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Person# Claudio Grimaldi

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Percolation theory

In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fractio

Quantum tunnelling

In physics, quantum tunnelling, barrier penetration, or simply tunnelling is a quantum mechanical phenomenon in which an object such as an electron or atom passes through a potential energy barrier

Thermal conductivity

The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa.
Heat transfer occurs at a

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For about the last 60 yr the search for extraterrestrial intelligence has been monitoring the sky for evidence of remotely detectable technological life beyond Earth, with no positive results to date. While the lack of detection can be attributed to the highly incomplete sampling of the search space, technological emissions may be actually rare enough that we are living in a time when none cross the Earth. Here we explore the latter possibility and derive the likelihood of the Earth not being crossed by signals for at least the last 60 yr to infer upper bounds on their rate of emission. Under the assumption that technological emitters are distributed uniformly in the Milky Way and that they generate technoemissions at a constant rate, we find less than about one to five emissions generated per century with 95% credible level. This implies optimistic waiting times until the next crossing event of no less than 60-1800 yr with a 50% probability. A significant fraction of highly directional signals increases the emission rates' upper bounds, but without systematically changing the waiting time. Although these probabilistic bounds are derived from a specific model and their validity depends on the model's assumptions, they are nevertheless quite robust against weak time dependences of the emission rate or nonuniform spatial distributions of the emitters. Our results provide therefore a benchmark for assessing the lack of detection and may serve as a basis to form optimal strategies for the search for extraterrestrial intelligence.

To assess the number of life-bearing worlds in astrophysical environments, it is necessary to take the intertwined processes of abiogenesis (birth), extinction (death), and transfer of life (migration) into account. We construct a mathematical model that incorporates this trio of mechanisms and accordingly derive the probability distribution function and other statistical properties (e.g. mean) for the number of worlds with biospheres. We show that a given astrophysical setting may become eventually saturated with life if the rate of successful transfers of organisms is higher than the extinction rate of biospheres. Based on the available data, we suggest that this criterion might be fulfilled for star-forming clusters (and perhaps the Galactic bulge under optimal circumstances), thereby indicating that such regions could constitute promising abodes for hosting and detecting life.

The connectedness percolation threshold (phi(c)) for spherically symmetric, randomly distributed fractal aggregates is investigated as a function of the fractal dimension (d(F)) of the aggregates through a mean-field approach. A pair of aggregates (each of radius R) are considered to be connected if a pair of primary particles (each of diameter delta), one from each assembly, are located within a prescribed distance of each other. An estimate for the number of such contacts between primary particles for a pair of aggregates is combined with a mapping onto the model for fully penetrable spheres to calculate phi(c). For sufficiently large aggregates, our analysis reveals the existence of two regimes for the dependence of fc upon R/delta namely: (i) when d(F) > 1.5 aggregates form contacts near to tangency, and phi(c) approximate to (R/delta)(dF-3), whereas (ii) when d(F) < 1.5 deeper interpenetration of the aggregates is required to achieve contact formation, and phi(c) approximate to (R/delta)(-dF). For a fixed (large) value of R/delta, a minimum for fc as a function of dF occurs when d(F) = 1.5. Taken together, these dependencies consistently describe behaviors observed over the domain 1