The Anisotropic Bak-Sneppen model

The Bak-Sneppen model is shown to fall into a different universality class with the introduction of a preferred direction, mirroring the situation in spin systems. This is first demonstrated by numerical simulations and subsequently confirmed by analysis of the multitrait version of the model, which admits exact solutions in the extremes of zero and maximal anisotropy. For intermediate anisotropies, we show that the spatiotemporal evolution of the avalanche has a power law `tail' which passes through the system for any non-zero anisotropy but remains fixed for the isotropic case, thus explaining the crossover in behaviour. Finally, we identify the maximally anisotropic model which is more tractable and yet more generally applicable than the isotropic system

Energy Distribution in disordered elastic Networks

Disordered networks are found in many natural and artificial materials, from gels or cytoskeletal structures to metallic foams or bones. Here, the energy distribution in this type of networks is modeled, taking into account the orientation of the struts. A correlation between the orientation and the energy per unit volume is found and described as a function of the connectivity in the network and the relative bending stiffness of the struts. If one or both parameters have relatively large values, the struts aligned in the loading direction present the highest values of energy. On the contrary, if these have relatively small values, the highest values of energy can be reached in the struts oriented transversally. This result allows explaining in a simple way remodeling processes in biological materials, for example, the remodeling of trabecular bone and the reorganization in the cytoskeleton. Additionally, the correlation between the orientation, the affinity, and the bending-stretching ratio in the network is discussed

Volume-controlled buckling of thin elastic shells: Application to crusts formed on evaporating partially-wetted droplets

Motivated by the buckling of glassy crusts formed on evaporating droplets of polymer and colloid solutions, we numerically model the deformation and buckling of spherical elastic caps controlled by varying the volume between the shell and the substrate. This volume constraint mimics the incompressibility of the unevaporated solvent. Discontinuous buckling is found to occur for sufficiently thin and/or large contact angle shells, and robustly takes the form of a single circular region near the boundary that `snaps' to an inverted shape, in contrast to externally pressurised shells. Scaling theory for shallow shells is shown to well approximate the critical buckling volume, the subsequent enlargement of the inverted region and the contact line force.Comment: 7 pages in J. Phys. Cond. Mat. spec; 4 figs (2 low-quality to reach LANL's over-restrictive size limits; ask for high-detailed versions if required

Factorization in Formal Languages

We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an quadratic upper and lower bound on the length of the shortest word not in uf(L). We observe that uf(L) need not be context-free if L is context-free. Next, we consider variations on unique factorization. We define a notion of "semi-unique" factorization, where every factorization has the same number of terms, and show that, if L is regular or even finite, the set of words having such a factorization need not be context-free. Finally, we consider additional variations, such as unique factorization "up to permutation" and "up to subset"

Rheological Chaos in a Scalar Shear-Thickening Model

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress \sigma is driven at a constant shear rate \dot\gamma and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(\sigma_1) and a linear decay at rate \lambda\sigma_2. Here \sigma_{1,2}(t) = \tau_{1,2}^{-1}\int_0^t\sigma(t')\exp[-(t-t')/\tau_{1,2}] {\rm d}t' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when \tau_2>\tau_1 and 0>R'(\sigma)>-\lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case \tau_1\to 0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.Comment: Reference added; typos corrected. To appear in PRE Rap. Com

Cardiovascular disease in a cohort exposed to the 1940-45 Channel Islands occupation

BACKGROUND To clarify the nature of the relationship between food deprivation/undernutrition during pre- and postnatal development and cardiovascular disease (CVD) in later life, this study examined the relationship between birth weight (as a marker of prenatal nutrition) and the incidence of hospital admissions for CVD from 1997–2005 amongst 873 Guernsey islanders (born in 1923–1937), 225 of whom had been exposed to food deprivation as children, adolescents or young adults (i.e. postnatal undernutrition) during the 1940–45 German occupation of the Channel Islands, and 648 of whom had left or been evacuated from the islands before the occupation began. METHODS Three sets of Cox regression models were used to investigate (A) the relationship between birth weight and CVD, (B) the relationship between postnatal exposure to the occupation and CVD and (C) any interaction between birth weight, postnatal exposure to the occupation and CVD. These models also tested for any interactions between birth weight and sex, and postnatal exposure to the occupation and parish of residence at birth (as a marker of parish residence during the occupation and related variation in the severity of food deprivation). RESULTS The first set of models (A) found no relationship between birth weight and CVD even after adjustment for potential confounders (hazard ratio (HR) per kg increase in birth weight: 1.12; 95% confidence intervals (CI): 0.70 – 1.78), and there was no significant interaction between birth weight and sex (p = 0.60). The second set of models (B) found a significant relationship between postnatal exposure to the occupation and CVD after adjustment for potential confounders (HR for exposed vs. unexposed group: 2.52; 95% CI: 1.54 – 4.13), as well as a significant interaction between postnatal exposure to the occupation and parish of residence at birth (p = 0.01), such that those born in urban parishes (where food deprivation was worst) had a greater HR for CVD than those born in rural parishes. The third model (C) found no interaction between birth weight and exposure to the occupation (p = 0.43). CONCLUSION These findings suggest that the levels of postnatal undernutrition experienced by children, adolescents and young adults exposed to food deprivation during the 1940–45 occupation of the Channel Islands were a more important determinant of CVD in later life than the levels of prenatal undernutrition experienced in utero prior to the occupatio