Currently Reading

Random fun items currently floating up through the arXivotubes include the following. Exercise: find the shortest science-fiction story which can connect all these e-prints, visiting each node only once.

Robert H. Brandenberger, “String Gas Cosmology” (arXiv:0808.0746).

String gas cosmology is a string theory-based approach to early universe cosmology which is based on making use of robust features of string theory such as the existence of new states and new symmetries. A first goal of string gas cosmology is to understand how string theory can effect the earliest moments of cosmology before the effective field theory approach which underlies standard and inflationary cosmology becomes valid. String gas cosmology may also provide an alternative to the current standard paradigm of cosmology, the inflationary universe scenario. Here, the current status of string gas cosmology is reviewed.

Dimitri Skliros, Mark Hindmarsh, “Large Radius Hagedorn Regime in String Gas Cosmology” (arXiv:0712.1254, to be published in Phys. Rev. D).

We calculate the equation of state of a gas of strings at high density in a large toroidal universe, and use it to determine the cosmological evolution of background metric and dilaton fields in the entire large radius Hagedorn regime, (ln S)^{1/d} << R << S^{1/d} (with S the total entropy). The pressure in this regime is not vanishing but of O(1), while the equation of state is proportional to volume, which makes our solutions significantly different from previously published approximate solutions. For example, we are able to calculate the duration of the high-density "Hagedorn" phase, which increases exponentially with increasing entropy, S. We go on to discuss the difficulties of the scenario, quantifying the problems of establishing thermal equilibrium and producing a large but not too weakly-coupled universe.

V. M. Kenkre, Niraj Kumar, “Nonlinearity in Bacterial Population Dynamics: Proposal for Experiments for the Observation of Abrupt Transitions in Patches” (arXiv:0808.0172).

An explicit proposal for experiments leading to abrupt transitions in spatially extended bacterial populations in a Petri dish is presented on the basis of an exact formula obtained through an analytic theory. The theory provides accurately the transition expressions in spite of the fact that the actual solutions, which involve strong nonlinearity, are inaccessible to it. The analytic expressions are verified through numerical solutions of the relevant nonlinear equation. The experimental set-up suggested uses opaque masks in a Petri dish bathed in ultraviolet radiation as in Lin et al., Biophys. J. {\bf 87}, 75 (2004) and Perry, J. R. Soc. Interface {\bf 2}, 379 (2005) but is based on the interplay of two distances the bacteria must traverse, one of them favorable and the other adverse. As a result of this interplay feature, the experiments proposed introduce highly enhanced reliability in interpretation of observations and in the potential for extraction of system parameters.

Authors: M. S. Baptista, F. Moukam Kakmeni, Gianluigi Del Magno, M. S. Hussein, “Bounds for Kolmogorov-Sinai entropy of active networks” (arXiv:0805.3487).

According to the Pesin entropy formula [Y. B. Pesin, Russia Mathematical Survey vol. 32, 55 (1977)], the sum of all the positive Lyapunov exponents of a dynamical system (with smooth invariant measure) provides the Kolmogorov-Sinai (KS) entropy. Such result allows one to calculate this entropy even for very complex chaotic networks, by only using the Lyapunov exponents. However, when the size of the network becomes large, even the Pesin formula becomes unpractical, as the Lyapunov exponents demand heavy numerical computations. Here, we show that for a large class of dynamical systems, the sum of all the positive Lyapunov exponents of an active network (formed by nodes that are not necessarely synchronous) is bounded by the sum of all the positive Lyapunov exponents of the synchronization manifold, a quantity that can be straightforwardly calculated by only knowing the connecting matrix of the network and the low-dimensional dynamics of the synchronization manifold. This fact enables one to predict the behavior of a large network by using information provided by only two coupled nodes.

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