12,202 research outputs found
Existence of optima and equilibria for traffic flow on networks
This paper is concerned with a conservation law model of traffic flow on a
network of roads, where each driver chooses his own departure time in order to
minimize the sum of a departure cost and an arrival cost. The model includes
various groups of drivers, with different origins and destinations and having
different cost functions. Under a natural set of assumptions, two main results
are proved: (i) the existence of a globally optimal solution, minimizing the
sum of the costs to all drivers, and (ii) the existence of a Nash equilibrium
solution, where no driver can lower his own cost by changing his departure time
or the route taken to reach destination. In the case of Nash solutions, all
departure rates are uniformly bounded and have compact support.Comment: 22 pages, 5 figure
Continuity of the Effective Path Delay Operator for Networks Based on the Link Delay Model
This paper is concerned with a dynamic traffic network performance model,
known as dynamic network loading (DNL), that is frequently employed in the
modeling and computation of analytical dynamic user equilibrium (DUE). As a key
component of continuous-time DUE models, DNL aims at describing and predicting
the spatial-temporal evolution of traffic flows on a network that is consistent
with established route and departure time choices of travelers, by introducing
appropriate dynamics to flow propagation, flow conservation, and travel delays.
The DNL procedure gives rise to the path delay operator, which associates a
vector of path flows (path departure rates) with the corresponding path travel
costs. In this paper, we establish strong continuity of the path delay operator
for networks whose arc flows are described by the link delay model (Friesz et
al., 1993). Unlike result established in Zhu and Marcotte (2000), our
continuity proof is constructed without assuming a priori uniform boundedness
of the path flows. Such a more general continuity result has a few important
implications to the existence of simultaneous route-and-departure choice DUE
without a priori boundedness of path flows, and to any numerical algorithm that
allows convergence to be rigorously analyzed.Comment: 12 pages, 1 figur
On the Control of Non Holonomic Systems by Active Constraints
The paper is concerned with mechanical systems which are controlled by
implementing a number of time-dependent, frictionless holonomic constraints.
The main novelty is due to the presence of additional non-holonomic
constraints. We develop a general framework to analyze these problems, deriving
the equations of motion and studying the continuity properties of the
"control-to-trajectory" maps. Various geometric characterizations are provided,
in order that the equations be affine w.r.t. the time derivative of the
control. In this case the system is fit for jumps, and the evolution is well
defined also in connection with discontinuous control functions. The classical
Roller Racer provides an example where the non-affine dependence of the
equations on the derivative of the control is due only to the non-holonomic
constraint. This is a case where the presence of quadratic terms in the
equations can be used for controllability purposes.Comment: 26 pages, 3 figures. The current version will appear on Discrete and
Continuous Dynamical Systems, Series
General Volume-Preserving Mechanical Systems
In this letter, we present the general form of equations that generate a
volume-preserving flow on a symplectic manifold (M, \omega). It is shown that
every volume-preserving flow has some 2-forms acting the role of the
Hamiltonian functions in the Hamiltonian mechanics and the ordinary Hamilton
equations are included as a special case with a 2-form \frac{1}{n-1} H \omega
where H is the corresponding Hamiltonian.Comment: Plain LaTeX, 13 pages, no figure
On Torsion and Nieh-Yan Form
Using the well-known Chern-Weil formula and its generalization, we
systematically construct the Chern-Simons forms and their generalization
induced by torsion as well as the Nieh-Yan (N-Y) forms. We also give an
argument on the vanishing of integration of N-Y form on any compact manifold
without boundary. A systematic construction of N-Y forms in D=4n dimension is
also given.Comment: 7 pages, latex, no figure
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