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We present an explicit analysis of wave-resonant instability of swirling flows inside fast rotating cylindrical containers. The linear dynamics are decomposed into the interaction between the horizontal inner centrifugal edge waves, the outer vertical gravity waves with the aim of understanding the dynamics of the centrifugal waves. We show how the far field velocity induced respectively by the centrifugal and the gravity waves affect each other's propagation rates and amplitude growth. We follow this with an analysis of the instability in terms of a four wave interaction, two centrifugal and two gravity ones, and explain why the resonant instability can be obtained only between a pair of two counter-propagating waves, one centrifugal and one gravity. Furthermore, a near resonant regime which does not yield instability is shown to result from a phase-locking configuration between a pair of a counter-propagating centrifugal wave and a pro-propagating gravity one, where the interaction affects the waves' propagation rates but not the amplitude growth.

Mode-dependent loss (MDL) is known to be a major issue in space-division multiplexed (SMD) systems. Its effect on performance is complex as it affects both the data carrying signal and the accumulated amplification noise. In this paper we propose a procedure for characterizing the MDL of SDM systems by means of standard measurements that are routinely performed on SDM setups. The figure of merit that we present for quantifying MDL incorporates the effect on the transmitted signal and the noise and is directly related to the spectral efficiency reduction.

Active galactic nuclei (AGN) are prominent environments for stellar capture, growth and formation. These environments may catalyze stellar mergers and explosive transients, such as thermonuclear and core-collapse supernovae (SNe). SN explosions in AGN discs generate strong shocks, leading to unique observable signatures. We develop an analytical model which follows the evolution of the shock propagating in the disc until it eventually breaks out. We derive the peak luminosity, bolometric lightcurve, and breakout time. The peak luminosities may exceed $10^{45}$ erg s$^{-1}$ and last from hours to days. The brightest explosions occur in regions of reduced density; either off-plane, or in discs around low-mass central black holes ($\sim 10^6\ M_\odot$), or in starved subluminous AGNs. Explosions in the latter two sites are easier to observe due to a reduced AGN background luminosity. We perform suites of 1D Lagrangian radiative hydrodynamics SNEC code simulations to validate our results and obtain the luminosity in different bands, and 2D axisymmetric Eulerian hydrodynamics code HORMONE simulations to study the morphology of the ejecta and its deviation from spherical symmetry. The observed signature is expected to be a bright blue, UV, or X-ray flare on top of the AGN luminosity from the initial shock breakout, while the subsequent red part of the lightcurve will largely be unobservable. We estimate the upper limit for the total event rate to be $\mathcal{R}\lesssim 100\ \rm yr^{-1}\ Gpc^{-3}$ for optimal conditions and discuss the large uncertainties in this estimate. Future high-cadence transient searches may reveal these events. Some existing tidal disruption event candidates may originate from AGN supernovae. Accepted to MNRAS

We consider a compartmental model for ribosome flow during RNA translation called the RFM. This model includes a set of positive transition rates that control the flow from every site to the consecutive site. It has been shown that when these rates are time-varying and jointly T-periodic every solution of the RFM converges to a unique periodic solution with period T. In other words, the RFM entrains to the periodic excitation. In particular, the protein production rate converges to a unique T-periodic pattern. From a biological point of view, one may argue that the average of the periodic production rate, and not the instantaneous rate, is the relevant quantity. Here, we study a problem that can be roughly stated as: can periodic rates yield a higher average production rate than constant rates? We rigorously formulate this question and show via simulations, and rigorous analysis in one simple case, that the answer is no.

AbstractThe number and distribution of recessive alleles in the population for various diseases are not known at genome-wide-scale. Based on 6447 exome-sequences of healthy, genetically-unrelated Europeans of two distinct ancestries, we estimate that every individual is a carrier of at least 2 pathogenic variants in currently known autosomal recessive (AR) genes, and that 0.8-1% of European couples are at-risk of having a child affected with a severe AR genetic disorder. This risk is 16.5-fold higher for first cousins, but is significantly more increased for skeletal disorders and intellectual disabilities due to their distinct genetic architecture.

Let $M$ be a compact $C^{\infty}$ Riemannian manifold. Given $p$ and $q$ in $M$ and $T>0$, define $n_{T}(p,q)$ as the number of geodesic segments joining $p$ and $q$ with length $\leq T$. Mañé showed in [7] that \[ \lim_{T\rightarrow \infty}\frac{1}{T}\log \int_{M\times M}n_{T}(p,q)\,dp\,dq = h_{\rm top}, \] where $h_{\rm top}$ denotes the topological entropy of the geodesic flow of $M$.In this paper we exhibit an open set of metrics on the two-sphere for which \[ \limsup_{T\rightarrow\infty}\frac{1}{T}\log n_{T}(p,q)< h_{\rm top}, \] for a positive measure set of $(p,q)\in M\times M$. This answers in the negative questions raised by Mañé in [7].

We introduce a discrete model for binary spin-orbit-coupled (SOC) Bose-Einstein condensates (BEC) trapped in a deep one-dimensional optical lattice. Two different types of the couplings are considered, with spatial derivatives acting inside each species, or between the species. The discrete system with inter-site couplings dominated by the SOC, while the usual hopping is negligible, \textit{emulates} condensates composed of extremely heavy atoms, as well as those with opposite signs of the effective atomic masses in the two components.\ Stable localized composite states of miscible and immiscible types are constructed. The effect of the SOC on the immiscibility-miscibility transition in the localized complexes, which emulates the phase transition between insulating and conducting states in semiconductors, is studied. Comment: Journal of Physics B , in press

We discuss the spectrum phenomenon for Lipschitz functions on the infinite-dimensional torus. Suppose that [Formula: see text] is a measurable, real-valued, Lipschitz function on the torus [Formula: see text]. We prove that there exists a number [Formula: see text] with the following property: For any [Formula: see text], there exists a parallel, infinite-dimensional subtorus [Formula: see text] such that the restriction of the function [Formula: see text] to the subtorus [Formula: see text] has an [Formula: see text]-norm of at most [Formula: see text].

Abstract We present an open-source MATLAB package, entitled OpenPIV-MATLAB, for analyzing particle image velocimetry (PIV) data. We extend the PIV analysis with additional tools for post-processing the PIV results including the estimation of aero/hydrodynamic forces from the PIV data of a wake behind an immersed (bluff or streamlined) body. The paper presents a detailed description of the packages, covering the three main parts: generating two-dimensional two component velocity fields from pairs of images (OpenPIV-MATLAB), spatial and temporal flow analysis based on the velocity fields (Spatial and Temporal Analysis Toolbox), and wake flow analysis along with the force estimates (getWAKE Toolbox). A complete analysis with a variety of post-processing capabilities is demonstrated using time-resolved PIV wake data of a freely flying European starling (Sturnus vulgaris) in a wind tunnel.

We argue that the asymmetric morphology of the blue and red shifted components of the outflow at hundreds of AU from the massive binary system Eta Carinae can be understood from the collision of the primary stellar wind with the slowly expanding dense equatorial gas. Recent high spatial observations of some forbidden lines, e.g. [Fe III] lambda4659, reveal the outflowing gas within about one arcsecond (2300 AU) from Eta Car. The distribution of the blue and red shifted components are not symmetric about the center, and they are quite different from each other. The morphologies of the blue and red shifted components correlate with the location of dense slowly moving equatorial gas (termed the Weigelt blob environment; WBE), that is thought to have been ejected during the 1887 - 1895 Lesser Eruption. In our model the division to the blue and red shifted components is caused by the postshock flow of the primary wind on the two sides of the equatorial plane after it collides with the WBE. The fast wind from the secondary star plays no role in our model for these components, and it is the freely expanding primary wind that collides with the WBE. Because the line of sight is inclined to the binary axis, the two components are not symmetric. We show that the postshock gas can also account for the observed intensity in the [Fe III] lambda4659 line. Comment: 15 pages, 3 figures. Accepted to New Astronomy