59,918 research outputs found
Shaped extensions of singular spectrum analysis
Extensions of singular spectrum analysis (SSA) for processing of
non-rectangular images and time series with gaps are considered. A circular
version is suggested, which allows application of the method to the data given
on a circle or on a cylinder, e.g. cylindrical projection of a 3D ellipsoid.
The constructed Shaped SSA method with planar or circular topology is able to
produce low-rank approximations for images of complex shapes. Together with
Shaped SSA, a shaped version of the subspace-based ESPRIT method for frequency
estimation is developed. Examples of 2D circular SSA and 2D Shaped ESPRIT are
presented
A deformable microswimmer in a swirl: capturing and scattering dynamics
Inspired by the classical Kepler and Rutherford problem, we investigate an
analogous set-up in the context of active microswimmers: the behavior of a
deformable microswimmer in a swirl flow. First we identify new steady bound
states in the swirl flow and analyze their stability. Second we study the
dynamics of a self-propelled swimmer heading towards the vortex center, and we
observe the subsequent capturing and scattering dynamics. We distinguish
between two major types of swimmers, those that tend to elongate
perpendicularly to the propulsion direction and those that pursue a parallel
elongation. While the first ones can get caught by the swirl, the second ones
were always observed to be scattered, which proposes a promising escape
strategy. This offers a route to design artificial microswimmers that show the
desired behavior in complicated flow fields. It should be straightforward to
verify our results in a corresponding quasi-two-dimensional experiment using
self-propelled droplets on water surfaces.Comment: 13 pages, 8 figure
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