Unstable Attractors: Existence and Robustness in Networks of Oscillators With Delayed Pulse Coupling

We consider unstable attractors; Milnor attractors $A$ such that, for some neighbourhood $U$ of $A$, almost all initial conditions leave $U$. Previous research strongly suggests that unstable attractors exist and even occur robustly (i.e. for open sets of parameter values) in a system modelling biological phenomena, namely in globally coupled oscillators with delayed pulse interactions. In the first part of this paper we give a rigorous definition of unstable attractors for general dynamical systems. We classify unstable attractors into two types, depending on whether or not there is a neighbourhood of the attractor that intersects the basin in a set of positive measure. We give examples of both types of unstable attractor; these examples have non-invertible dynamics that collapse certain open sets onto stable manifolds of saddle orbits. In the second part we give the first rigorous demonstration of existence and robust occurrence of unstable attractors in a network of oscillators with delayed pulse coupling. Although such systems are technically hybrid systems of delay differential equations with discontinuous `firing' events, we show that their dynamics reduces to a finite dimensional hybrid system system after a finite time and hence we can discuss Milnor attractors for this reduced finite dimensional system. We prove that for an open set of phase resetting functions there are saddle periodic orbits that are unstable attractors.Comment: 29 pages, 8 figures,submitted to Nonlinearit

Engineering and Tuning of Quantum Emitters in Few-Layer Hexagonal Boron Nitride

© 2019 American Chemical Society. Quantum technologies require robust and photostable single photon emitters (SPEs). Hexagonal boron nitride (hBN) has recently emerged as a promising candidate to host bright and optically stable SPEs operating at room temperature. However, the emission wavelength of the fluorescent defects in hBN has, to date, been shown to be uncontrolled, with a widespread of zero phonon line (ZPL) energies spanning a broad spectral range (hundreds of nanometers), which hinders the potential development of hBN-based devices and applications. Here we demonstrate chemical vapor deposition growth of large-area, few-layer hBN films that host large quantities of SPEs: -100-200 per 10 × 10 μm 2 . More than 85% of the emitters have a ZPL at (580 ± 10) nm, a distribution that is an order of magnitude narrower than reported previously. Furthermore, we demonstrate tuning of the ZPL wavelength using ionic liquid devices over a spectral range of up to 15 nm-the largest obtained to date from any solid-state SPE. The fabricated devices illustrate the potential of hBN for the development of hybrid quantum nanophotonic and optoelectronic devices based on two-dimensional materials

The Viscous Nonlinear Dynamics of Twist and Writhe

Exploiting the "natural" frame of space curves, we formulate an intrinsic dynamics of twisted elastic filaments in viscous fluids. A pair of coupled nonlinear equations describing the temporal evolution of the filament's complex curvature and twist density embodies the dynamic interplay of twist and writhe. These are used to illustrate a novel nonlinear phenomenon: ``geometric untwisting" of open filaments, whereby twisting strains relax through a transient writhing instability without performing axial rotation. This may explain certain experimentally observed motions of fibers of the bacterium B. subtilis [N.H. Mendelson, et al., J. Bacteriol. 177, 7060 (1995)].Comment: 9 pages, 4 figure

Spatio-selection in Expanding Bacterial Colonies

Segregation of populations is a key question in evolution theory. One important aspect is the relation between spatial organization and the population's composition. Here we study a specific example -- sectors in expanding bacterial colonies. Such sectors are spatially segregated sub-populations of mutants. The sectors can be seen both in disk-shaped colonies and in branching colonies. We study the sectors using two models we have used in the past to study bacterial colonies -- a continuous reaction-diffusion model with non-linear diffusion and a discrete ``Communicating Walkers'' model. We find that in expanding colonies, and especially in branching colonies, segregation processes are more likely than in a spatially static population. One such process is the establishment of stable sub- population having neutral mutation. Another example is the maintenance of wild-type population along side with sub-population of advantageous mutants. Understanding such processes in bacterial colonies is an important subject by itself, as well as a model system for similar processes in other spreading populations

Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model

Suspensions of self-propelled particles are studied in the framework of two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the effective viscosity of such suspensions in the limit of small concentrations. This formula includes the two terms that are found in the 2D version of Einstein's classical result for passive suspensions. To this, the main result of the paper is added, an additional term due to self-propulsion which depends on the physical and geometric properties of the active suspension. This term explains the experimental observation of a decrease in effective viscosity in active suspensions.Comment: 15 pages, 3 figures, submitted to Physical Biolog

Twirling and Whirling: Viscous Dynamics of Rotating Elastica

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two dynamical regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.Comment: To be published in Physical Review Letter

Labels for non-individuals

Quasi-set theory is a first order theory without identity, which allows us to cope with non-individuals in a sense. A weaker equivalence relation called ``indistinguishability'' is an extension of identity in the sense that if $x$ is identical to $y$ then $x$ and $y$ are indistinguishable, although the reciprocal is not always valid. The interesting point is that quasi-set theory provides us a useful mathematical background for dealing with collections of indistinguishable elementary quantum particles. In the present paper, however, we show that even in quasi-set theory it is possible to label objects that are considered as non-individuals. We intend to prove that individuality has nothing to do with any labelling process at all, as suggested by some authors. We discuss the physical interpretation of our results.Comment: 11 pages, no figure

Photodynamics and quantum efficiency of germanium vacancy color centers in diamond

Color centers in diamond-especially group IV defects-have been advanced as a viable solid-state platform for quantum photonics and information technologies. We investigate the photodynamics and characteristics of germanium-vacancy (GeV) centers hosted in high-pressure high-temperature diamond nanocrystals. Through back-focal plane imaging, we analyze the far-field radiation pattern of the investigated emitters and derive a crossed-dipole emission, which is strongly aligned along one axis. We use this information in combination with lifetime measurements to extract the decay rate statistics of the GeV emitters and determine their quantum efficiency, which we estimated to be ∼ (22 ± 2) %. Our results offer further insight into the photodynamic properties of the GeV center in nanodiamonds and confirm its suitability as a desirable system for quantum technologies

Photoplethysmographic measurements from central nervous system tissue

A new system for measuring the oxygen saturation of blood within tissue has been developed, for a number of potential patient monitoring applications. This proof of concept project aims to address the unmet need of real-time measurement of oxygen saturation in the central nervous system (CNS) for patients recovering from neurosurgery or trauma, by developing a fibre optic signal acquisition system for internal placement through small apertures. The development and testing of a two-wavelength optical fibre reflectance photoplethysmography (PPG) system is described together with measurements in rats and preliminary results from a clinical trial of the system in patients undergoing neurosurgery. It was found that good quality red and near-infrared PPG signals could be consistently obtained from the rat spinal cord (n=6) and human cerebral cortex (n=4) using the fibre optic probe. These findings justify further development and clinical evaluation of this fibre optic system

Lubricating Bacteria Model for Branching growth of Bacterial Colonies

Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial cooperative self-organization. Central part of the cooperation is the collective formation of lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by nonlinear diffusion coefficient branching patterns evolves. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.Comment: 1 latex file, 16 jpeg files, submitted to Phys. Rev.