A new inequality about matrix products and a Berger-Wang formula

We prove an inequality relating the norm of a product of matrices $A_n\cdots A_1$ with the spectral radii of subproducts $A_j\cdots A_i$ with $1\leq i\leq j\leq n$. Among the consequences of this inequality, we obtain the classical Berger-Wang formula as an immediate corollary, and give an easier proof of a characterization of the upper Lyapunov exponent due to I. Morris. As main ingredient for the proof of this result, we prove that for a large enough $n$, the product $A_n\cdots A_1$ is zero under the hypothesis that $A_j\cdots A_i$ are nilpotent for all $1\leq i \leq j\leq n$.Comment: Final version, to appear in Journal de l Ecole polytechnique. Mathematique

Hadron spectra from a non-relativistic model with confining harmonic potential

Hadron spectra and other properties of quark systems are studied in the framework of a non-relativistic spin-independent phenomenological model. The chosen confining potential is harmonic, which allowed us to obtain analytical solutions for both meson and baryon (of equal constituent quarks) spectra. The introduced parameters are fixed from the low-lying levels of heavy quark mesons. The requirement of flavor independence is imposed, and it restricts the possible choices of inter-quark potentials. The hyper-spherical coordinates are considered for the solution of the three-body problem.Comment: Revtex file, 8 figures, 18 pages. Content and references added, some tables changed by figure

Outer rise seismicity related to the Maule, Chile 2010 mega-thrust earthquake and hydration of the incoming oceanic lithosphere

Most of the recent published geodetic models of the 2010 Maule, Chile mega-thrust earthquake (Mw=8.8) show a pronounced slip maximum of 15-20 m offshore Iloca (similar to 35 degrees S), indicating that co-seismic slip was largest north of the epicenter of the earthquake rupture area. A secondary slip maximum 8-10 m appears south of the epicenter west of the Arauco Peninsula. During the first weeks following the main shock and seaward of the main slip maximum, an outer rise seismic cluster of >450 events, mainly extensional, with magnitudes Mw=4-6 was formed. In contrast, the outer rise located seaward of the secondary slip maximum presents little seismicity. This observation suggests that outer rise seismicity following the Maule earthquake is strongly correlated with the heterogeneous coseismic slip distribution of the main megathrust event. In particular, the formation of the outer-rise seismic cluster in the north, which spatially correlates with the main maximum slip, is likely linked to strong extensional stresses transfered from the large slip of the subducting oceanic plate. In addition, high resolution bathymetric data reveals that bending-related faulting is more intense seaward of the main maximum slip, where well developed extensional faults strike parallel to the trench axis. Also published seismic constraints reveal reduced P-wave velocities in the uppermost mantle at the trench-outer rise region (7.5-7.8 km/s), which suggest serpentinization of the uppermost mantle. Seawater percolation up to mantle depths is likely driven by bending related-faulting at the outer rise. Water percolation into the upper mantle is expected to be more efficient during the co-seismic and early post-seismic periods of large megathrust earthquakes when intense extensional faulting of the oceanic lithospher