Defining the Circumstellar Habitable Zone

The study of habitable exoplanets is a rapidly expanding field in astronomy. Exoplanets are planets that orbit stars other than our own sun. One of the keys to knowing whether or not an exoplanet is habitable is by studying the circumstellar habitable zone, or CHZ. Over the past several years, the defined limits of the CHZ have become susceptible to change as new parameters and factors are found to affect a planets habitability. There are many factors that affect its habitability, including the composition of the star, the mass of the planet, the planets atmosphere, etc. Our focus is divided into two parts. The first is to study how recent discoveries of physical parameters affect a planet’s habitability. The second is a radically new direction: to explore life that results from different biological processes than those found on Earth. By reviewing and summarizing ongoing developments and discoveries in the field, we conclude that the many new factors that were previously unconsidered have major implications for an exoplanet’s habitability

Enumerative Combinatorics of Intervals in the Dyck Pattern Poset

We initiate the study of the enumerative combinatorics of the intervals in the Dyck pattern poset. More specifically, we find some closed formulas to express the size of some specific intervals, as well as the number of their covering relations. In most of the cases, we are also able to refine our formulas by rank. We also provide the first results on the Möbius function of the Dyck pattern poset, giving for instance a closed expression for the Möbius function of initial intervals whose maximum is a Dyck path having exactly two peaks

The classical and quantum dynamics of molecular spins on graphene

PMCID: PMC4800001.-- et al.Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic and quantum computing devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics and electrical spin manipulation. However, the influence of the graphene environment on the spin systems has yet to be unravelled. Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets on graphene. Whereas the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly developed model. Coupling to Dirac electrons introduces a dominant quantum relaxation channel that, by driving the spins over Villain's threshold, gives rise to fully coherent, resonant spin tunnelling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin manipulation in graphene nanodevices.Financial support from Italian MIUR, Spanish MINECO (MAT2012-38318-C03-01), BW-Stiftung (Kompetenznetz Funktionelle Nanostrukturen), ERC StG-338258 “OptoQMol”, the Royal Society (URF fellowship and grant) and the AvH Stiftung (Sofja Kovalevskaja award).Peer Reviewe