Mapping the train model for earthquakes onto the stochastic sandpile model

We perform a computational study of a variant of the ``train'' model for earthquakes [PRA 46, 6288 (1992)], where we assume a static friction that is a stochastic function of position rather than being velocity dependent. The model consists of an array of blocks coupled by springs, with the forces between neighbouring blocks balanced by static friction. We calculate the probability, P(s), of the occurrence of avalanches with a size s or greater, finding that our results are consistent with the phenomenology and also with previous models which exhibit a power law over a wide range. We show that the train model may be mapped onto a stochastic sandpile model and study a variant of the latter for non-spherical grains. We show that, in this case, the model has critical behaviour only for grains with large aspect ratio, as was already shown in experiments with real ricepiles. We also demonstrate a way to introduce randomness in a physically motivated manner into the model.Comment: 14 pages and 6 figures. Accepted in European Physical Journal

Strategies for Optimize Off-Lattice Aggregate Simulations

We review some computer algorithms for the simulation of off-lattice clusters grown from a seed, with emphasis on the diffusion-limited aggregation, ballistic aggregation and Eden models. Only those methods which can be immediately extended to distinct off-lattice aggregation processes are discussed. The computer efficiencies of the distinct algorithms are compared.Comment: 6 pages, 7 figures and 3 tables; published at Brazilian Journal of Physics 38, march, 2008 (http://www.sbfisica.org.br/bjp/files/v38_81.pdf

String Evolution with Friction

We study the effects of friction on the scaling evolution of string networks in condensed matter and cosmological contexts. We derive a generalized `one-scale' model with the string correlation length $L$ and velocity $v$ as dynamical variables. In non-relativistic systems, we obtain a well-known $L\propto t^{1/2}$ law, showing that loop production is important. For electroweak cosmic strings, we show transient damped epoch scaling with $L\propto t^{5/4}$ (or, in the matter era, $L\propto t^{3/2}$). A low initial density implies an earlier period with $L\propto t^{1/2}$. For GUT strings, the approach to linear scaling $L\propto t$ is faster than previously estimated.Comment: 8 pages, uuencoded gziped .ps file. Paper submitted to Phys. Rev. Let

Curved Graphene Nanoribbons: Structure and Dynamics of Carbon Nanobelts

Carbon nanoribbons (CNRs) are graphene (planar) structures with large aspect ratio. Carbon nanobelts (CNBs) are small graphene nanoribbons rolled up into spiral-like structures, i. e., carbon nanoscrolls (CNSs) with large aspect ratio. In this work we investigated the energetics and dynamical aspects of CNBs formed from rolling up CNRs. We have carried out molecular dynamics simulations using reactive empirical bond-order potentials. Our results show that similarly to CNSs, CNBs formation is dominated by two major energy contribution, the increase in the elastic energy due to the bending of the initial planar configuration (decreasing structural stability) and the energetic gain due to van der Waals interactions of the overlapping surface of the rolled layers (increasing structural stability). Beyond a critical diameter value these scrolled structures can be even more stable (in terms of energy) than their equivalent planar configurations. In contrast to CNSs that require energy assisted processes (sonication, chemical reactions, etc.) to be formed, CNBs can be spontaneously formed from low temperature driven processes. Long CNBs (length of $\sim$ 30.0 nm) tend to exhibit self-folded racket-like conformations with formation dynamics very similar to the one observed for long carbon nanotubes. Shorter CNBs will be more likely to form perfect scrolled structures. Possible synthetic routes to fabricate CNBs from graphene membranes are also addressed

Ultrasensitivity in phosphorylation-dephosphorylation cycles with little substrate

Cellular decision-making is driven by dynamic behaviours, such as the preparations for sunrise enabled by circadian rhythms and the choice of cell fates enabled by positive feedback. Such behaviours are often built upon ultrasensitive responses where a linear change in input generates a sigmoidal change in output. Phosphorylation-dephosphorylation cycles are one means to generate ultrasensitivity. Using bioinformatics, we show that in vivo levels of kinases and phosphatases frequently exceed the levels of their corresponding substrates in budding yeast. This result is in contrast to the conditions often required by zero-order ultrasensitivity, perhaps the most well known means for how such cycles become ultrasensitive. We therefore introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than numbers of substrates. Our model combines distributive and non-distributive actions of the enzymes with two-stage binding and concerted allosteric transitions of the substrate. We use analytical and numerical methods to calculate the Hill number of the response. For a substrate with [Formula: see text] phosphosites, we find an upper bound of the Hill number of [Formula: see text], and so even systems with a single phosphosite can be ultrasensitive. Two-stage binding, where an enzyme must first bind to a binding site on the substrate before it can access the substrate's phosphosites, allows the enzymes to sequester the substrate. Such sequestration combined with competition for each phosphosite provides an intuitive explanation for the sigmoidal shifts in levels of phosphorylated substrate. Additionally, we find cases for which the response is not monotonic, but shows instead a peak at intermediate levels of input. Given its generality, we expect the mechanism described by our model to often underlay decision-making circuits in eukaryotic cells