comment: This is a 72-page Postscript file, about 600K in length. Hardcopy
requests to [email protected] or [email protected]
The Order of Phase Transitions in Barrier Crossing
A spatially extended classical system with metastable states subject to weak
spatiotemporal noise can exhibit a transition in its activation behavior when
one or more external parameters are varied. Depending on the potential, the
transition can be first or second-order, but there exists no systematic theory
of the relation between the order of the transition and the shape of the
potential barrier. In this paper, we address that question in detail for a
general class of systems whose order parameter is describable by a classical
field that can vary both in space and time, and whose zero-noise dynamics are
governed by a smooth polynomial potential. We show that a quartic potential
barrier can only have second-order transitions, confirming an earlier
conjecture [1]. We then derive, through a combination of analytical and
numerical arguments, both necessary conditions and sufficient conditions to
have a first-order vs. a second-order transition in noise-induced activation
behavior, for a large class of systems with smooth polynomial potentials of
arbitrary order. We find in particular that the order of the transition is
especially sensitive to the potential behavior near the top of the barrier.Comment: 8 pages, 6 figures with extended introduction and discussion; version
accepted for publication by Phys. Rev.
Relationships Between the Performance of Time/Frequency Standards and Navigation/Communication Systems
The relationship between system performance and clock or oscillator performance is discussed. Tradeoffs discussed include: short term stability versus bandwidth requirements; frequency accuracy versus signal acquisition time; flicker of frequency and drift versus resynchronization time; frequency precision versus communications traffic volume; spectral purity versus bit error rate, and frequency standard stability versus frequency selection and adjustability. The benefits and tradeoffs of using precise frequency and time signals are various levels of precision and accuracy are emphasized
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