Polytechnic University of Milan

About: Polytechnic University of Milan is a education organization based out in Milan, Italy. It is known for research contribution in the topics: Computer science & Finite element method. The organization has 18231 authors who have published 58416 publications receiving 1229711 citations. The organization is also known as: PoliMi & L-NESS.

On the Size Distribution of Business Firms

Abstract: The size distribution of business firms is explained using number and size of firms' constituent components. It is a lognormal distribution multiplied by a stretching factor which can lead to a Pareto upper tail. This result is confirmed empirically.

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

Abstract: In this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms (input data of the model). The input data are assumed to depend on a finite number of random variables. The method consists in a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. It can be seen as a generalization of the stochastic Galerkin method proposed in [I. Babuscka, R. Tempone, and G. E. Zouraris, SIAM J. Numer. Anal., 42 (2004), pp. 800-825] and allows one to treat easily a wider range of situations, such as input data that depend nonlinearly on the random variables, diffusivity coefficients with unbounded second moments, and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate exponential convergence of the “probability error” with respect to the number of Gauss points in each direction in the probability space, under some regularity assumptions on the random input data. Numerical examples show the effectiveness of the method.

Excitons versus free charges in organo-lead tri-halide perovskites

Abstract: Excitonic solar cells, within which bound electron-hole pairs have a central role in energy harvesting, have represented a hot field of research over the last two decades due to the compelling prospect of low-cost solar energy. However, in such cells, exciton dissociation and charge collection occur with significant losses in energy, essentially due to poor charge screening. Organic-inorganic perovskites show promise for overcoming such limitations. Here, we use optical spectroscopy to estimate the exciton binding energy in the mixed-halide crystal to be in the range of 50 meV. We show that such a value is consistent with almost full ionization of the exciton population under photovoltaic cell operating conditions. However, increasing the total photoexcitation density, excitonic species become dominant, widening the perspective of this material for a host of optoelectronic applications.