208 research outputs found
A Mathematical Model for the Dynamics and Synchronization of Cows
We formulate a mathematical model for daily activities of a cow (eating,
lying down, and standing) in terms of a piecewise affine dynamical system. We
analyze the properties of this bovine dynamical system representing the single
animal and develop an exact integrative form as a discrete-time mapping. We
then couple multiple cow "oscillators" together to study synchrony and
cooperation in cattle herds. We comment on the relevant biology and discuss
extensions of our model. With this abstract approach, we not only investigate
equations with interesting dynamics but also develop interesting biological
predictions. In particular, our model illustrates that it is possible for cows
to synchronize \emph{less} when the coupling is increased.Comment: to appear in Physica
Developing a flexible and expressive realtime polyphonic wave terrain synthesis instrument based on a visual and multidimensional methodology
The Jitter extended library for Max/MSP is distributed with a gamut of tools for the generation, processing, storage, and visual display of multidimensional data structures. With additional support for a wide range of media types, and the interaction between these mediums, the environment presents a perfect working ground for Wave Terrain Synthesis. This research details the practical development of a realtime Wave Terrain Synthesis instrument within the Max/MSP programming environment utilizing the Jitter extended library. Various graphical processing routines are explored in relation to their potential use for Wave Terrain Synthesis
Visualizing Astrophysical N-body Systems
I begin with a brief history of N-body simulation and visualization and then
go on to describe various methods for creating images and animations of modern
simulations in cosmology and galactic dynamics. These techniques are
incorporated into a specialized particle visualization software library called
MYRIAD that is designed to render images within large parallel N-body
simulations as they run. I present several case studies that explore the
application of these methods to animations of star clusters, interacting
galaxies and cosmological structure formation.Comment: 25 pages, accepted in the New Journal of Physics for upcoming Focus
issue on Visualization in Physics. Accompanying animations including a free
bittorrent download of the DVD GRAVITAS are available at
http://www.galaxydynamics.org/gravitas.htm
Spatial discretizations of generic dynamical systems
How is it possible to read the dynamical properties (ie when the time goes to
infinity) of a system on numerical simulations? To try to answer this question,
we study in this manuscript a model reflecting what happens when the orbits of
a discrete time system (for example an homeomorphism) are computed
numerically . The computer working in finite numerical precision, it will
replace by a spacial discretization of , denoted by (where the
order of discretization stands for the numerical accuracy). In particular,
we will be interested in the dynamical behaviour of the finite maps for a
generic system and going to infinity, where generic will be taken in
the sense of Baire (mainly among sets of homeomorphisms or
-diffeomorphisms).
The first part of this manuscript is devoted to the study of the dynamics of
the discretizations , when is a generic conservative/dissipative
homeomorphism of a compact manifold. We show that it would be mistaken to try
to recover the dynamics of from that of a single discretization : its
dynamics strongly depends on the order . To detect some dynamical features
of , we have to consider all the discretizations when goes through
.
The second part deals with the linear case, which plays an important role in
the study of -generic diffeomorphisms, discussed in the third part of this
manuscript. Under these assumptions, we obtain results similar to those
established in the first part, though weaker and harder to prove.Comment: 322 pages. This is an improved version of the thesis of the author
(among others, the introduction and conclusion have been translated into
English). In particular, it contains works already published on arXiv.
Comments welcome
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