4,218 research outputs found
A perturbative approach to the spectral zeta functions of strings, drums and quantum billiards
We have obtained an explicit expression for the spectral zeta functions and
for the heat kernel of strings, drums and quantum billiards working to third
order in perturbation theory, using a generalization of the binomial theorem to
operators. The perturbative parameter used in the expansion is either the small
deformation of a reference domain (for instance a square), or a small variation
of the density around a constant value (in two dimensions both cases can
apply). This expansion is well defined even in presence of degenerations of the
unperturbed spectrum. We have discussed several examples in one, two and three
dimensions, obtaining in some cases the analytic continuation of the series,
which we have then used to evaluate the corresponding Casimir energy. For the
case of a string with piecewise constant density, subject to different boundary
conditions, and of two concentric cylinders of very close radii, we have
reproduced results previously published, thus obtaining a useful check of our
method.Comment: 23 pages, 5 figures, 2 tables; version accepted on Journal of
Mathematical Physic
Hack Weeks as a model for Data Science Education and Collaboration
Across almost all scientific disciplines, the instruments that record our
experimental data and the methods required for storage and data analysis are
rapidly increasing in complexity. This gives rise to the need for scientific
communities to adapt on shorter time scales than traditional university
curricula allow for, and therefore requires new modes of knowledge transfer.
The universal applicability of data science tools to a broad range of problems
has generated new opportunities to foster exchange of ideas and computational
workflows across disciplines. In recent years, hack weeks have emerged as an
effective tool for fostering these exchanges by providing training in modern
data analysis workflows. While there are variations in hack week
implementation, all events consist of a common core of three components:
tutorials in state-of-the-art methodology, peer-learning and project work in a
collaborative environment. In this paper, we present the concept of a hack week
in the larger context of scientific meetings and point out similarities and
differences to traditional conferences. We motivate the need for such an event
and present in detail its strengths and challenges. We find that hack weeks are
successful at cultivating collaboration and the exchange of knowledge.
Participants self-report that these events help them both in their day-to-day
research as well as their careers. Based on our results, we conclude that hack
weeks present an effective, easy-to-implement, fairly low-cost tool to
positively impact data analysis literacy in academic disciplines, foster
collaboration and cultivate best practices.Comment: 15 pages, 2 figures, submitted to PNAS, all relevant code available
at https://github.com/uwescience/HackWeek-Writeu
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