Disorder induced brittle to quasi-brittle transition in fiber bundles

We investigate the fracture process of a bundle of fibers with random Young modulus and a constant breaking strength. For two component systems we show that the strength of the mixture is always lower than the strength of the individual components. For continuously distributed Young modulus the tail of the distribution proved to play a decisive role since fibers break in the decreasing order of their stiffness. Using power law distributed stiffness values we demonstrate that the system exhibits a disorder induced brittle to quasi-brittle transition which occurs analogously to continuous phase transitions. Based on computer simulations we determine the critical exponents of the transition and construct the phase diagram of the system.Comment: 6 pages, 6 figure

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

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

Li abundance/surface activity connections in solar-type Pleiades

The relation between the lithium abundance, <i>A<sub>Li</sub></i>, and photospheric activity of solar-type Pleiads is investigated for the first time via acquisition and analysis of B and V-band data. Predictions of activity levels of target stars were made according to the <i>A<sub>Li</sub></i>/ (B-V) relation and then compared with new CCD photometric measurements. Six sources behaved according to the predictions while one star (HII 676), with low predicted activity, exhibited the largest variability of the study; another star (HII 3197), with high predicted activity, was surprisingly quiet. Two stars displayed non-periodic fadings, this being symptomatic of orbiting disk-like structures with irregular density distributions. Although the observation windows were not ideal for rotational period detection, some periodograms provided possible values; the light-curve obtained for HII 1532 is consistent with that previously recorded

Are the Tails of Percolation Thresholds Gaussians ?

The probability distribution of percolation thresholds in finite lattices were first believed to follow a normal Gaussian behaviour. With increasing computer power and more efficient simulational techniques, this belief turned to a stretched exponential behaviour, instead. Here, based on a further improvement of Monte Carlo data, we show evidences that this question is not yet answered at all.Comment: 7 pages including 3 figure

Mapping functions and critical behavior of percolation on rectangular domains

The existence probability $E_p$ and the percolation probability $P$ of the bond percolation on rectangular domains with different aspect ratios $R$ are studied via the mapping functions between systems with different aspect ratios. The superscaling behavior of $E_p$ and $P$ for such systems with exponents $a$ and $b$, respectively, found by Watanabe, Yukawa, Ito, and Hu in [Phys. Rev. Lett. \textbf{93}, 190601 (2004)] can be understood from the lower order approximation of the mapping functions $f_R$ and $g_R$ for $E_p$ and $P$, respectively; the exponents $a$ and $b$ can be obtained from numerically determined mapping functions $f_R$ and $g_R$, respectively.Comment: 17 pages with 6 figure

Memory effects on the statistics of fragmentation

We investigate through extensive molecular dynamics simulations the fragmentation process of two-dimensional Lennard-Jones systems. After thermalization, the fragmentation is initiated by a sudden increment to the radial component of the particles' velocities. We study the effect of temperature of the thermalized system as well as the influence of the impact energy of the ``explosion'' event on the statistics of mass fragments. Our results indicate that the cumulative distribution of fragments follows the scaling ansatz $F(m)\propto m^{-\alpha}\exp{[-(m/m_0)^\gamma]}$, where $m$ is the mass, $m_0$ and $\gamma$ are cutoff parameters, and $\alpha$ is a scaling exponent that is dependent on the temperature. More precisely, we show clear evidence that there is a characteristic scaling exponent $\alpha$ for each macroscopic phase of the thermalized system, i.e., that the non-universal behavior of the fragmentation process is dictated by the state of the system before it breaks down.Comment: 5 pages, 8 figure

Finite-temperature ordering in a two-dimensional highly frustrated spin model

We investigate the classical counterpart of an effective Hamiltonian for a strongly trimerized kagome lattice. Although the Hamiltonian only has a discrete symmetry, the classical groundstate manifold has a continuous global rotational symmetry. Two cases should be distinguished for the sign of the exchange constant. In one case, the groundstate has a 120^\circ spin structure. To determine the transition temperature, we perform Monte-Carlo simulations and measure specific heat, the order parameter as well as the associated Binder cumulant. In the other case, the classical groundstates are macroscopically degenerate. A thermal order-by-disorder mechanism is predicted to select another 120^\circ spin-structure. A finite but very small transition temperature is detected by Monte-Carlo simulations using the exchange method.Comment: 11 pages including 9 figures, uses IOP style files; to appear in J. Phys.: Condensed Matter (proceedings of HFM2006

The resistance of randomly grown trees

Copyright @ 2011 IOP Publishing Ltd. This is a preprint version of the published article which can be accessed from the link below.An electrical network with the structure of a random tree is considered: starting from a root vertex, in one iteration each leaf (a vertex with zero or one adjacent edges) of the tree is extended by either a single edge with probability p or two edges with probability 1 − p. With each edge having a resistance equal to 1 omega, the total resistance Rn between the root vertex and a busbar connecting all the vertices at the nth level is considered. A dynamical system is presented which approximates Rn, it is shown that the mean value (Rn) for this system approaches (1 + p)/(1 − p) as n → ∞, the distribution of Rn at large n is also examined. Additionally, a random sequence construction akin to a random Fibonacci sequence is used to approximate Rn; this sequence is shown to be related to the Legendre polynomials and its mean is shown to converge with |(Rn) − (1 + p)/(1 − p)| ∼ n−1/2.Engineering and Physical Sciences Research Council (EPSRC