79,731 research outputs found
Fractal fractal dimensions of deterministic transport coefficients
If a point particle moves chaotically through a periodic array of scatterers
the associated transport coefficients are typically irregular functions under
variation of control parameters. For a piecewise linear two-parameter map we
analyze the structure of the associated irregular diffusion coefficient and
current by numerically computing dimensions from box-counting and from the
autocorrelation function of these graphs. We find that both dimensions are
fractal for large parameter intervals and that both quantities are themselves
fractal functions if computed locally on a uniform grid of small but finite
subintervals. We furthermore show that there is a simple functional
relationship between the structure of fractal fractal dimensions and the
difference quotient defined on these subintervals.Comment: 16 pages (revtex) with 6 figures (postscript
Formal executable descriptions of biological systems
The similarities between systems of living entities and systems of concurrent processes may support biological experiments in silico. Process calculi offer a formal framework to describe biological systems, as well as to analyse their behaviour, both from a qualitative and a quantitative point of view. A couple of little examples help us in showing how this can be done. We mainly focus our attention on the qualitative and quantitative aspects of the considered biological systems, and briefly illustrate which kinds of analysis are possible. We use a known stochastic calculus for the first example. We then present some statistics collected by repeatedly running the specification, that turn out to agree with those obtained by experiments in vivo. Our second example motivates a richer calculus. Its stochastic extension requires a non trivial machinery to faithfully reflect the real dynamic behaviour of biological systems
Injecting Abstract Interpretations into Linear Cost Models
We present a semantics based framework for analysing the quantitative
behaviour of programs with regard to resource usage. We start from an
operational semantics equipped with costs. The dioid structure of the set of
costs allows for defining the quantitative semantics as a linear operator. We
then present an abstraction technique inspired from abstract interpretation in
order to effectively compute global cost information from the program.
Abstraction has to take two distinct notions of order into account: the order
on costs and the order on states. We show that our abstraction technique
provides a correct approximation of the concrete cost computations
A Parametric Study of the Coalescence of Liquid Drops in a Viscous Gas
The coalescence of two liquid drops surrounded by a viscous gas is considered
in the framework of the conventional model. The problem is solved numerically
with particular attention to resolving the very initial stage of the process
which only recently has become accessible both experimentally and
computationally. A systematic study of the parameter space of practical
interest allows the influence of the governing parameters in the system to be
identified and the role of viscous gas to be determined. In particular, it is
shown that the viscosity of the gas suppresses the formation of toroidal bubble
predicted in some cases by early computations where the gas' dynamics was
neglected. Focussing computations on the very initial stages of coalescence and
considering the large parameter space allows us to examine the accuracy and
limits of applicability of various `scaling laws' proposed for different
`regimes' and, in doing so, reveal certain inconsistencies in recent works. A
comparison to experimental data shows that the conventional model is able to
reproduce many qualitative features of the initial stages of coalescence, such
as a collapse of calculations onto a `master curve' but, quantitatively,
overpredicts the observed speed of coalescence and there are no free parameters
to improve the fit. Finally, a phase diagram of parameter space, differing from
previously published ones, is used to illustrate the key findings.Comment: Accepted for publication in the Journal of Fluid Mechanic
Spatial Aggregation: Theory and Applications
Visual thinking plays an important role in scientific reasoning. Based on the
research in automating diverse reasoning tasks about dynamical systems,
nonlinear controllers, kinematic mechanisms, and fluid motion, we have
identified a style of visual thinking, imagistic reasoning. Imagistic reasoning
organizes computations around image-like, analogue representations so that
perceptual and symbolic operations can be brought to bear to infer structure
and behavior. Programs incorporating imagistic reasoning have been shown to
perform at an expert level in domains that defy current analytic or numerical
methods. We have developed a computational paradigm, spatial aggregation, to
unify the description of a class of imagistic problem solvers. A program
written in this paradigm has the following properties. It takes a continuous
field and optional objective functions as input, and produces high-level
descriptions of structure, behavior, or control actions. It computes a
multi-layer of intermediate representations, called spatial aggregates, by
forming equivalence classes and adjacency relations. It employs a small set of
generic operators such as aggregation, classification, and localization to
perform bidirectional mapping between the information-rich field and
successively more abstract spatial aggregates. It uses a data structure, the
neighborhood graph, as a common interface to modularize computations. To
illustrate our theory, we describe the computational structure of three
implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the
spatial aggregation generic operators by mixing and matching a library of
commonly used routines.Comment: See http://www.jair.org/ for any accompanying file
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