Meunier Conjecture

Fr\'ed\'eric Meunier's question about a multicolored Sperner lemma is addressed, leaving the question of connectivity for the color hypergraphs of such a multicolored simplex. Sperner's lemma asserts the existence of a simplex using all the colors for any vertex coloring of a subdivision of a large simplex with appropriate boundary conditions. Meunier's questions generalizes this to the situation of having several such colorings and asserts the existence of a simplex using enough different colors from each coloring

Evolution of the rates of mass wasting and fluvial sediment transfer from the epicentral area of the 1999, Mw 7.6 earthquake

The 1999 Chichi earthquake (Mw=7.6) triggered more than 20,000 landslides in the epicentral area in central west Taiwan, and subsequent typhoons have caused an even larger number of slope failures. As a result, the suspended sediment load of the epi- central Choshui River has increased dramatically. Measurements of suspended sedi- ment at a downstream gauging station indicate that the unit sediment concentration increased about six times due to the earthquake, and decreased exponentially due to flushing by subsequent typhoons. The e-folding time scale of the seismic perturbation of sediment transfer in the Choshui River is 3-5 years. Based on this estimate of the de- cay of the erosional response to the earthquake, a mass balance can be calculated for the earthquake, including co-seismic uplift and subsidence, post-seismic relaxation, and erosion. This mass balance shows that the Chi-Chi earthquake has acted to build ridge topography in the hanging wall of the fault, but in the far field, some destruc- tion of topography has occurred. However, our estimate of seismically-driven erosion may be incomplete. A detailed analysis of landsliding in the Chenyoulan tributary of the Choshui River indicates that most co-and post seismic landslide debris remains on hillslopes within the catchment. Recent typhoons have continued to cause high rates of landsliding high in the landscape, but rates of mass wasting near the stream net- work have decreased. The full geomorphic response to the Chi-Chi earthquake may be much larger, and more protracted than indicated by river gauging data

A new function of hydrocarbons in insect communication : maternal care and offspring signalling in the European earwig

International audienc

Accretion, disks, and magnetic activity in the TW Hya association

We present new photometric and spectroscopic data for the M-type members of the TW Hya association with the aim of a comprehensive study of accretion, disks and magnetic activity at the critical age of ~10 Myr where circumstellar matter disappears.Comment: 4 pages, to appear in Proceedings IAU Symposium No. 314, Young Stars & Planets Near the Sun, 201

Critical holes in undercooled wetting layers

The profile of a critical hole in an undercooled wetting layer is determined by the saddle-point equation of a standard interface Hamiltonian supported by convenient boundary conditions. It is shown that this saddle-point equation can be mapped onto an autonomous dynamical system in a three-dimensional phase space. The corresponding flux has a polynomial form and in general displays four fixed points, each with different stability properties. On the basis of this picture we derive the thermodynamic behaviour of critical holes in three different nucleation regimes of the phase diagram.Comment: 18 pages, LaTeX, 6 figures Postscript, submitted to J. Phys.

Stability problem in dynamo

It is shown, that the saturated $\alpha$-effect taken from the nonlinear dynamo equations for the thin disk can still produce exponentially growing magnetic field in the case, when this field does not feed back on the $\alpha$. For negative dynamo number (stationary regime) stability is defined by the structure of the spectra of the linear problem for the positive dynamo numbers. Stability condition for the oscillatory solution (positive dynamo number) is also obtained and related to the phase shift of the original magnetic field, which produced saturated $\alpha$ and magnetic field in the kinematic regime. Results can be used for explanation of the similar effect observed in the shell models simulations as well in the 3D dynamo models in the plane layer and sphere