19,534 research outputs found
Aubry-Mather measures in the non convex setting
The adjoint method, introduced in [L. C. Evans, Arch. Ration. Mech. Anal., 197 (2010), pp. 1053ā1088] and [H. V. Tran, Calc. Var. Partial Differential Equations, 41 (2011), pp. 301ā319], is used to construct analogues to the AubryāMather 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 Ā© 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 Li + Bi are
analyzed in the framework of the DPP approach.Comment: 12 pages, 2 figure
- ā¦