12 research outputs found
On the connection between the Nekhoroshev theorem and Arnold Diffusion
The analytical techniques of the Nekhoroshev theorem are used to provide
estimates on the coefficient of Arnold diffusion along a particular resonance
in the Hamiltonian model of Froeschl\'{e} et al. (2000). A resonant normal form
is constructed by a computer program and the size of its remainder
at the optimal order of normalization is calculated as a function
of the small parameter . We find that the diffusion coefficient
scales as , while the size of the optimal remainder
scales as in the range
. A comparison is made with the numerical
results of Lega et al. (2003) in the same model.Comment: Accepted in Celestial Mechanics and Dynamical Astronom
Non-Gaussian Velocity Distribution Function in a Vibrating Granular Bed
The simulation of granular particles in a quasi two-dimensional container
under the vertical vibration as an experimental accessible model for granular
gases is performed. The velocity distribution function obeys an
exponential-like function during the vibration and deviates from the
exponential function in free-cooling states. It is confirmed that this
exponential-like distribution function is produced by Coulomb's friction force.
A Langevin equation with Coulomb's friction is proposed to describe the motion
of such the system.Comment: 4 pages, 4 figures. to be published in Journal of Physical Society of
Japan Vol.73 No.
Continuum theory of partially fluidized granular flows
A continuum theory of partially fluidized granular flows is developed. The
theory is based on a combination of the equations for the flow velocity and
shear stresses coupled with the order parameter equation which describes the
transition between flowing and static components of the granular system. We
apply this theory to several important granular problems: avalanche flow in
deep and shallow inclined layers, rotating drums and shear granular flows
between two plates. We carry out quantitative comparisons between the theory
and experiment.Comment: 28 pages, 23 figures, submitted to Phys. Rev.
Classical Mechanics and Renormalization Group
The KAM theory is discussed in detail from the point of view of the
"renormalization group approach". We discuss also some aspects of the
possible existence of universal structures in the chaotic transition. The
quasi-periodic Schroedinger equation in one dimension is discussed as a
special case