pH‐Controlled network formation in a mixture of oppositely charged cellulose nanocrystals and poly(allylamine)

The behavior of a mixture of negatively charged cellulose nanocrystals (CNCs) and positively charged poly(allylamine) (PAAm) is examined in aqueous media. By modulating the pH, the acting Coulomb forces can be varied that can lead not only to adsorption of PAAm chains on the CNC surface but also to the development of a supermolecular structure by bridging of CNC rods by extended PAAm chains. This bridging can result in the formation of CNC clusters, which was demonstrated experimentally. Light scattering and rheological studies showed that these clusters begin to grow and merge, ultimately forming a global percolated network above a critical degree of PAAm ionization. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1527–1536     

Nonlinear damping in a micromechanical oscillator

Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). A Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast, nonlinear dissipation effects in micromechanical oscillators are often overlooked. In this work, we consider a doubly clamped micromechanical beam oscillator, which exhibits nonlinearity in both elastic and dissipative properties. The dynamics of the oscillator is measured in both frequency and time domains and compared to theoretical predictions based on a Duffing-like model with nonlinear dissipation. We especially focus on the behavior of the system near bifurcation points. The results show that nonlinear dissipation can have a significant impact on the dynamics of micromechanical systems. To account for the results, we have developed a continuous model of a geometrically nonlinear beam-string with a linear Voigt–Kelvin viscoelastic constitutive law, which shows a relation between linear and nonlinear damping. However, the experimental results suggest that this model alone cannot fully account for all the experimentally observed nonlinear dissipation, and that additional nonlinear dissipative processes exist in our devices.     

Nonlinear dynamics of a microelectromechanical mirror in an optical resonance cavity

The nonlinear dynamical behavior of a micromechanical resonator acting as one of the mirrors in an optical resonance cavity is investigated. The mechanical motion is coupled to the optical power circulating inside the cavity both directly through the radiation pressure and indirectly through heating that gives rise to a frequency shift in the mechanical resonance and to thermal deformation. The energy stored in the optical cavity is assumed to follow the mirror displacement without any lag. In contrast, a finite thermal relaxation rate introduces retardation effects into the mechanical equation of motion through temperature dependent terms. Using a combined harmonic balance and averaging technique, slow envelope evolution equations are derived. In the limit of small mechanical vibrations, the micromechanical system can be described as a nonlinear Duffing-like oscillator. Coupling to the optical cavity is shown to introduce corrections to the linear dissipation, the nonlinear dissipation and the nonlinear elastic constants of the micromechanical mirror. The magnitude and the sign of these corrections depend on the exact position of the mirror and on the optical power incident on the cavity. In particular, the effective linear dissipation can become negative, causing self-excited mechanical oscillations to occur as a result of either a subcritical or supercritical Hopf bifurcation. The full slow envelope evolution equations are used to derive the amplitudes and the corresponding oscillation frequencies of different limit cycles, and the bifurcation behavior is analyzed in detail. Finally, the theoretical results are compared to numerical simulations using realistic values of various physical parameters, showing a very good correspondence.     

On the Maximum Number of Edges in Topological Graphs with no Four Pairwise Crossing Edges

A topological graph is called k -quasi-planar if it does not contain k pairwise crossing edges. It is conjectured that for every fixed k, the maximum number of edges in a k-quasi-planar graph on n vertices is O(n). We provide an affirmative answer to the case k=4.     

Circulating spatial solitons

A class of optical spatial solitons exhibiting propagation in a closed-loop orbit in a two-dimensional plane is presented. A closed-form particlelike model is derived, indicating that the quasi-centrifugal force acting on these solitons can be balanced by an inhomogeneity in the nonlinear index of refraction. Specifically, a circular-shaped nonlinear interface is shown to facilitate stable orbital propagation of solitons that carve their own circular cavity for a wide range of nonlinearity parameters.     

Upper bound imposed on responsivity of optical modulators

I study theoretically the responsivity of optical modulators. For the case of a linear response, by using perturbation theory I find an upper bound imposed on the responsivity. For the case of a two-mode modulator I find a lower bound imposed on the optical path required for achieving full modulation when the maximum birefringence strength is given.     

Enzymatic/Immunoassay Dual‐Biomarker Sensing Chip: Towards Decentralized Insulin/Glucose Detection

Performing bioassay formats based on enzyme and antibody recognition reactions with a single detection chip remains an unmet challenge owing to the different requirements of such bioassays. Herein, we describe a dual‐marker biosensor chip, integrating enzyme and antibody‐based assays for simultaneous electrochemical measurements of insulin (I) and glucose (G). Simultaneous G/I sensing has been realized by addressing key fabrication and operational challenges associated with the different assay requirements and surface chemistry. The I immunosensor relies on a peroxidase‐labeled sandwich immunoassay, while G is monitored through reaction with glucose oxidase. The dual diabetes biomarker chip offers selective and reproducible detection of picomolar I and millimolar G concentrations in a single microliter sample droplet within less than 30 min, including direct measurements in whole blood and saliva samples. The resulting integrated enzymatic‐immunoassay biosensor chip opens a new realm in point‐of‐care multiplexed biomarker detection.     

Analytic Hessian derivation for the quasi-one-dimensional Euler equations

The Hessian for the quasi-one-dimensional Euler equations is derived. A pressure minimization problem and a pressure matching inverse problem are considered. The flow sensitivity, adjoint sensitivity, gradient and Hessian are calculated analytically using a direct approach that is specific to the model problems. For the pressure minimization problem we find that the Hessian exists and it contains elements with significantly larger values around the shock location. For the pressure matching inverse problem we find at least one case for which the gradient as well as the Hessian do not exist. In addition, two formulations for calculating the Hessian are proposed and implemented for the given problems. Both methods can be implemented in industrial applications such as large scale aerodynamic optimization.     

Spatial averaging of oceanic rainfall variability using underwater sound: Ionian Sea rainfall experiment 2004

An experiment to evaluate the inherent spatial averaging of the underwater acoustic signal from rainfall was conducted in the winter of 2004 in the Ionian Sea southwest of Greece. A mooring with four passive aquatic listeners (PALs) at 60, 200, 1000, and 2000 m was deployed at 36.85 degrees N, 21.52 degrees E, 17 km west of a dual-polarization X-band coastal radar at Methoni, Greece. The acoustic signal is classified into wind, rain, shipping, and whale categories. It is similar at all depths and rainfall is detected at all depths. A signal that is consistent with the clicking of deep-diving beaked whales is present 2% of the time, although there was no visual confirmation of whale presence. Co-detection of rainfall with the radar verifies that the acoustic detection of rainfall is excellent. Once detection is made, the correlation between acoustic and radar rainfall rates is high. Spatial averaging of the radar rainfall rates in concentric circles over the mooring verifies the larger inherent spatial averaging of the rainfall signal with recording depth. For the PAL at 2000 m, the maximum correlation was at 3-4 km, suggesting a listening area for the acoustic rainfall measurement of roughly 30-50 km(2).     

Poly[(2-chloroethyl)oxirane], poly[(3-chloropropyl)-oxirane] and poly[(4-chlorobutyl)oxirane]: New polyether elastomers of improved chemical reactivity

(2-Chloroethyl)oxirane, (3-chloropropyl)oxirane, and (4-chlorobutyl)oxirane were prepared from the corresponding alkenols and polymerized using a triethylaluminum-water-acetylacetone initiator system. Copolymerizations with propylene oxide and epichlorohydrin were also accomplished; the copolymerization activities of the (chloroalkyl)oxiranes were similar to the activity of epichlorohydrin. Poly[(2-chloroethyl)oxirane], poly[(3-chloropropyl)oxirane], and poly[(4-chlorobutyl)oxirane] exhibit elastomeric properties and are highly reactive in nucleophilic substitution reactions.