45,687 research outputs found
Optimal Taylor-Couette flow: direct numerical simulations
We numerically simulate turbulent Taylor-Couette flow for independently
rotating inner and outer cylinders, focusing on the analogy with turbulent
Rayleigh-B\'enard flow. Reynolds numbers of and
of the inner and outer cylinders, respectively, are
reached, corresponding to Taylor numbers Ta up to . Effective scaling
laws for the torque and other system responses are found. Recent experiments
with the Twente turbulent Taylor-Couette () setup and with a similar
facility in Maryland at very high Reynolds numbers have revealed an optimum
transport at a certain non-zero rotation rate ratio
of about . For large enough in the numerically
accessible range we also find such an optimum transport at non-zero
counter-rotation. The position of this maximum is found to shift with the
driving, reaching a maximum of for . An
explanation for this shift is elucidated, consistent with the experimental
result that becomes approximately independent of the driving strength
for large enough Reynolds numbers. We furthermore numerically calculate the
angular velocity profiles and visualize the different flow structures for the
various regimes. By writing the equations in a frame co-rotating with the outer
cylinder a link is found between the local angular velocity profiles and the
global transport quantities.Comment: Under consideration for publication in JFM, 31 pages, 25 figure
Measure preserving homomorphisms and independent sets in tensor graph powers
In this note, we study the behavior of independent sets of maximum
probability measure in tensor graph powers. To do this, we introduce an upper
bound using measure preserving homomorphisms. This work extends some previous
results about independence ratios of tensor graph powers.Comment: 5 page
An Exact No Free Lunch Theorem for Community Detection
A precondition for a No Free Lunch theorem is evaluation with a loss function
which does not assume a priori superiority of some outputs over others. A
previous result for community detection by Peel et al. (2017) relies on a
mismatch between the loss function and the problem domain. The loss function
computes an expectation over only a subset of the universe of possible outputs;
thus, it is only asymptotically appropriate with respect to the problem size.
By using the correct random model for the problem domain, we provide a
stronger, exact No Free Lunch theorem for community detection. The claim
generalizes to other set-partitioning tasks including core/periphery
separation, -clustering, and graph partitioning. Finally, we review the
literature of proposed evaluation functions and identify functions which
(perhaps with slight modifications) are compatible with an exact No Free Lunch
theorem
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