Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure

Additively manufactured hierarchical stainless steels with high strength and ductility

Many traditional approaches for strengthening steels typically come at the expense of useful ductility, a dilemma known as strength–ductility trade-off. New metallurgical processing might offer the possibility of overcoming this. Here we report that austenitic 316L stainless steels additively manufactured via a laser powder-bed-fusion technique exhibit a combination of yield strength and tensile ductility that surpasses that of conventional 316L steels. High strength is attributed to solidification-enabled cellular structures, low-angle grain boundaries, and dislocations formed during manufacturing, while high uniform elongation correlates to a steady and progressive work-hardening mechanism regulated by a hierarchically heterogeneous microstructure, with length scales spanning nearly six orders of magnitude. In addition, solute segregation along cellular walls and low-angle grain boundaries can enhance dislocation pinning and promote twinning. This work demonstrates the potential of additive manufacturing to create alloys with unique microstructures and high performance for structural applications

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE