On the complexity of some birational transformations

Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions

Breakdown of self-organized criticality

We introduce two sandpile models which show the same behavior of real sandpiles, that is, an almost self-organized critical behavior for small systems and the dominance of large avalanches as the system size increases. The systems become fully self-organized critical, with the critical exponents of the Bak, Tang and Wiesenfeld model, as the system parameters are changed, showing that these systems can make a bridge between the well known theoretical and numerical results and what is observed in real experiments. We find that a simple mechanism determines the boundary where self-organized can or cannot exist, which is the presence of local chaos.Comment: 3 pages, 4 figure

Possible Stratification Mechanism in Granular Mixtures

We propose a mechanism to explain what occurs when a mixture of grains of different sizes and different shapes (i.e. different repose angles) is poured into a quasi-two-dimensional cell. Specifically, we develop a model that displays spontaneous stratification of the large and small grains in alternating layers. We find that the key requirement for stratification is a difference in the repose angles of the two pure species, a prediction confirmed by experimental findings. We also identify a kink mechanism that appears to describe essential aspects of the dynamics of stratification.Comment: 4 pages, 4 figures, http://polymer.bu.edu/~hmakse/Home.htm

Nearest pattern interaction and global pattern formation

We studied the effect of nearest pattern interaction on a globally pattern formation in a 2-dimensional space, where patterns are to grow initially from a noise in the presence of periodic supply of energy. Although our approach is general, we found that this study is relevant in particular to the pattern formation on a periodically vibrated granular layer, as it gives a unified perspective of the experimentally observed pattern dynamics such as oscillon and stripe formations, skew-varicose and crossroll instabilities, and also a kink formation and decoration

SPIROC (SiPM Integrated Read-Out Chip): Dedicated very front-end electronics for an ILC prototype hadronic calorimeter with SiPM read-out

The SPIROC chip is a dedicated very front-end electronics for an ILC prototype hadronic calorimeter with Silicon photomultiplier (or MPPC) readout. This ASIC is due to equip a 10,000-channel demonstrator in 2009. SPIROC is an evolution of FLC_SiPM used for the ILC AHCAL physics prototype [1]. SPIROC was submitted in June 2007 and will be tested in September 2007. It embeds cutting edge features that fulfil ILC final detector requirements. It has been realized in 0.35m SiGe technology. It has been developed to match the requirements of large dynamic range, low noise, low consumption, high precision and large number of readout channels needed. SPIROC is an auto-triggered, bi-gain, 36-channel ASIC which allows to measure on each channel the charge from one photoelectron to 2000 and the time with a 100ps accurate TDC. An analogue memory array with a depth of 16 for each channel is used to store the time information and the charge measurement. A 12-bit Wilkinson ADC has been embedded to digitize the analogue memory content (time and charge on 2 gains). The data are then stored in a 4kbytes RAM. A very complex digital part has been integrated to manage all theses features and to transfer the data to the DAQ which is described on [2]

Type II supernovae as probes of environment metallicity: observations of host HII regions

Spectral modelling of SNII atmospheres indicates a clear dependence of metal line strengths on progenitor metallicity. This motivates further work to evaluate the accuracy with which these SNe can be used as metallicity indicators. To assess this accuracy we present a sample of SNII HII-region spectroscopy, from which environment abundances are derived. These environment abundances are compared to the observed strength of metal lines in SN spectra. Combining our sample with measurements from the literature, we present oxygen abundances of 119 host HII regions, by extracting emission line fluxes and using abundance diagnostics. Then, following Dessart et al., these abundances are compared to equivalent widths of Fe 5018 A at various time and colour epochs. Our distribution of inferred SNII host HII-region abundances has a range of ~0.6 dex. We confirm the dearth of SNeII exploding at metallicities lower than those found (on average) in the Large Magellanic Cloud. The equivalent width of Fe 5018 A at 50 days post explosion shows a statistically significant correlation with host HII-region oxygen abundance. The strength of this correlation increases if one excludes abundance measurements derived far from SN explosion sites. The correlation significance also increases if we only analyse a 'gold' IIP sample, and if a colour epoch is used in place of time. In addition, no evidence is found of correlation between progenitor metallicity and SN light-curve or spectral properties - except for that stated above with respect to Fe 5018 A equivalent width - suggesting progenitor metallicity is not a driving factor in producing the diversity observed in our sample. This study provides observational evidence of the usefulness of SNII as metallicity indicators. We finish with a discussion of the methodology needed to use SN spectra as independent metallicity diagnostics throughout the Universe.Comment: Accepted for publication in Astronomy and Astrophyci

Silicates in D-type symbiotic stars: an ISO overview

We investigate the IR spectral features of a sample of D-type symbiotic stars. Analyzing unexploited ISO-SWS data, deriving the basic observational parameters of dust bands and comparing them with respect to those observed in other astronomical sources, we try to highlight the effect of environment on grain chemistry and physic. We find strong amorphous silicate emission bands at 10 micron and 18 micron in a large fraction of the sample. The analysis of the 10 micron band, along with a direct comparison with several astronomical sources, reveals that silicate dust in symbiotic stars shows features between the characteristic circumstellar environments and the interstellar medium. This indicates an increasing reprocessing of grains in relation to specific symbiotic behavior of the objects. A correlation between the central wavelength of the 10 and 18 micron dust bands is found. By the modeling of IR spectral lines we investigate also dust grains conditions within the shocked nebulae. Both the unusual depletion values and the high sputtering efficiency might be explained by the formation of SiO moleculae, which are known to be a very reliable shock tracer. We conclude that the signature of dust chemical disturbance due to symbiotic activity should be looked for in the outer, circumbinary, expanding shells where the environmental conditions for grain processing might be achieved. Symbiotic stars are thus attractive targets for new mid-infrared and mm observations.Comment: 24 pages, 6 figures, 5 tables - to be published in A

SPIROC (SiPM Integrated Read-Out Chip): Dedicated very front-end electronics for an ILC prototype hadronic calorimeter with SiPM read-out

The SPIROC chip is a dedicated very front-end electronics for an ILC prototype hadronic calorimeter with Silicon photomultiplier (or MPPC) readout. This ASIC is due to equip a 10,000-channel demonstrator in 2009. SPIROC is an evolution of FLC_SiPM used for the ILC AHCAL physics prototype [1]. SPIROC was submitted in June 2007 and will be tested in September 2007. It embeds cutting edge features that fulfil ILC final detector requirements. It has been realized in 0.35m SiGe technology. It has been developed to match the requirements of large dynamic range, low noise, low consumption, high precision and large number of readout channels needed. SPIROC is an auto-triggered, bi-gain, 36-channel ASIC which allows to measure on each channel the charge from one photoelectron to 2000 and the time with a 100ps accurate TDC. An analogue memory array with a depth of 16 for each channel is used to store the time information and the charge measurement. A 12-bit Wilkinson ADC has been embedded to digitize the analogue memory content (time and charge on 2 gains). The data are then stored in a 4kbytes RAM. A very complex digital part has been integrated to manage all theses features and to transfer the data to the DAQ which is described on [2]. After an exhaustive description, the extensive measurement results of that new front-end chip will be presented

Cooperativity in sandpiles: statistics of bridge geometries

Bridges form dynamically in granular media as a result of spatiotemporal inhomogeneities. We classify bridges as linear and complex, and analyse their geometrical characteristics. In particular, we find that the length distribution of linear bridges is exponential. We then turn to the analysis of the orientational distribution of linear bridges and find that, in three dimensions, they are {\it vertically diffusive but horizontally superdiffusive}; thus, when they exist, long linear bridges form `domes'. Our results are in good accord with Monte Carlo simulations of bridge structure; we make predictions for quantities that are experimentally accessible, and suggest that bridges are very closely related to force chains.Comment: 15 pages, 10 figures. Minor changes and update