634 research outputs found
About Dynamical Systems Appearing in the Microscopic Traffic Modeling
Motivated by microscopic traffic modeling, we analyze dynamical systems which
have a piecewise linear concave dynamics not necessarily monotonic. We
introduce a deterministic Petri net extension where edges may have negative
weights. The dynamics of these Petri nets are well-defined and may be described
by a generalized matrix with a submatrix in the standard algebra with possibly
negative entries, and another submatrix in the minplus algebra. When the
dynamics is additively homogeneous, a generalized additive eigenvalue may be
introduced, and the ergodic theory may be used to define a growth rate under
additional technical assumptions. In the traffic example of two roads with one
junction, we compute explicitly the eigenvalue and we show, by numerical
simulations, that these two quantities (the additive eigenvalue and the growth
rate) are not equal, but are close to each other. With this result, we are able
to extend the well-studied notion of fundamental traffic diagram (the average
flow as a function of the car density on a road) to the case of two roads with
one junction and give a very simple analytic approximation of this diagram
where four phases appear with clear traffic interpretations. Simulations show
that the fundamental diagram shape obtained is also valid for systems with many
junctions. To simulate these systems, we have to compute their dynamics, which
are not quite simple. For building them in a modular way, we introduce
generalized parallel, series and feedback compositions of piecewise linear
concave dynamics.Comment: PDF 38 page
Topological aspect of black hole with Skyrme hair
Based on the -mapping topological current theory, we show that the
presence of the black hole leaves fractional baryon charge outside the horizon
in the Einstein-Skyrme theory. A topological current is derived from the
Einstein-Skyrme system, which corresponds to the monopoles around the black
hole. The branch process (splitting, merging and intersection) is simply
discussed during the evolution of the monopoles.Comment: 10 pages,0 figure
The perturbed Bessel equation, I. A Duality Theorem
The Euler-Gauss linear transformation formula for the hypergeometric function
was extended by Goursat for the case of logarithmic singularities. By replacing
the perturbed Bessel differential equation by a monodromic functional equation,
and studying this equation separately from the differential equation by an
appropriate Laplace-Borel technique, we associate with the latter equation
another monodromic relation in the dual complex plane. This enables us to prove
a duality theorem and to extend Goursat's formula to much larger classes of
functions
Inner topological structure of Hopf invariant
In light of -mapping topological current theory, the inner topological
structure of Hopf invariant is investigated. It is revealed that Hopf invariant
is just the winding number of Gauss mapping. According to the inner structure
of topological current, a precise expression for Hopf invariant is also
presented. It is the total sum of all the self-linking and all the linking
numbers of the knot family.Comment: 13pages, no figure. Accepted by J.Math.Phy
Characteristic Lie rings, finitely-generated modules and integrability conditions for 2+1 dimensional lattices
Characteristic Lie rings for Toda type 2+1 dimensional lattices are defined.
Some properties of these rings are studied. Infinite sequence of special kind
modules are introduced. It is proved that for known integrable lattices these
modules are finitely generated. Classification algorithm based on this
observation is briefly discussed.Comment: 11 page
Modular Solutions to Equations of Generalized Halphen Type
Solutions to a class of differential systems that generalize the Halphen
system are determined in terms of automorphic functions whose groups are
commensurable with the modular group. These functions all uniformize Riemann
surfaces of genus zero and have --series with integral coefficients.
Rational maps relating these functions are derived, implying subgroup relations
between their automorphism groups, as well as symmetrization maps relating the
associated differential systems.Comment: PlainTeX 36gs. (Formula for Hecke operator corrected.
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