367 research outputs found
Gravitational Constraint Combinations Generate a Lie Algebra
We find a first--order partial differential equation whose solutions are all
ultralocal scalar combinations of gravitational constraints with Abelian
Poisson brackets between themselves. This is a generalisation of the Kucha\v{r}
idea of finding alternative constraints for canonical gravity. The new scalars
may be used in place of the hamiltonian constraint of general relativity and,
together with the usual momentum constraints, replace the Dirac algebra for
pure gravity with a true Lie algebra: the semidirect product of the Abelian
algebra of the new constraint combinations with the algebra of spatial
diffeomorphisms.Comment: 10 pages, latex, submitted to Classical and Quantum Gravity. Section
3 is expanded and an additional solution provided, minor errors correcte
Hazard Avoidance Alerting With Markov Decision Processes
This thesis describes an approach to designing hazard avoidance alerting systems based on a
Markov decision process (MDP) model of the alerting process, and shows its benefits over
standard design methods. One benefit of the MDP method is that it accounts for future decision
opportunities when choosing whether or not to alert, or in determining resolution guidance.
Another benefit is that it provides a means of modeling uncertain state information, such as
knowledge about unmeasurable mode variables, so that decisions are more informed.
A mode variable is an index for distinct types of behavior that a system exhibits at different
times. For example, in many situations normal system behavior is safe, but rare deviations from
the normal increase the likelihood of a harmful incident. Accurate modeling of mode
information is needed to minimize alerting system errors such as unnecessary or late alerts.
The benefits of the method are illustrated with two alerting scenarios where a pair of aircraft
must avoid collisions when passing one another. The first scenario has a fully observable state
and the second includes an uncertain mode describing whether an intruder aircraft levels off
safely above the evader or is in a hazardous blunder mode.
In MDP theory, outcome preferences are described in terms of utilities of different state
trajectories. In keeping with this, alerting system requirements are stated in the form of a reward
function. This is then used with probabilistic dynamic and sensor models to compute an alerting
logic (policy) that maximizes expected utility. Performance comparisons are made between the
MDP-based logics and alternate logics generated with current methods. It is found that in terms
of traditional performance measures (incident rate and unnecessary alert rate), the MDP-based
logic can meet or exceed that of alternate logics
Generalized Philosophy of Alerting with Applications for Parallel Approach Collision Prevention
An alerting system is automation designed to reduce the likelihood of undesirable
outcomes that are due to rare failures in a human-controlled system. It accomplishes this
by monitoring the system, and issuing warning messages to the human operators when
thought necessary to head off a problem. On examination of existing and recently
proposed logics for alerting it appears that few commonly accepted principles guide the
design process. Different logics intended to address the same hazards may take disparate
forms and emphasize different aspects of performance, because each reflects the intuitive
priorities of a different designer. Because performance must be satisfactory to all users
of an alerting system (implying a universal meaning of acceptable performance) and not
just one designer, a proposed logic often undergoes significant piecemeal modification
before gaining general acceptance. This report is an initial attempt to clarify the common
performance goals by which an alerting system is ultimately judged. A better
understanding of these goals will hopefully allow designers to reach the final logic in a
quicker, more direct and repeatable manner. As a case study, this report compares three
alerting logics for collision prevention during independent approaches to parallel
runways, and outlines a fourth alternative incorporating elements of the first three, but
satisfying stated requirements.NASA grant NAG1-218
Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a Torus in the Ashtekar Formulation
We examine the reduced phase space of the Barbero-Varadarajan solutions of
the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We
show that it is a finite-dimensional space due to existence of an infinite
dimensional residual gauge invariance which reduces the infinite-dimensional
space of solutions to a finite-dimensional space of gauge-inequivalent
solutions. This is in agreement with general arguments which imply that the
number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on
a torus is finite.Comment: 13 pages, Latex. More details have been included and the expression
for the finite residual gauge transformations has been worked ou
High frequency conductivity in the quantum Hall effect
We present high frequency measurements of the diagonal conductivity sigma_xx
of a two dimensional electron system in the integer quantum Hall regime. The
width of the sigma_xx peaks between QHE minima is analyzed within the framework
of scaling theory using both temperature T=100-700 mK and frequency f <= 6 GHz
in a two parameter scaling ansatz. For the plateau transition width we find
scaling behaviour for both its temperature dependence as well as its frequency
dependence. However, the corresponding scaling exponent for temperature
kappa=0.42 significantly differs from the one deduced for frequency scaling
(c=0.6). Additionally we use the high frequency experiments to suppress the
contact resistances that strongly influences DC measurements. We find an
intrinsic critical conductivity sigma_c=0.17e^2/h, virtually independent of
temperature and filling factor, and deviating significantly from the proposed
universal value 0.5e^2/h.Comment: Proceedings of the '14th international conference on high magnetic
fields in semiconductor physics' (Semimag-2000) in Matsue, Japa
Canonical Gravity, Diffeomorphisms and Objective Histories
This paper discusses the implementation of diffeomorphism invariance in
purely Hamiltonian formulations of General Relativity. We observe that, if a
constrained Hamiltonian formulation derives from a manifestly covariant
Lagrangian, the diffeomorphism invariance of the Lagrangian results in the
following properties of the constrained Hamiltonian theory: the diffeomorphisms
are generated by constraints on the phase space so that a) The algebra of the
generators reflects the algebra of the diffeomorphism group. b) The Poisson
brackets of the basic fields with the generators reflects the space-time
transformation properties of these basic fields. This suggests that in a purely
Hamiltonian approach the requirement of diffeomorphism invariance should be
interpreted to include b) and not just a) as one might naively suppose. Giving
up b) amounts to giving up objective histories, even at the classical level.
This observation has implications for Loop Quantum Gravity which are spelled
out in a companion paper. We also describe an analogy between canonical gravity
and Relativistic particle dynamics to illustrate our main point.Comment: Latex 16 Pages, no figures, revised in the light of referees'
comments, accepted for publication in Classical and Quantum Gravit
Action and Hamiltonian for eternal black holes
We present the Hamiltonian, quasilocal energy, and angular momentum for a
spacetime region spatially bounded by two timelike surfaces. The results are
applied to the particular case of a spacetime representing an eternal black
hole. It is shown that in the case when the boundaries are located in two
different wedges of the Kruskal diagram, the Hamiltonian is of the form , where and are the Hamiltonian functions for the right
and left wedges respectively. The application of the obtained results to the
thermofield dynamics description of quantum effects in black holes is briefly
discussed.Comment: 24 pages, Revtex, 5 figures (available upon request
Dynamical scaling of the quantum Hall plateau transition
Using different experimental techniques we examine the dynamical scaling of
the quantum Hall plateau transition in a frequency range f = 0.1-55 GHz. We
present a scheme that allows for a simultaneous scaling analysis of these
experiments and all other data in literature. We observe a universal scaling
function with an exponent kappa = 0.5 +/- 0.1, yielding a dynamical exponent z
= 0.9 +/- 0.2.Comment: v2: Length shortened to fulfil Journal criteri
Time evolution and observables in constrained systems
The discussion is limited to first-class parametrized systems, where the
definition of time evolution and observables is not trivial, and to finite
dimensional systems in order that technicalities do not obscure the conceptual
framework. The existence of reasonable true, or physical, degrees of freedom is
rigorously defined and called {\em local reducibility}. A proof is given that
any locally reducible system admits a complete set of perennials. For locally
reducible systems, the most general construction of time evolution in the
Schroedinger and Heisenberg form that uses only geometry of the phase space is
described. The time shifts are not required to be 1symmetries. A relation
between perennials and observables of the Schroedinger or Heisenberg type
results: such observables can be identified with certain classes of perennials
and the structure of the classes depends on the time evolution. The time
evolution between two non-global transversal surfaces is studied. The problem
is posed and solved within the framework of the ordinary quantum mechanics. The
resulting non-unitarity is different from that known in the field theory
(Hawking effect): state norms need not be preserved so that the system can be
lost during the evolution of this kind.Comment: 31 pages, Latex fil
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