2,917 research outputs found
Output functions and fractal dimensions in dynamical systems
We present a novel method for the calculation of the fractal dimension of
boundaries in dynamical systems, which is in many cases many orders of
magnitude more efficient than the uncertainty method. We call it the Output
Function Evaluation (OFE) method. The OFE method is based on an efficient
scheme for computing output functions, such as the escape time, on a
one-dimensional portion of the phase space. We show analytically that the OFE
method is much more efficient than the uncertainty method for boundaries with
, where is the dimension of the intersection of the boundary with a
one-dimensional manifold. We apply the OFE method to a scattering system, and
compare it to the uncertainty method. We use the OFE method to study the
behavior of the fractal dimension as the system's dynamics undergoes a
topological transition.Comment: Uses REVTEX; to be published in Phys. Rev. Let
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Engineering a static verification tool for GPU kernels
We report on practical experiences over the last 2.5 years related to the engineering of GPUVerify, a static verification tool for OpenCL and CUDA GPU kernels, plotting the progress of GPUVerify from a prototype to a fully functional and relatively efficient analysis tool. Our hope is that this experience report will serve the verification community by helping to inform future tooling efforts. © 2014 Springer International Publishing
Random fluctuation leads to forbidden escape of particles
A great number of physical processes are described within the context of
Hamiltonian scattering. Previous studies have rather been focused on
trajectories starting outside invariant structures, since the ones starting
inside are expected to stay trapped there forever. This is true though only for
the deterministic case. We show however that, under finitely small random
fluctuations of the field, trajectories starting inside Arnold-Kolmogorov-Moser
(KAM) islands escape within finite time. The non-hyperbolic dynamics gains then
hyperbolic characteristics due to the effect of the random perturbed field. As
a consequence, trajectories which are started inside KAM curves escape with
hyperbolic-like time decay distribution, and the fractal dimension of a set of
particles that remain in the scattering region approaches that for hyperbolic
systems. We show a universal quadratic power law relating the exponential decay
to the amplitude of noise. We present a random walk model to relate this
distribution to the amplitude of noise, and investigate this phenomena with a
numerical study applying random maps.Comment: 6 pages, 6 figures - Up to date with corrections suggested by
referee
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