72 research outputs found
A hierarchy of coupled maps
A large number of logistic maps are coupled together as a mathematical metaphor for complex natural systems with hierarchical organization. The elementary maps are first collected into globally coupled lattices. These lattices are then coupled together in a hierarchical way to form a system with many degrees of freedom. We summarize the behavior of the individual blocks, and then explore the dynamics of the hierarchy. We offer some ideas that guide our understanding of this type of system
Bulldozing of granular material
We investigate the bulldozing motion of a granular sandpile driven forwards by a vertical plate. The problem is set up in the laboratory by emplacing the pile on a table rotating underneath a stationary plate; the continual circulation of the bulldozed material allows the dynamics to be explored over relatively long times, and the variation of the velocity with radius permits one to explore the dependence on bulldozing speed within a single experiment. We measure the time-dependent surface shape of the dune for a range of rotation rates, initial volumes and radial positions, for four granular materials, ranging from glass spheres to irregularly shaped sand. The evolution of the dune can be separated into two phases: a rapid initial adjustment to a state of quasi-steady avalanching perpendicular to the blade, followed by a much slower phase of lateral spreading and radial migration. The quasi-steady avalanching sets up a well-defined perpendicular profile with a nearly constant slope. This profile can be scaled by the depth against the bulldozer to collapse data from different times, radial positions and experiments onto common ‘master curves' that are characteristic of the granular material and depend on the local Froude number. The lateral profile of the dune along the face of the bulldozer varies more gradually with radial position, and evolves by slow lateral spreading. The spreading is asymmetrical, with the inward progress of the dune eventually arrested and its bulk migrating to larger radii. A one-dimensional depth-averaged model recovers the nearly linear perpendicular profile of the dune, but does not capture the finer nonlinear details of the master curves. A two-dimensional version of the model leads to an advection-diffusion equation that reproduces the lateral spreading and radial migration. Simulations using the discrete element method reproduce in more quantitative detail many of the experimental findings and furnish further insight into the flow dynamic
Stellar turbulence and mode physics
An overview of selected topical problems on modelling oscillation properties
in solar-like stars is presented. High-quality oscillation data from both
space-borne intensity observations and ground-based spectroscopic measurements
provide first tests of the still-ill-understood, superficial layers in distant
stars. Emphasis will be given to modelling the pulsation dynamics of the
stellar surface layers, the stochastic excitation processes and the associated
dynamics of the turbulent fluxes of heat and momentum.Comment: Proc. HELAS Workshop on 'Synergies between solar and stellar
modelling', eds M. Marconi, D. Cardini, M. P. Di Mauro, Astrophys. Space
Sci., in the pres
Two–dimensional viscoplastic dambreaks
We report the results of computations for two–dimensional dambreaks of viscoplastic fluid, focusing on the phenomenology of the collapse, the mode of initial failure, and the final shape of the slump. The volume-of-fluid method is used to evolve the surface of the viscoplastic fluid, and its rheology is captured by either regularizing the viscosity or using an augmented-Lagrangian scheme. We outline a modification to the volume-of-fluid scheme that eliminates resolution problems associated with the no-slip condition applied on the underlying surface. We establish that the regularized and augmented-Lagrangian methods yield comparable results, except for the stress field at the initiation or termination of motion. The numerical results are compared with asymptotic theories valid for relatively shallow or vertically slender flow, with a series of previously reported experiments, and with predictions based on plasticity theory
Stochastic excitation of acoustic modes in stars
For more than ten years, solar-like oscillations have been detected and
frequencies measured for a growing number of stars with various characteristics
(e.g. different evolutionary stages, effective temperatures, gravities, metal
abundances ...).
Excitation of such oscillations is attributed to turbulent convection and
takes place in the uppermost part of the convective envelope. Since the
pioneering work of Goldreich & Keely (1977), more sophisticated theoretical
models of stochastic excitation were developed, which differ from each other
both by the way turbulent convection is modeled and by the assumed sources of
excitation. We review here these different models and their underlying
approximations and assumptions.
We emphasize how the computed mode excitation rates crucially depend on the
way turbulent convection is described but also on the stratification and the
metal abundance of the upper layers of the star. In turn we will show how the
seismic measurements collected so far allow us to infer properties of turbulent
convection in stars.Comment: Notes associated with a lecture given during the fall school
organized by the CNRS and held in St-Flour (France) 20-24 October 2008 ; 39
pages ; 11 figure
Diffusive transport and self-consistent dynamics in coupled maps
The study of diffusion in Hamiltonian systems has been a problem of interest
for a number of years.
In this paper we explore the influence of self-consistency on the diffusion
properties of systems described by coupled symplectic maps. Self-consistency,
i.e. the back-influence of the transported quantity on the velocity field of
the driving flow, despite of its critical importance, is usually overlooked in
the description of realistic systems, for example in plasma physics. We propose
a class of self-consistent models consisting of an ensemble of maps globally
coupled through a mean field. Depending on the kind of coupling, two different
general types of self-consistent maps are considered: maps coupled to the field
only through the phase, and fully coupled maps, i.e. through the phase and the
amplitude of the external field. The analogies and differences of the diffusion
properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure
Frozen spatial chaos induced by boundaries
We show that rather simple but non-trivial boundary conditions could induce
the appearance of spatial chaos (that is stationary, stable, but spatially
disordered configurations) in extended dynamical systems with very simple
dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion
equation in a two-dimensional undulated domain. Concepts from the theory of
dynamical systems, and a transverse-single-mode approximation are used to
describe the spatially chaotic structures.Comment: 9 pages, 6 figures, submitted for publication; for related work visit
http://www.imedea.uib.es/~victo
Discrete kink dynamics in hydrogen-bonded chains I: The one-component model
We study topological solitary waves (kinks and antikinks) in a nonlinear
one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse
type. This chain is used to describe the collective proton dynamics in
quasi-one-dimensional networks of hydrogen bonds, where the on-site potential
plays role of the proton potential in the hydrogen bond. The system supports a
rich variety of stationary kink solutions with different symmetry properties.
We study the stability and bifurcation structure of all these stationary kink
states. An exactly solvable model with a piecewise ``parabola-constant''
approximation of the double-Morse potential is suggested and studied
analytically. The dependence of the Peierls-Nabarro potential on the system
parameters is studied. Discrete travelling-wave solutions of a narrow permanent
profile are shown to exist, depending on the anharmonicity of the Morse
potential and the cooperativity of the hydrogen bond (the coupling constant of
the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure
Prospects for asteroseismology
The observational basis for asteroseismology is being dramatically
strengthened, through more than two years of data from the CoRoT satellite, the
flood of data coming from the Kepler mission and, in the slightly longer term,
from dedicated ground-based facilities. Our ability to utilize these data
depends on further development of techniques for basic data analysis, as well
as on an improved understanding of the relation between the observed
frequencies and the underlying properties of the stars. Also, stellar modelling
must be further developed, to match the increasing diagnostic potential of the
data. Here we discuss some aspects of data interpretation and modelling,
focussing on the important case of stars with solar-like oscillations.Comment: Proc. HELAS Workshop on 'Synergies between solar and stellar
modelling', eds M. Marconi, D. Cardini & M. P. Di Mauro, Astrophys. Space
Sci., in the press Revision: correcting abscissa labels on Figs 1 and
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