684 research outputs found
Stability Analysis of Optimal Velocity Model for Traffic and Granular Flow under Open Boundary Condition
We analyzed the stability of the uniform flow solution in the optimal
velocity model for traffic and granular flow under the open boundary condition.
It was demonstrated that, even within the linearly unstable region, there is a
parameter region where the uniform solution is stable against a localized
perturbation. We also found an oscillatory solution in the linearly unstable
region and its period is not commensurate with the periodicity of the car index
space. The oscillatory solution has some features in common with the
synchronized flow observed in real traffic.Comment: 4 pages, 6 figures. Typos removed. To appear in J. Phys. Soc. Jp
Algebras with ternary law of composition and their realization by cubic matrices
We study partially and totally associative ternary algebras of first and
second kind. Assuming the vector space underlying a ternary algebra to be a
topological space and a triple product to be continuous mapping we consider the
trivial vector bundle over a ternary algebra and show that a triple product
induces a structure of binary algebra in each fiber of this vector bundle. We
find the sufficient and necessary condition for a ternary multiplication to
induce a structure of associative binary algebra in each fiber of this vector
bundle. Given two modules over the algebras with involutions we construct a
ternary algebra which is used as a building block for a Lie algebra. We
construct ternary algebras of cubic matrices and find four different totally
associative ternary multiplications of second kind of cubic matrices. It is
proved that these are the only totally associative ternary multiplications of
second kind in the case of cubic matrices. We describe a ternary analog of Lie
algebra of cubic matrices of second order which is based on a notion of
j-commutator and find all commutation relations of generators of this algebra.Comment: 17 pages, 1 figure, to appear in "Journal of Generalized Lie Theory
and Applications
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
Steady state solutions of hydrodynamic traffic models
We investigate steady state solutions of hydrodynamic traffic models in the
absence of any intrinsic inhomogeneity on roads such as on-ramps. It is shown
that typical hydrodynamic models possess seven different types of inhomogeneous
steady state solutions. The seven solutions include those that have been
reported previously only for microscopic models. The characteristic properties
of wide jam such as moving velocity of its spatiotemporal pattern and/or
out-flux from wide jam are shown to be uniquely determined and thus independent
of initial conditions of dynamic evolution. Topological considerations suggest
that all of the solutions should be common to a wide class of traffic models.
The results are discussed in connection with the universality conjecture for
traffic models. Also the prevalence of the limit-cycle solution in a recent
study of a microscopic model is explained in this approach.Comment: 9 pages, 6 figure
Congested Traffic States in Empirical Observations and Microscopic Simulations
We present data from several German freeways showing different kinds of
congested traffic forming near road inhomogeneities, specifically lane
closings, intersections, or uphill gradients. The states are localized or
extended, homogeneous or oscillating. Combined states are observed as well,
like the coexistence of moving localized clusters and clusters pinned at road
inhomogeneities, or regions of oscillating congested traffic upstream of nearly
homogeneous congested traffic. The experimental findings are consistent with a
recently proposed theoretical phase diagram for traffic near on-ramps [D.
Helbing, A. Hennecke, and M. Treiber, Phys. Rev. Lett. {\bf 82}, 4360 (1999)].
We simulate these situations with a novel continuous microscopic single-lane
model, the ``intelligent driver model'' (IDM), using the empirical boundary
conditions. All observations, including the coexistence of states, are
qualitatively reproduced by describing inhomogeneities with local variations of
one model parameter.
We show that the results of the microscopic model can be understood by
formulating the theoretical phase diagram for bottlenecks in a more general
way. In particular, a local drop of the road capacity induced by parameter
variations has practically the same effect as an on-ramp.Comment: Now published in Phys. Rev. E. Minor changes suggested by a referee
are incorporated; full bibliographic info added. For related work see
http://www.mtreiber.de/ and http://www.helbing.org
Macroscopic traffic models from microscopic car-following models
We present a method to derive macroscopic fluid-dynamic models from
microscopic car-following models via a coarse-graining procedure. The method is
first demonstrated for the optimal velocity model. The derived macroscopic
model consists of a conservation equation and a momentum equation, and the
latter contains a relaxation term, an anticipation term, and a diffusion term.
Properties of the resulting macroscopic model are compared with those of the
optimal velocity model through numerical simulations, and reasonable agreement
is found although there are deviations in the quantitative level. The
derivation is also extended to general car-following models.Comment: 12 pages, 4 figures; to appear in Phys. Rev.
On Deformations of n-Lie algebras
The aim of this paper is to review the deformation theory of -Lie
algebras. We summarize the 1-parameter formal deformation theory and provide a
generalized approach using any unital commutative associative algebra as a
deformation base. Moreover, we discuss degenerations and quantization of
-Lie algebras.Comment: Proceeding of the conference Dakar's Workshop in honor of Pr Amin
Kaidi. arXiv admin note: text overlap with arXiv:hep-th/9602016 by other
author
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