Aubry-Mather measures in the non convex setting

The adjoint method, introduced in [L. C. Evans, Arch. Ration. Mech. Anal., 197 (2010), pp. 1053–1088] and [H. V. Tran, Calc. Var. Partial Differential Equations, 41 (2011), pp. 301–319], is used to construct analogues to the Aubry–Mather measures for nonconvex Hamiltonians. More precisely, a general construction of probability measures, which in the convex setting agree with Mather measures, is provided. These measures may fail to be invariant under the Hamiltonian flow and a dissipation arises, which is described by a positive semidefinite matrix of Borel measures. However, in the case of uniformly quasiconvex Hamiltonians the dissipation vanishes, and as a consequence the invariance is guaranteed. Copyright © 2011 Society for Industrial and Applied Mathematic

Plastic Deformation of 2D Crumpled Wires

When a single long piece of elastic wire is injected trough channels into a confining two-dimensional cavity, a complex structure of hierarchical loops is formed. In the limit of maximum packing density, these structures are described by several scaling laws. In this paper it is investigated this packing process but using plastic wires which give origin to completely irreversible structures of different morphology. In particular, it is studied experimentally the plastic deformation from circular to oblate configurations of crumpled wires, obtained by the application of an axial strain. Among other things, it is shown that in spite of plasticity, irreversibility, and very large deformations, scaling is still observed.Comment: 5 pages, 6 figure

The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector Nonlinear Schrodinger equations appear as lowest negative and second positive flows within the extended hierarchy. This is fully analogous to the well-known connection between the sine-Gordon and mKdV equations within the extended mKdV hierarchy. A general formalism for a Toda-like symmetry occupying the ``negative'' sector of sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.Comment: 8 pages, LaTeX, typos corrected, references update

Structural properties of crumpled cream layers

The cream layer is a complex heterogeneous material of biological origin which forms spontaneously at the air-milk interface. Here, it is studied the crumpling of a single cream layer packing under its own weight at room temperature in three-dimensional space. The structure obtained in these circumstances has low volume fraction and anomalous fractal dimensions. Direct means and noninvasive NMR imaging technique are used to investigate the internal and external structure of these systems.Comment: 9 pages, 4 figures, accepted in J. Phys. D: Appl. Phy

Complete Fusion Enhancement and Suppression of Weakly Bound Nuclei at Near Barrier Energies

We consider the influence of breakup channels on the complete fusion of weakly bound systems in terms of dynamic polarization potentials. It is argued that the enhancement of the cross section at sub-barrier energies may be consistent with recent experimental observations that nucleon transfer, often leading to breakup, is dominant compared to direct breakup. The main trends of the experimental complete fusion cross section for $^{6,7}$Li + $^{209}$Bi are analyzed in the framework of the DPP approach.Comment: 12 pages, 2 figure