A variational approach to probing extreme events in turbulent dynamical systems

Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large scale networks and biological systems. Here, we propose a variational framework for probing conditions that trigger intermittent extreme events in high-dimensional nonlinear dynamical systems. We seek the triggers as the probabilistically feasible solutions of an appropriately constrained optimization problem, where the function to be maximized is a system observable exhibiting intermittent extreme bursts. The constraints are imposed to ensure the physical admissibility of the optimal solutions, i.e., significant probability for their occurrence under the natural flow of the dynamical system. We apply the method to a body-forced incompressible Navier--Stokes equation, known as the Kolmogorov flow. We find that the intermittent bursts of the energy dissipation are independent of the external forcing and are instead caused by the spontaneous transfer of energy from large scales to the mean flow via nonlinear triad interactions. The global maximizer of the corresponding variational problem identifies the responsible triad, hence providing a precursor for the occurrence of extreme dissipation events. Specifically, monitoring the energy transfers within this triad, allows us to develop a data-driven short-term predictor for the intermittent bursts of energy dissipation. We assess the performance of this predictor through direct numerical simulations.Comment: Minor revisions, generalized the constraints in Eq. (2

Spinor algebra and null solutions of the wave equation

In this paper we exploit the ideas and formalisms of twistor theory, to show how, on Minkowski space, given a null solution of the wave equation, there are precisely two null directions in $\ker df$, at least one of which is a shear-free ray congruence

Sum-Rate Analysis for High Altitude Platform (HAP) Drones with Tethered Balloon Relay

High altitude platform (HAP) drones can provide broadband wireless connectivity to ground users in rural areas by establishing line-of-sight (LoS) links and exploiting effective beamforming techniques. However, at high altitudes, acquiring the channel state information (CSI) for HAPs, which is a key component to perform beamforming, is challenging. In this paper, by exploiting an interference alignment (IA) technique, a novel method for achieving the maximum sum-rate in HAP-based communications without CSI is proposed. In particular, to realize IA, a multiple-antenna tethered balloon is used as a relay between multiple HAP drones and ground stations (GSs). Here, a multiple-input multiple-output X network system is considered. The capacity of the considered M*N X network with a tethered balloon relay is derived in closed-form. Simulation results corroborate the theoretical findings and show that the proposed approach yields the maximum sum-rate in multiple HAPs-GSs communications in absence of CSI. The results also show the existence of an optimal balloon's altitude for which the sum-rate is maximized.Comment: Accepted in IEEE Communications Letter

Label-Free Metabolic Classification of Single Cells in Droplets Using the Phasor Approach to Fluorescence Lifetime Imaging Microscopy.

Characterization of single cell metabolism is imperative for understanding subcellular functional and biochemical changes associated with healthy tissue development and the progression of numerous diseases. However, single-cell analysis often requires the use of fluorescent tags and cell lysis followed by genomic profiling to identify the cellular heterogeneity. Identifying individual cells in a noninvasive and label-free manner is crucial for the detection of energy metabolism which will discriminate cell types and most importantly critical for maintaining cell viability for further analysis. Here, we have developed a robust assay using the droplet microfluidic technology together with the phasor approach to fluorescence lifetime imaging microscopy to study cell heterogeneity within and among the leukemia cell lines (K-562 and Jurkat). We have extended these techniques to characterize metabolic differences between proliferating and quiescent cells-a critical step toward label-free single cancer cell dormancy research. The result suggests a droplet-based noninvasive and label-free method to distinguish individual cells based on their metabolic states, which could be used as an upstream phenotypic platform to correlate with genomic statistics. © 2018 International Society for Advancement of Cytometry

Optical circulation in a multimode optomechanical resonator

Optical circulators are important components of modern day communication technology. With their ability to route photons directionally, these nonreciprocal elements provide useful functionality in photonic circuits and offer prospects for fundamental research on information processing. Developing highly efficient optical circulators thus presents an important challenge, in particular to realize compact reconfigurable implementations that do not rely on a magnetic field bias to break reciprocity. We demonstrate optical circulation based on radiation pressure interactions in an on-chip multimode optomechanical system. We show that mechanically-mediated optical mode conversion in a silica microtoroid provides a synthetic gauge bias for light, which enables a 4-port circulator by exploiting tailored interference between appropriate light paths. We identify two sideband conditions under which ideal circulation is approached. This allows to experimentally demonstrate $\sim$10 dB isolation and $<$ 3 dB insertion loss in all relevant channels. We show the possibility of actively controlling the bandwidth, isolation ratio, noise performance and circulation direction, enabling ideal opportunities for reconfigurable integrated nanophotonic circuits