In this work we investigate, by way of experiments and theory, the Faraday instability threshold in cylinders at low frequencies. This implies large wavelengths where effects from mode discretization cannot be ignored. Careful selection of the working fluids has resulted in an immiscible interface whose apparent contact line with the sidewall can glide over a tiny film of the more wetting fluid, without detachment of its actual contact line. This unique behaviour has allowed for a system whose primary dissipation is defined by the bulk viscous effects, and in doing so, for the first time, close connection is seen with the viscous linear stability theory for which a stress-free condition is assumed at the sidewalls. As predicted, mode selection and co-dimension 2 points are observed in the experiment for a frequency range including subharmonic, harmonic, and superharmonic modes. While agreement with the predictions are generally excellent, there are deviations from the theory for certain modes and these are explained in the context of harmonic meniscus waves. A review of previous work on single-mode excitation in cylinders is given, along with comparison to the viscous model and analysis based upon the conclusions of the current experiments.

m-Poly(phenylene ethynylene)s (mPPEs) are a class of synthetic molecules being used for biocide coatings, catalysis, as well as chemical and biomolecule sensing because they exhibit a propensity to form a helical secondary structure in solution. Additionally, the folding of mPPEs into such helical arrangements may generally be controlled by varying the primary structure of the mPPE and/or the nature of the solvent. As such, several attempts have been made at developing heuristics for predicting a priori whether a particular mPPE will fold into a helix in a given solvent based on energetic and structural considerations. However, the experimental evidence shows that the formation of helical structures by mPPEs cannot be reliably predicted using such simple models. In this work, we demonstrate that replica-exchange molecular dynamics (REMD) simulations provide excellent agreement with experimental observations. We have simulated 20 different mPPE variations in five different solvent environments. Experimental results are available for eight of these one hundred systems, and in all eight of these cases the REMD results were in agreement with the experiments. Additionally, we simulated and then synthesized two previously unreported mPPEs having both ester and nitrile functional groups. After studying their folding behaviors in chloroform and acetonitrile, it was found that experimental results were in agreement with our predictions. This illustrates how REMD simulations, which are easily carried out with publicly available software on most modern computing systems, can be used to guide synthesis efforts focused on the formation of macromolecules with specific secondary structures.

In this work we consider a new class of oscillatory instabilities that pertain to thermocapillary destabilization of a liquid film heated by a solid substrate. We assume the substrate thickness and substrate-film thermal conductivity ratio are large so that the effect of substrate thermal diffusion is retained at leading order in the long-wave approximation. As a result, system dynamics are described by a nonlinear partial differential equation for the film thickness that is nonlocally coupled to the full substrate heat equation. Perturbing about a steady quiescent state, we find that its stability is described by a non-self adjoint eigenvalue problem. We show that, under appropriate model parameters, the linearized eigenvalue problem admits complex eigenvalues that physically correspond to oscillatory (in time) instabilities of the thin film height. As the principal results of our work, we provide a complete picture of the susceptibility to oscillatory instabilities for different model parameters. Using this description, we conclude that oscillatory instabilities are more relevant experimentally for films heated by insulating substrates. Furthermore, we show that oscillatory instability where the fastest-growing (most unstable) wavenumber is complex, arises only for systems with sufficiently large substrate thicknesses.1 oscillatory instability can be a challenging task. Alternatively, the long wave approximation offers a convenient means to couple free surface deformation to other time-dependent physical processes of interest.Several authors have investigated oscillatory instabilities of thin liquid films in the context of the long-wave approximation. In many cases, e.g. Podolny et al. (2005) and Bestehorn and Borcia (2010), such instabilities originate from the coupling between the local thickness and bulk concentration of a film composed of a binary mixture. In addition to the bulk concentration dynamics, Morozov et al. (2014) investigated oscillatory instability with the added effect of absorption/desorption kinetics between interfacial and bulk film surfactant concentration. In other cases, oscillatory instabilities have been uncovered in multiple stacked layers of films, as described theoretically by coupled sets of film thickness evolution equations (Nepomnyashchy and Simanovskii (2007), Beerman and Brush (2007)). Multi-layer film configurations do not, however, guarantee oscillatory modes: for example, such instabilities were not obtained by Pototsky et al. (2005) who investigated the dewetting dynamics of isothermal, ultrathin bilayers. Of particular interest to the present work are oscillatory instabilities reported by Shklyaev et al. (2012) in a model of thin-film thermocapillary destabilization from below. While there are similarities between that work and the present, we point out one important difference: in Shklyaev et al. (2012), the instability is driven by imposing a heat flux at the film-substrate interface; instead, in the present work we consider the full time-dependent heat-transfer in the ...