48,920 research outputs found
Dynamics of Oscillators Coupled by a Medium with Adaptive Impact
In this article we study the dynamics of coupled oscillators. We use
mechanical metronomes that are placed over a rigid base. The base moves by a
motor in a one-dimensional direction and the movements of the base follow some
functions of the phases of the metronomes (in other words, it is controlled to
move according to a provided function). Because of the motor and the feedback,
the phases of the metronomes affect the movements of the base while on the
other hand, when the base moves, it affects the phases of the metronomes in
return.
For a simple function for the base movement (such as in which is the velocity of the base,
is a multiplier, is a proportion and and
are phases of the metronomes), we show the effects on the dynamics of the
oscillators. Then we study how this function changes in time when its
parameters adapt by a feedback. By numerical simulations and experimental
tests, we show that the dynamic of the set of oscillators and the base tends to
evolve towards a certain region. This region is close to a transition in
dynamics of the oscillators; where more frequencies start to appear in the
frequency spectra of the phases of the metronomes
The Topology ToolKit
This system paper presents the Topology ToolKit (TTK), a software platform
designed for topological data analysis in scientific visualization. TTK
provides a unified, generic, efficient, and robust implementation of key
algorithms for the topological analysis of scalar data, including: critical
points, integral lines, persistence diagrams, persistence curves, merge trees,
contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots,
Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due
to a tight integration with ParaView. It is also easily accessible to
developers through a variety of bindings (Python, VTK/C++) for fast prototyping
or through direct, dependence-free, C++, to ease integration into pre-existing
complex systems. While developing TTK, we faced several algorithmic and
software engineering challenges, which we document in this paper. In
particular, we present an algorithm for the construction of a discrete gradient
that complies to the critical points extracted in the piecewise-linear setting.
This algorithm guarantees a combinatorial consistency across the topological
abstractions supported by TTK, and importantly, a unified implementation of
topological data simplification for multi-scale exploration and analysis. We
also present a cached triangulation data structure, that supports time
efficient and generic traversals, which self-adjusts its memory usage on demand
for input simplicial meshes and which implicitly emulates a triangulation for
regular grids with no memory overhead. Finally, we describe an original
software architecture, which guarantees memory efficient and direct accesses to
TTK features, while still allowing for researchers powerful and easy bindings
and extensions. TTK is open source (BSD license) and its code, online
documentation and video tutorials are available on TTK's website
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