In this paper we provide emission estimates due to vehicular traffic via Generic Second Order Models. We generalize them to model road networks with merge and diverge junctions. The procedure consists on solving the Riemann Problem at junction assuming the maximization of the flow and a priority rule for the incoming roads. We provide some numerical results for a single-lane roundabout and we propose an application of the given procedure to estimate the production of nitrogen oxides (NOx) emission rates.

The aim of this paper is to solve an inverse problem which regards a mass moving in a bounded domain. We assume that the mass moves following an unknown velocity field and that the evolution of the mass density can be described by a partial differential equation, which is also unknown. The input data of the problems are given by some snapshots of the mass distribution at certain times, while the sought output is the velocity field that drives the mass along its displacement.

Let P and (P) over tilde be the laws of two discrete-time stochastic processes defined on the sequence space S-N,where S is a finite set of points. In this paper we derive a bound on the total variation distance d(TV)(P, (P) over tilde) in terms of the cylindrical projections of P and (P) over tilde. We apply the result to Markov chains with finite state space and random walks on Z with not necessarily independent increments, and we consider several examples.

Gathering together some existing results, we show that the solutions to the one-dimensional Burgers equation converge for long times towards the stationary solutions to the steady Burgers equation, whose Fourier spectrum is not integrable. This is one of the main features of wave turbulence.