A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays

This paper describes a general spectral element approach to study the stability of multiple time delay systems (MTDS). We show, for the first time, how this approach can be applied to periodic MTDS where the delays and the period are incommensurate. In contrast to prior works on MTDS, the spectral element approach is applicable to both autonomous as well as non-autonomous MTDS. Both MTDS of first order or higher can be obtained and systems with or without damping can be investigated. Since the spectral element approach uses efficient interpolation and a set of well-distributed interpolation points, the size of the matrices necessary for convergence is kept small. Further, since the spectral element approach is a semi-analytical procedure, it avoids the need to use tedious time marching algorithms to explore the stability behavior of the system.     

Linear and nonlinear electromagnetic coupling models in vibration-based energy harvesting

This paper investigates the response of an energy harvester that uses electromagnetic induction to convert ambient vibration into electrical energy. A unique aspect of the present study is the comparison of the system's response behavior when either a linear or a physically motivated form of nonlinear coupling is applied. The motivating hypothesis for this work was that nonlinear coupling could be used to improve the performance of an energy harvester by broadening its frequency response. Combined theoretical and numerical studies investigate the harvester's response for both single and multi-frequency base excitation. Our investigations unveil regions in the parameter space where nonlinear coupling is better than linear coupling and regions where the opposite is true. The meaningful conclusion is that nonlinear coupling can sometimes be detrimental, but it can also be beneficial if properly designed into the system.     

A Free Energy Model for Curved Surfaces and Curved Thin Films in Emulsions

The formulation of surface thermodynamics for flat surfaces has been done so as to be free of the Gibbs surface construction. The advantage of these formulations is that it allows the choice of thermodynamic field variables that is more general than the traditional construction. However, a generalization to curved surfaces including thin films that exist in emulsion structures has not been published. The Hansen-Cahn construction is developed in a setting that allows curvature terms to be added to the free energy expression. The Laplace equation extended to include bending elasticity and spontaneous bending elasticity is derived by computing functional derivatives of the free energy. Results for both single interfaces and double interfaces are reported. Stability conditions for profile fluctuations are developed to include these additional properties.     

Impact of the Synergistic Collaboration of Oligothiophene Bridges and Ruthenium Complexes on the Optical Properties of Dumbbell‐Shaped Compounds

The linear and non‐linear optical properties of a family of dumbbell‐shaped dinuclear complexes, in which an oligothiophene chain with various numbers of rings (1, 3, and 6) acts as a bridge between two homoleptic tris(2,2′‐bipyridine)ruthenium(II) complexes, have been fully investigated by using a range of spectroscopic techniques (absorption and luminescence, transient absorption, Raman, and non‐linear absorption), together with density functional theory calculations. Our results shed light on the impact of the synergistic collaboration between the electronic structures of the two chemical moieties on the optical properties of these materials. Experiments on the linear optical properties of these compounds indicated that the length of the oligothiophene bridge was critical for luminescent behavior. Indeed, no emission was detected for compounds with long oligothiophene bridges (compounds 3 and 4 , with 3 and 6 thiophene rings, respectively), owing to the presence of the ³π? π* state of the conjugated bridge below the ³MLCT‐emitting states of the end‐capping Ru^II complexes. In contrast, the compound with the shortest bridge ( 2 , one thiophene ring) shows excellent photophysical features. Non‐linear optical experiments showed that the investigated compounds were strong non‐linear absorbers in wide energy ranges. Indeed, their non‐linear absorption was augmented upon increasing the length of the oligothiophene bridge. In particular, the compound with the longest oligothiophene bridge not only showed strong two‐photon absorption (TPA) but also noteworthy three‐photon‐absorption behavior, with a cross‐section value of 4×10^?78 cm⁶ s² at 1450 nm. This characteristic was complemented by the strong excited‐state absorption (ESA) that was observed for compounds 3 and 4 . As a matter of fact, the overlap between the non‐linear absorption and ESA establishes compounds 3 and 4 as good candidates for optical‐power‐limiting applications.     

Quantum Defects as a Toolbox for the Covalent Functionalization of Carbon Nanotubes with Peptides and Proteins

Single‐walled carbon nanotubes (SWCNTs) are a 1D nanomaterial that shows fluorescence in the near‐infrared (NIR, >800 nm). In the past, covalent chemistry was less explored to functionalize SWCNTs as it impairs NIR emission. However, certain sp³ defects (quantum defects) in the carbon lattice have emerged that preserve NIR fluorescence and even introduce a new, red‐shifted emission peak. Here, we report on quantum defects, introduced using light‐driven diazonium chemistry, that serve as anchor points for peptides and proteins. We show that maleimide anchors allow conjugation of cysteine‐containing proteins such as a GFP‐binding nanobody. In addition, an Fmoc‐protected phenylalanine defect serves as a starting point for conjugation of visible fluorophores to create multicolor SWCNTs and in situ peptide synthesis directly on the nanotube. Therefore, these quantum defects are a versatile platform to tailor both the nanotube's photophysical properties as well as their surface chemistry.