4,486 research outputs found
Chaotic dynamics of three-dimensional H\'enon maps that originate from a homoclinic bifurcation
We study bifurcations of a three-dimensional diffeomorphism, , that has
a quadratic homoclinic tangency to a saddle-focus fixed point with multipliers
(\lambda e^{i\vphi}, \lambda e^{-i\vphi}, \gamma), where
and . We show that in a
three-parameter family, g_{\eps}, of diffeomorphisms close to , there
exist infinitely many open regions near \eps =0 where the corresponding
normal form of the first return map to a neighborhood of a homoclinic point is
a three-dimensional H\'enon-like map. This map possesses, in some parameter
regions, a "wild-hyperbolic" Lorenz-type strange attractor. Thus, we show that
this homoclinic bifurcation leads to a strange attractor. We also discuss the
place that these three-dimensional H\'enon maps occupy in the class of
quadratic volume-preserving diffeomorphisms.Comment: laTeX, 25 pages, 6 eps figure
Simulations of driven overdamped frictionless hard spheres
We introduce an event-driven simulation scheme for overdamped dynamics of
frictionless hard spheres subjected to external forces, neglecting hydrodynamic
interactions. Our event-driven approach is based on an exact equation of motion
which relates the driving force to the resulting velocities through the
geometric information characterizing the underlying network of contacts between
the hard spheres. Our method allows for a robust extraction of the
instantaneous coordination of the particles as well as contact force statistics
and dynamics, under any chosen driving force, in addition to shear flow and
compression. It can also be used for generating high-precision jammed packings
under shear, compression, or both. We present a number of additional
applications of our method.Comment: 12 pages, 9 figure
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