Biomarker evidence for recent turf cultivation in Northeast Brazil (Lagoa do Boqueirao, RN State)

The first meter of sediment in Lagoa do Boqueirao [Rio Grande do Norte State (RN), Brazil] is characterized by low sedimentation rates over the period 1000 BC-1500 AD and a high sedimentation rate in the top 20 cm, corresponding to the last 10 years Several pentacyclic triterpene methyl ethers (PTMEs) such as taraxer-14-en-3 alpha-ol ME (crusgallin) and arbor-9(11)-en-3 beta-ol ME (cylindrin) occur in all the samples selected The major change in sedimentation rate recorded at 20 cm is accompanied by a change in PTME concentration and distribution Sediments deposited during the period 1000 BC-1500 AD contain PTMEs in low concentration (1 3 mu g/g sed), which could constitute a geochemical background of the grass that naturally developed in the catchment High PTME concentrations occur during the period 1996-2000. These result mainly from high concentrations of a compound tentatively assigned as arbor-8-en-3 beta ol ME, a potential diagenetic derivative of cylindrin The increase corresponds to the beginning of intensive cultivation of Cynodon dactylon and Zoysia japonica (arundoin and cylindrin producers), for the production of turf to cover Brazilian football stadiums and golf practices The results constitute a novel application of PTMEs to reconstruct land-use changes from lake sediment archives (C) 2009 Elsevier Ltd All rights reserve

On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation

We consider the problem of the speed selection mechanism for the one dimensional nonlinear diffusion equation $u_t = u_{xx} + f(u)$. It has been rigorously shown by Aronson and Weinberger that for a wide class of functions $f$, sufficiently localized initial conditions evolve in time into a monotonic front which propagates with speed $c^*$ such that $2 \sqrt{f'(0)} \leq c^* < 2 \sqrt{\sup(f(u)/u)}$. The lower value $c_L = 2 \sqrt{f'(0)}$ is that predicted by the linear marginal stability speed selection mechanism. We derive a new lower bound on the the speed of the selected front, this bound depends on $f$ and thus enables us to assess the extent to which the linear marginal selection mechanism is valid.Comment: 9 pages, REVTE

Prospectus, January 18, 2012

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Fluctuating "Pulled" Fronts: the Origin and the Effects of a Finite Particle Cutoff

Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed $v^*$ for $N \to \infty$ is extremely slow -- going only as $\ln^{-2}N$. In this paper, we study the front propagation in a simple stochastic lattice model. A detailed analysis of the microscopic picture of the front dynamics shows that for the description of the far tip of the front, one has to abandon the idea of a uniformly translating front solution. The lattice and finite particle effects lead to a ``stop-and-go'' type dynamics at the far tip of the front, while the average front behind it ``crosses over'' to a uniformly translating solution. In this formulation, the effect of stochasticity on the asymptotic front speed is coded in the probability distribution of the times required for the advancement of the ``foremost bin''. We derive expressions of these probability distributions by matching the solution of the far tip with the uniformly translating solution behind. This matching includes various correlation effects in a mean-field type approximation. Our results for the probability distributions compare well to the results of stochastic numerical simulations. This approach also allows us to deal with much smaller values of $N$ than it is required to have the $\ln^{-2}N$ asymptotics to be valid.Comment: 26 pages, 11 figures, to appear in Phys. rev.

Multiple Front Propagation Into Unstable States

The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable periodic pattern. It is found by a numerical solution of a model of the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of decay of such periodic unstable states is the propagation of a second front which replaces the unstable pattern by a another unstable periodic state with larger wavelength. The speed of this second front and the periodicity of the new state are analytically calculated with a generalization of the marginal stability formalism suited to the study of front propagation into periodic unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+rComment: 12 page