Effects of boundary conditions on the critical spanning probability

The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we find $p_c = 0.311605(5)$ in the cubic lattice.Comment: 8 pages Latex, To appear in Int. J. Mod. Phys.

Isostaticity of Constraints in Jammed Systems of Soft Frictionless Platonic Solids

The average number of constraints per particle $$ in mechanically stable systems of Platonic solids (except cubes) approaches the isostatic limit at the jamming point ($\rightarrow 12$), though average number of contacts are hypostatic. By introducing angular alignment metrics to classify the degree of constraint imposed by each contact, constraints are shown to arise as a direct result of local orientational order reflected in edge-face and face-face alignment angle distributions. With approximately one face-face contact per particle at jamming chain-like face-face clusters with finite extent form in these systems.Comment: 4 pages, 3 figures, 4 tabl

The lower mass function of the young open cluster Blanco 1: from 30 M_(Jup) to 3 M_☉

Aims. We performed a deep wide field optical survey of the young (~100−150 Myr) open cluster Blanco 1 to study its low mass population well down into the brown dwarf regime and estimate its mass function over the whole cluster mass range. Methods. The survey covers 2.3 square degrees in the I and z-bands down to I ≃ z ≃ 24 with the CFH12K camera. Considering two different cluster ages (100 and 150 Myr), we selected cluster member candidates on the basis of their location in the (I, I − z) CMD relative to the isochrones, and estimated the contamination by foreground late-type field dwarfs using statistical arguments, infrared photometry and low-resolution optical spectroscopy. Results. We find that our survey should contain about 57% of the cluster members in the 0.03−0.6 M_☉ mass range, including 30–40 brown dwarfs. The candidate’s radial distribution presents evidence that mass segregation has already occured in the cluster. We took it into account to estimate the cluster mass function across the stellar/substellar boundary. We find that, between 0.03 M_☉ and 0.6 M_☉, the cluster mass distribution does not depend much on its exact age, and is well represented by a single power-law, with an index α = 0.69 ± 0.15. Over the whole mass domain, from 0.03 M_☉ to 3 M_☉, the mass function is better fitted by a log-normal function with m_0 = 0.36 ± 0.07 M_☉ and σ = 0.58 ± 0.06. Conclusions. Comparison between the Blanco 1 mass function, other young open clusters’ MF, and the galactic disc MF suggests that the IMF, from the substellar domain to the higher mass part, does not depend much on initial conditions. We discuss the implications of this result on theories developed to date to explain the origin of the mass distribution

Multifractality in a broad class of disordered systems

We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model the angles specifying the directions of the spins) at the percolation threshold. Each of the cumulants has its own independent critical exponent, i.e., there are infinitely many critical exponents involved in the problem. Working out the connection to the random resistor network, we determine these multifractal exponents to two-loop order. Depending on the specifics of the Hamiltonian of each individual model, the amplitudes of the higher cumulants can vanish and in this case, effectively, only some of the multifractal exponents are required.Comment: 4 pages, 1 figur

The lower mass function of young open clusters

We report new estimates for the lower mass function of 5 young open clusters spanning an age range from 80 to 150 Myr. In all studied clusters, the mass function across the stellar/substellar boundary (~0.072 Mo) and up to 0.4 Mo is consistent with a power-law with an exponent alpha of -0.5 +/- 0.1, i.e., dN/dM ~ M**(-0.5).Comment: 8 pages, 4 figure

Influence of a small fraction of individuals with enhanced mutations on a population genetic pool

Computer simulations of the Penna ageing model suggest that already a small fraction of births with enhanced number of new mutations can negatively influence the whole population.Comment: 10 pages including 6 figures; draf

Model for Cumulative Solar Heavy Ion Energy and Linear Energy Transfer Spectra

A probabilistic model of cumulative solar heavy ion energy and LET spectra is developed for spacecraft design applications. Spectra are given as a function of confidence level, mission time period during solar maximum and shielding thickness. It is shown that long-term solar heavy ion fluxes exceed galactic cosmic ray fluxes during solar maximum for shielding levels of interest. Cumulative solar heavy ion fluences should therefore be accounted for in single event effects rate calculations and in the planning of space missions