1,754 research outputs found
Z_3-graded exterior differential calculus and gauge theories of higher order
We present a possible generalization of the exterior differential calculus,
based on the operator d such that d^3=0, but d^2\not=0. The first and second
order differentials generate an associative algebra; we shall suppose that
there are no binary relations between first order differentials, while the
ternary products will satisfy the cyclic relations based on the representation
of cyclic group Z_3 by cubic roots of unity. We shall attribute grade 1 to the
first order differentials and grade 2 to the second order differentials; under
the associative multiplication law the grades add up modulo 3. We show how the
notion of covariant derivation can be generalized with a 1-form A, and we give
the expression in local coordinates of the curvature 3-form. Finally, the
introduction of notions of a scalar product and integration of the Z_3-graded
exterior forms enables us to define variational principle and to derive the
differential equations satisfied by the curvature 3-form. The Lagrangian
obtained in this way contains the invariants of the ordinary gauge field tensor
F_{ik} and its covariant derivatives D_i F_{km}.Comment: 13 pages, no figure
Mariner Mars 1969 SCAN control subsystem design and analysis
Design and analysis of self correcting automatic navigation system for Mariner Mars spacecraf
Traffic Network Optimum Principle - Minimum Probability of Congestion Occurrence
We introduce an optimum principle for a vehicular traffic network with road
bottlenecks. This network breakdown minimization (BM) principle states that the
network optimum is reached, when link flow rates are assigned in the network in
such a way that the probability for spontaneous occurrence of traffic breakdown
at one of the network bottlenecks during a given observation time reaches the
minimum possible value. Based on numerical simulations with a stochastic
three-phase traffic flow model, we show that in comparison to the well-known
Wardrop's principles the application of the BM principle permits considerably
greater network inflow rates at which no traffic breakdown occurs and,
therefore, free flow remains in the whole network.Comment: 22 pages, 6 figure
Phase diagram of congested traffic flow: an empirical study
We analyze traffic data from a highway section containing one effective
on-ramp. Based on two criteria, local velocity variation patterns and expansion
(or nonexpansion) of congested regions, three distinct congested traffic states
are identified. These states appear at different levels of the upstream flux
and the on-ramp flux, thereby generating a phase diagram of the congested
traffic flow. Compared to our earliear reports (including cond-mat/9905292)
based on 14 day traffic data, the present paper uses a much larger data set
(107 days) and the analysis is carried in a more systematic way, which leads to
the modification of a part of interpretation in the earlier reports. Observed
traffic states are compared with recent theoretical analyses and both agreeing
and disagreeing features are found.Comment: More extensive and systematic version of earlier reports (including
cond-mat/9905292). A part of interpretation in earlier reports is modified. 6
two-column pages. To appear in Phys. Rev. E (tentatively scheduled for Oct. 1
issue
Geodesic Deviation in Kaluza-Klein Theories
We study in detail the equations of the geodesic deviation in
multidimensional theories of Kaluza-Klein type. We show that their
4-dimensional space-time projections are identical with the equations obtained
by direct variation of the usual geodesic equation in the presence of the
Lorentz force, provided that the fifth component of the deviation vector
satisfies an extra constraint derived here.Comment: 5 pages, Revtex, 1 figure. To appear in Phys. Rev. D (Brief Report
General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems
An asymptotic method for finding instabilities of arbitrary -dimensional
large-amplitude patterns in a wide class of reaction-diffusion systems is
presented. The complete stability analysis of 2- and 3-dimensional localized
patterns is carried out. It is shown that in the considered class of systems
the criteria for different types of instabilities are universal. The specific
nonlinearities enter the criteria only via three numerical constants of order
one. The performed analysis explains the self-organization scenarios observed
in the recent experiments and numerical simulations of some concrete
reaction-diffusion systems.Comment: 21 pages (RevTeX), 8 figures (Postscript). To appear in Phys. Rev. E
(April 1st, 1996
Memory effects in microscopic traffic models and wide scattering in flow-density data
By means of microscopic simulations we show that non-instantaneous adaptation
of the driving behaviour to the traffic situation together with the
conventional measurement method of flow-density data can explain the observed
inverse- shape and the wide scattering of flow-density data in
``synchronized'' congested traffic. We model a memory effect in the response of
drivers to the traffic situation for a wide class of car-following models by
introducing a new dynamical variable describing the adaptation of drivers to
the surrounding traffic situation during the past few minutes (``subjective
level of service'') and couple this internal state to parameters of the
underlying model that are related to the driving style. % For illustration, we
use the intelligent-driver model (IDM) as underlying model, characterize the
level of service solely by the velocity and couple the internal variable to the
IDM parameter ``netto time gap'', modelling an increase of the time gap in
congested traffic (``frustration effect''), that is supported by single-vehicle
data. % We simulate open systems with a bottleneck and obtain flow-density data
by implementing ``virtual detectors''. Both the shape, relative size and
apparent ``stochasticity'' of the region of the scattered data points agree
nearly quantitatively with empirical data. Wide scattering is even observed for
identical vehicles, although the proposed model is a time-continuous,
deterministic, single-lane car-following model with a unique fundamental
diagram.Comment: 8 pages, submitted to Physical Review
An assessment of body force representations for compressor stall simulation
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 71-72).This thesis examines an axial compressor body force representation constructed from 3D CFD calculations. The radial distribution of body forces is compared to that of a body force representation based on axisymmetric streamline curvature (SLC) calculations, and shown to be in qualitative agreement except in the vicinity of the blade tip. In terms of stall inception type and stall point, computations based on both representations exhibit agreement with rig test data. A parametric study is undertaken in which the magnitude of the forces in the blade tip region of both representations is reduced so as to obtain reductions in compressor pressure rise similar to those observed experimentally due to increased tip clearance. It is shown that on a back-to-back basis, a given change to the end wall forces produces similar effects on the computed stall point, whether the underlying body force representation derives from 3D CFD or SLC. Based on this result one route to capturing effects of tip clearance on stall prediction can be the development of a tip clearance body force model for use in conjunction with SLC calculations.by Jonathan Kerner.S.M
Physics of traffic gridlock in a city
Based of simulations of a stochastic three-phase traffic flow model, we
reveal that at a signalized city intersection under small link inflow rates at
which a vehicle queue developed during the red phase of light signal dissolves
fully during the green phase, i.e., no traffic gridlock should be expected,
nevertheless, traffic breakdown with the subsequent city gridlock occurs with
some probability after a random time delay. This traffic breakdown is initiated
by a first-order phase transition from free flow to synchronized flow occurring
upstream of the vehicle queue at light signal. The probability of traffic
breakdown at light signal is an increasing function of the link inflow rate and
duration of the red phase of light signal
Covariant EBK quantization of the electromagnetic two-body problem
We discuss a method to transform the covariant Fokker action into an implicit
two-degree-of-freedom Hamiltonian for the electromagnetic two-body problem with
arbitrary masses. This dynamical system appeared 100 years ago and it was
popularized in the 1940's by the still incomplete Wheeler and Feynman program
to quantize it as a means to overcome the divergencies of perturbative QED. Our
finite-dimensional implicit Hamiltonian is closed and involves no series
expansions. The Hamiltonian formalism is then used to motivate an EBK
quantization based on the classical trajectories with a non-perturbative
formula that predicts energies free of infinities.Comment: 21 page
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