Stochastic modelling of regional archaeomagnetic series

SUMMARY We report a new method to infer continuous time series of the declination, inclination and intensity of the magnetic field from archeomagnetic data. Adopting a Bayesian perspective, we need to specify a priori knowledge about the time evolution of the magnetic field. It consists in a time correlation function that we choose to be compatible with present knowledge about the geomagnetic time spectra. The results are presented as distributions of possible values for the declination, inclination or intensity. We find that the methodology can be adapted to account for the age uncertainties of archeological artefacts and we use Markov Chain Monte Carlo to explore the possible dates of observations. We apply the method to intensity datasets from Mari, Syria and to intensity and directional datasets from Paris, France. Our reconstructions display more rapid variations than previous studies and we find that the possible values of geomagnetic field elements are not necessarily normally distributed. Another output of the model is better age estimates of archeological artefacts

Testing statistical palaeomagnetic field models against directional data affected by measurement errors

International audienceIn a previous paper, Khokhlov et al. introduced a method to test the compatibility of so-called 'giant Gaussian process' (GGP) statistical models of the palaeomagnetic field against any palaeosecular variation database. This method did not take measurement errors into account. It therefore lacked practical usefulness. In the present paper, we remedy this and generalize the method to account for measurement errors in a way consistent with both the assumptions underlying the GGP approach and the nature of those errors. The method is implemented to test GGP models against any directional data set affected by Fisherian errors. Simulations show that the method can usefully discriminate which GGP model best explains a given data set. Applying the method to test six published GGP models against a test Bruhnes stable polarity data set extracted from the Quidelleur et al. database, it is found that all but one model (that of Quidelleur and Courtillot) should be rejected. Although this result should be taken with care, and does not necessarily imply that this model is superior to other models (Quidelleur and Courtillot precisely used the Quidelleur et al. database to infer their model), it clearly shows that in practice also, and with the databases currently available, the method can discriminate various candidate GGP models. It also shows that the statistical behaviour of the geomagnetic field at times of stable polarity can indeed be described in a consistent way in terms of a GGP model. This 'forward' testing method could ultimately be used to design an 'inverse' approach to GGP modelling of the palaeomagnetic field

Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation

Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact and connected manifold and let u be a semi-concave function defined on M. If E (u) is the set of all the super-differentials of u and (\phi t) the Hamiltonian flow of H, we prove that for t > 0 small enough, \phi-t (E (u)) is an exact Lagrangian Lipschitz graph. This provides a geometric interpretation/explanation of a regularization tool that was introduced by P.~Bernard to prove the existence of C 1,1 subsolutions

Chemists and the School of nature

International audienceBiomimetism is an umbrella covering a variety of research fields ranging from the chemistry of natural products to nanocomposites, via biomaterials and supramolecular chemistry. . It is an informal movement and the concept itself is so loose that one can wonder whether biomimetism is more than a slogan forged by chemists in order to hop on the "green" bandwagon. Or could it bring a revolution into chemistry with a profound transformation of its practices

The cuttlefish Sepia officinalis (Sepiidae, Cephalopoda) constructs cuttlebone from a liquid-crystal precursor

Cuttlebone, the sophisticated buoyancy device of cuttlefish, is made of extensive superposed chambers that have a complex internal arrangement of calcified pillars and organic membranes. It has not been clear how this structure is assembled. We find that the membranes result from a myriad of minor membranes initially filling the whole chamber, made of nanofibres evenly oriented within each membrane and slightly rotated with respect to those of adjacent membranes, producing a helical arrangement. We propose that the organism secretes a chitin-protein complex, which self-organizes layer-by-layer as a cholesteric liquid crystal, whereas the pillars are made by viscous fingering. The liquid crystallization mechanism permits us to homologize the elements of the cuttlebone with those of other coleoids and with the nacreous septa and the shells of nautiloids. These results challenge our view of this ultra-light natural material possessing desirable mechanical, structural and biological properties, suggesting that two self-organizing physical principles suffice to understand its formation.Spanish Ministerio de Ciencia e Innovacion [CGL2010-20748-CO2-01, CGL2013-48247-P, FIS2013-48444-C2-2-P]; Andalusian Consejeria de Innovacion Ciencia y Tecnologia [RNM6433]; (Sepiatech, PROMAR program) of the Portuguese Ministerio da Agricultura e do Mar, Portugal [31.03.05.FEP.002]; Junta de Andalucia [RNM363]; FP7 COST Action of the European Community. [TD0903]info:eu-repo/semantics/publishedVersio

An analysis of the fluctuations of the geomagnetic dipole

The time evolution of the strength of the Earth's virtual axial dipole moment (VADM) is analyzed by relating it to the Fokker-Planck equation, which describes a random walk with VADM-dependent drift and diffusion coefficients. We demonstrate first that our method is able to retrieve the correct shape of the drift and diffusion coefficients from a time series generated by a test model. Analysis of the Sint-2000 data shows that the geomagnetic dipole mode has a linear growth time of 13 to 33 kyr, and that the nonlinear quenching of the growth rate follows a quadratic function of the type [1-(x/x0)^2]. On theoretical grounds, the diffusive motion of the VADM is expected to be driven by multiplicative noise, and the corresponding diffusion coefficient to scale quadratically with dipole strength. However, analysis of the Sint-2000 VADM data reveals a diffusion which depends only very weakly on the dipole strength. This may indicate that the magnetic field quenches the amplitude of the turbulent velocity in the Earth's outer core.Comment: 11 pages, 6 figure