Unilateral problems with degenerate coercivity

In this note we prove some existence and regularity results for unilateral problems with degenerate coercivity

La Lingua Matematica: un'esperienza didattica nel Liceo Matematico

In questo lavoro si presenta un modulo didattico dal titolo La Lingua Matematica, rivolto a studenti del primo anno di scuola secondaria di secondo grado.Il modulo è stato presentato in classi di Liceo Matematico, ma può essere proposto anche in altri contesti. Esso ha un duplice obiettivo: introdurre questioni relative a matematica e linguaggio da un lato e introdurre i concetti di teorema e dimostrazione dall'altro. Il percorso ha permesso di introdurre nozioni di aritmetica modulare e ha condotto gli studenti a confrontarsi, elaborare ipotesi, produrre argomentazioni e generare nuovi teoremi

The nature of singlet exciton fission in carotenoid aggregates.

Singlet exciton fission allows the fast and efficient generation of two spin triplet states from one photoexcited singlet. It has the potential to improve organic photovoltaics, enabling efficient coupling to the blue to ultraviolet region of the solar spectrum to capture the energy generally lost as waste heat. However, many questions remain about the underlying fission mechanism. The relation between intermolecular geometry and singlet fission rate and yield is poorly understood and remains one of the most significant barriers to the design of new singlet fission sensitizers. Here we explore the structure-property relationship and examine the mechanism of singlet fission in aggregates of astaxanthin, a small polyene. We isolate five distinct supramolecular structures of astaxanthin generated through self-assembly in solution. Each is capable of undergoing intermolecular singlet fission, with rates of triplet generation and annihilation that can be correlated with intermolecular coupling strength. In contrast with the conventional model of singlet fission in linear molecules, we demonstrate that no intermediate states are involved in the triplet formation: instead, singlet fission occurs directly from the initial 1B(u) photoexcited state on ultrafast time scales. This result demands a re-evaluation of current theories of polyene photophysics and highlights the robustness of carotenoid singlet fission.This work was supported by the EPSRC (UK) (EP/G060738/ 1), the European Community (LASERLAB-EUROPE, grant agreement no. 284464, EC’s Seventh Framework Programme; and Marie-Curie ITN-SUPERIOR, PITN-GA-2009-238177), and the Winton Programme for the Physics of Sustainability. G.C. acknowledges support by the European Research Council Advanced Grant STRATUS (ERC-2011-AdG No. 291198). J.C. acknowledges support by the Royal Society Dorothy Hodgkin Fellowship and The University of Sheffield’s Vice- Chancellor’s Fellowship scheme.This is the final published version. It was first made available by ACS at http://pubs.acs.org/doi/abs/10.1021/jacs.5b01130

Some elliptic equations with W01,1W_0^1,1 solutions

We consider some nonlinear Dirichlet problems and we study how lower order terms can give a regularizing effect on the solutions: the existence of distributional solutions with minimal properties (solutions in W0^1,1 , functional space not so usual for finding solutions of elliptic problems) or finite energy solutions, even with nonregular data

Morrey estimates for a class of elliptic equations with drift term

We consider the following boundary value proble

The regularizing effect of lower order terms in elliptic problems involving Hardy potential

We study existence and summability of solutions for elliptic problems with a power-like lower order term and a Hardy potential. We prove that, due to the presence of the lower order term, solutions exist and are more summable under weaker assumptions than those needed for the existence without it

White-light generation with sub-ps pulses

We generate white light supercontinuum from slightly sub-picosecond pulses at 1.03 µm and 515 nm. We compare the spectra and stability for various crystals, focusing conditions and pulse durations, and determine the best parameters for sub-picosecond driver pulse duration. Comparing the experimental observations with the theory of white-light generation from Brodeur and Chin, it appears that in this particular range of pump pulse duration, two mechanisms interact and prevent a catastrophic collapse of the beam: multi-photon excitation (typical for ~100-fs-long pulses) and avalanche ionization (typical for >1-ps pulses). The two processes both manifest themselves in different experimental observations