A macroscopic crowd motion model of gradient flow type

A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the incompressibility constraint prevents this velocity field to be realized and the actual velocity is the projection of the desired one onto the set of admissible velocities. Instead of looking at a microscopic setting (where individuals are represented by rigid discs), here the macroscopic approach is investigated, where the unknwon is the evolution of the density . If a gradient structure is given, say U is the opposite of the gradient of D where D is, for instance, the distance to the exit door, the problem is presented as a Gradient Flow in the Wasserstein space of probability measures. The functional which gives the Gradient Flow is neither finitely valued (since it takes into account the constraints on the density), nor geodesically convex, which requires for an ad-hoc study of the convergence of a discrete scheme

Parameters of the two generator discrete elementary groups : a thesis presented in partial fulfillment of the requirements for the degree of Master of Science in Mathematics at Massey University, Albany, New Zealand

Let f, g be elements of M, the group of Möbius transformations of the extended complex plane Ĉ = C U ∞. We identify each element of M with a 2 × 2 complex matrix with determinant 1. The three complex numbers, β(f) = tr2 (f) - 4,β(g) = tr2 (g) - 4,γ(f,g) = tr[f,g] - 2, define the group ‹f,g› uniquely up to conjugacy whenever γ(f,g) ≠ 0; where tr(f) and tr(g) denote the traces of representive matrices of f and g respectively, [f,g] denotes the multiplicative commutator fgf-1 g-1 . We call these three complex numbers the parameters of ‹f,g›. This thesis is concerned with the parameters of discrete and elementary subgroups of M

Impact of nanostructure configuration on the photovoltaic performance of quantum dot arrays

In this work, a mesoscopic model based on the non-equilibrium Green's function formalism for a tight-binding-like effective Hamiltonian is used to investigate a selectively contacted quantum dot array designed for operation as a single junction quantum dot solar cell. By establishing a direct relation between nanostructure configuration and optoelectronic properties, the investigation reveals the influence of inter-dot and dot-contact coupling strengths on the rates of charge carrier photogeneration, radiative recombination, and extraction at contacts, and consequently on the ultimate performance of photovoltaic devices with finite quantum dot arrays as the active medium. For long carrier lifetimes, the dominant configuration effects originate in the dependence of the joint density of states on the inter-dot coupling in terms of band width and effective band gap. In the low carrier lifetime regime, where recombination competes with carrier extraction, the extraction efficiency shows a critical dependence on the dot-contact coupling.Comment: 11 pages, 15 figures; extensively revised and substantially extended versio

Reconstruction of the transit signal in the presence of stellar variability

Intrinsic stellar variability can hinder the detection of shallow transits, particularly in space-based data. Therefore, this variability has to be filtered out before running the transit search. Unfortunately, filtering out the low frequency signal of the stellar variability also modifies the transit shape. This results in errors in the measured transit depth and duration used to derive the planet radius, and orbital inclination. We present an evaluation of the magnitude of this effect based on 20 simulated light curves from the CoRoT blind exercise 2 (BT2). We then present an iterative filter which uses the strictly periodic nature of the transits to separate them from other forms of variability, so as to recover the original transit shape before deriving the planet parameters. On average with this filter, we improve the estimation of the transit depth and duration by 15% and 10% respectively.Comment: 4 pages, 2 figures. Accepted for publication in the Proceedings of IAU Symposium 249: Exoplanet: Detection, Formation and Dynamic

A proximal approach to the inversion of ill-conditioned matrices

We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization parameter) belongs to the class of {\sl fixed point} methods. Convergence of the algorithm is also discussed

Unexpected Media Coverage and Stock Market Outcomes : Evidence from Chemical Disasters.

Using the event-study methodology and multivariate regressions, this paper examines the intensity of media coverage, its determinants and its marginal effect on stock returns following chemical disasters. To do this, we build an original dataset of chemical explosions that occurred worldwide from 1990-2005. First, our results show that news coverage increases with the social and environmental consequences of the accident. Second, to deal with the fact that news coverage is determined simultaneously with stock returns, we suggest two valid and original instrumental variables: a measure of the firm’s newsworthiness and a measure of daily news pressure at the time of the disaster. We find that unexpected news coverage due to chemical disasters also respond to these conjunctural factors, and is truly exogenous to abnormal returns. Third, we show that, all else being equal (pollution, number of casualties, and firm profile), the stock market reaction to intense press coverage is delayed, and becomes negative in the long-term. At the same time, there is clear evidence that in the first days news coverage mitigates the market value losses. We interpret these results as evidence that investors are slow to recognize the extent of the loss associated with the public implications of news coverage (e.g., image and public trust deterioration). In addition, in contrast toprevious studies, we argue that press coverage is not necessarily associated with increased investor attention.Corporate Social Responsibility; Pollution; Media; Efficient Market Hypothesis; Behavioral Finance;