1,236 research outputs found
Fundamental diagrams for kinetic equations of traffic flow
In this paper we investigate the ability of some recently introduced discrete
kinetic models of vehicular traffic to catch, in their large time behavior,
typical features of theoretical fundamental diagrams. Specifically, we address
the so-called "spatially homogeneous problem" and, in the representative case
of an exploratory model, we study the qualitative properties of its solutions
for a generic number of discrete microstates. This includes, in particular,
asymptotic trends and equilibria, whence fundamental diagrams originate.Comment: 14 page
A fully-discrete-state kinetic theory approach to modeling vehicular traffic
This paper presents a new mathematical model of vehicular traffic, based on
the methods of the generalized kinetic theory, in which the space of
microscopic states (position and velocity) of the vehicles is genuinely
discrete. While in the recent literature discrete-velocity kinetic models of
car traffic have already been successfully proposed, this is, to our knowledge,
the first attempt to account for all aspects of the physical granularity of car
flow within the formalism of the aforesaid mathematical theory. Thanks to a
rich but handy structure, the resulting model allows one to easily implement
and simulate various realistic scenarios giving rise to characteristic traffic
phenomena of practical interest (e.g., queue formation due to roadworks or to a
traffic light). Moreover, it is analytically tractable under quite general
assumptions, whereby fundamental properties of the solutions can be rigorously
proved.Comment: 22 pages, 3 figure
A fully-discrete-state kinetic theory approach to traffic flow on road networks
This paper presents a new approach to the modeling of vehicular traffic flows
on road networks based on kinetic equations. While in the literature the
problem has been extensively studied by means of macroscopic hydrodynamic
models, to date there are still not, to the authors' knowledge, contributions
tackling it from a genuine statistical mechanics point of view. Probably one of
the reasons is the higher technical complexity of kinetic traffic models,
further increased in case of several interconnected roads. Here such
difficulties of the theory are overcome by taking advantage of a discrete
structure of the space of microscopic states of the vehicles, which is also
significant in view of including the intrinsic microscopic granularity of the
system in the mesoscopic representation.Comment: 36 pages, 10 figure
A Statistical Model of Magnetic Islands in a Large Current Layer
We develop a statistical model describing the dynamics of magnetic islands in
very large current layers that develop in space plasma. Two parameters
characterize the island distribution: the flux contained in the island and the
area it encloses. We derive an integro-differential evolution equation for this
distribution function, based on rules that govern the small-scale generation of
secondary islands, the rates of island growth, and island merging. Our
numerical solutions of this equation produce island distributions relevant to
the magnetosphere and corona. We also derive and analytically solve a
differential equation for large islands that explicitly shows the role merging
plays in island growth.Comment: 4 pages, 3 figure
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