Surface-wave damping in a brimful circular cylinder

The natural frequencies and damping rates of surface waves in a circular cylinder with pinned-end boundary conditions are calculated in terms of the gravitational Reynolds and Bond numbers, C[minus sign]1 and B, and the slenderness of the cylinder [Lambda], in the limit C[rightward arrow]0. We consider higher-order approximations that include the effect of viscous dissipation in the Stokes boundary layers and the bulk. A comparison with clean-surface experiments by Henderson & Miles (1994) shows a satisfactory agreement except for the first axisymmetric mode, which exhibits a 26% discrepancy. The much larger dramatic discrepancy of former theoretical predictions is hereby improved and explained

RED: Deep Recurrent Neural Networks for Sleep EEG Event Detection

The brain electrical activity presents several short events during sleep that can be observed as distinctive micro-structures in the electroencephalogram (EEG), such as sleep spindles and K-complexes. These events have been associated with biological processes and neurological disorders, making them a research topic in sleep medicine. However, manual detection limits their study because it is time-consuming and affected by significant inter-expert variability, motivating automatic approaches. We propose a deep learning approach based on convolutional and recurrent neural networks for sleep EEG event detection called Recurrent Event Detector (RED). RED uses one of two input representations: a) the time-domain EEG signal, or b) a complex spectrogram of the signal obtained with the Continuous Wavelet Transform (CWT). Unlike previous approaches, a fixed time window is avoided and temporal context is integrated to better emulate the visual criteria of experts. When evaluated on the MASS dataset, our detectors outperform the state of the art in both sleep spindle and K-complex detection with a mean F1-score of at least 80.9% and 82.6%, respectively. Although the CWT-domain model obtained a similar performance than its time-domain counterpart, the former allows in principle a more interpretable input representation due to the use of a spectrogram. The proposed approach is event-agnostic and can be used directly to detect other types of sleep events.Comment: 8 pages, 5 figures. In proceedings of the 2020 International Joint Conference on Neural Networks (IJCNN 2020

Linear oscillations of axisymmetric viscous liquid bridges

Small amplitude free oscillations of axisymmetric capillary bridges are considered for varying values of the capillary Reynolds number C-1 and the slenderness of the bridge Λ . A semi-analytical method is presented that provides cheap and accurate results for arbitrary values of C-1 and Λ ; several asymptotic limits (namely, C>> 1, C>>1, Λ >> 1 \ {and} \ |π -Λ |>> 1 ) are considered in some detail, and the associated approximate results are checked. A fairly complete picture of the (fairly complex) spectrum of the linear problem is obtained for varying values of C and Λ . Two kinds of normal modes, called capillary and hydrodynamic respectively, are almost always clearly identified, the former being associated with free surface deformation and the latter, only with the internal flow field; when C is small the damping rate associated with both kind of modes is comparable, and the hydrodynamic ones explain the appearance of secondary (steady or slowly-varying) streaming flow

Infrared propagators of Yang-Mills theory from perturbation theory

We show that the correlation functions of ghosts and gluons for the pure Yang-Mills theory in Landau gauge can be accurately reproduced for all momenta by a one-loop calculation. The key point is to use a massive extension of the Faddeev-Popov action. The agreement with lattice simulation is excellent in d=4. The one-loop calculation also reproduces all the characteristic features of the lattice simulations in d=3 and naturally explains the pecularities of the propagators in d=2.Comment: 4 pages, 4 figures

A note on the effect of surface contamination in water wave damping

Asymptotic formulas are derived for the effect of contamination on surface wave damping in a brimful circular cylinder; viscosity is assumed to be small and contamination is modelled through Marangoni elasticity with insoluble surfactant. It is seen that an appropriately chosen finite Marangoni elasticity provides an explanation for a significant amount of the unexplained additional damping rate in a well-known experiment by Henderson & Miles (1994); discrepancies are within 15%, significantly lower than those encountered by Henderson & Miles (1994) under the assumption of inextensible film

Perfect Necklaces

We introduce a variant of de Bruijn words that we call perfect necklaces. Fix a finite alphabet. Recall that a word is a finite sequence of symbols in the alphabet and a circular word, or necklace, is the equivalence class of a word under rotations. For positive integers k and n, we call a necklace (k,n)-perfect if each word of length k occurs exactly n times at positions which are different modulo n for any convention on the starting point. We call a necklace perfect if it is (k,k)-perfect for some k. We prove that every arithmetic sequence with difference coprime with the alphabet size induces a perfect necklace. In particular, the concatenation of all words of the same length in lexicographic order yields a perfect necklace. For each k and n, we give a closed formula for the number of (k,n)-perfect necklaces. Finally, we prove that every infinite periodic sequence whose period coincides with some (k,n)-perfect necklace for any n, passes all statistical tests of size up to k, but not all larger tests. This last theorem motivated this work