10 research outputs found
Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model
The Aw-Rascle-Zhang (ARZ) model can be interpreted as a generalization of the
Lighthill-Whitham-Richards (LWR) model, possessing a family of fundamental
diagram curves, each of which represents a class of drivers with a different
empty road velocity. A weakness of this approach is that different drivers
possess vastly different densities at which traffic flow stagnates. This
drawback can be overcome by modifying the pressure relation in the ARZ model,
leading to the generalized Aw-Rascle-Zhang (GARZ) model. We present an approach
to determine the parameter functions of the GARZ model from fundamental diagram
measurement data. The predictive accuracy of the resulting data-fitted GARZ
model is compared to other traffic models by means of a three-detector test
setup, employing two types of data: vehicle trajectory data, and sensor data.
This work also considers the extension of the ARZ and the GARZ models to models
with a relaxation term, and conducts an investigation of the optimal relaxation
time.Comment: 30 pages, 10 figures, 3 table
Convergence of quantum random walks with decoherence
In this paper, we study the discrete-time quantum random walks on a line
subject to decoherence. The convergence of the rescaled position probability
distribution depends mainly on the spectrum of the superoperator
. We show that if 1 is an eigenvalue of the superoperator
with multiplicity one and there is no other eigenvalue whose modulus equals to
1, then converges to a convex combination of
normal distributions. In terms of position space, the rescaled probability mass
function , , converges in
distribution to a continuous convex combination of normal distributions. We
give an necessary and sufficient condition for a U(2) decoherent quantum walk
that satisfies the eigenvalue conditions.
We also give a complete description of the behavior of quantum walks whose
eigenvalues do not satisfy these assumptions. Specific examples such as the
Hadamard walk, walks under real and complex rotations are illustrated. For the
O(2) quantum random walks, an explicit formula is provided for the scaling
limit of and their moments. We also obtain exact critical exponents
for their moments at the critical point and show universality classes with
respect to these critical exponents
A proof of a conjecture in the Cram\'er-Lundberg model with investments
In this paper, we discuss the Cram\'er-Lundberg model with investments, where the price of the invested risk asset follows a geometric Brownian motion with drift and volatility By assuming there is a cap on the claim sizes, we prove that the probability of ruin has at least an algebraic decay rate if . More importantly, without this assumption, we show that the probability of ruin is certain for all initial capital , if .