We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability. Our study is motivated by nematic liquid crystal films; however we note that similar instability mechanisms, and forms of the effective disjoining pressure, appear in other contexts, such as the well-studied problem of polymeric films on twolayered substrates. The analysis is carried out within the framework of the long-wave approximation, which leads to a fourth order nonlinear partial different equation for the film thickness. Within the considered formulation, the nematic character of the film leads to an additional contribution to the disjoining pressure, changing its functional form. This effective disjoining pressure is characterised by the presence of a local maximum for nonvanishing film thickness. Such a form leads to complicated instability evolution that we study by analytical means, including application of marginal stability criteria, and by extensive numerical simulations that help us develop a better understanding of instability evolution in the nonlinear regime. This combination of analytical and computational techniques allows us to reach novel understanding of relevant instability mechanisms, and of their influence on transient and fully developed fluid film morphologies. arXiv:1704.03919v1 [cond-mat.soft]

The 'amyloid cascade hypothesis' links amyloid beta peptide (Abeta) with the pathological process of Alzheimer's disease (AD) and it still awaits universal acceptance. Amyloid precursor protein (APP), through the actions of the gamma-secretase complex, eventually becomes a different Abetaspecies. The various Abeta species have proven to be difficult to investigate under physiological conditions, and the species of Abeta responsible for neurotoxicity has yet to be unequivocally identified. The two important Abeta peptides involved are Abeta(1-40) and Abeta(1-42), and each has been ascribed both toxic and beneficial attributes. The ratio between the two species can be important in AD etiology. Additionally, shorter variants of Abeta peptides such as Abeta(1-8), Abeta(9-16) and Abeta(16) have also been shown to be potential participants in AD pathology. Interestingly, a new 56-kDa Abeta peptide (Abeta*56) disrupts memory when injected into the brains of young rats. Transgenic mice models are complicated by the interplay between various human Abeta types and the mouse Abeta types in the mouse brains. However, the accumulation of Abeta(1-42) in the brains of transgenic C. elegans worms and Drosophila is indeed detrimental. A less investigated aspect of AD is epigenetics, but in time the investigation of the role of epigenetics in AD may add to our understanding of the development of AD.

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We present the results of large scale simulations of 4th order nonlinear partial differential equations of diffusion type that are typically encountered when modeling dynamics of thin fluid films on substrates. The simulations are based on the alternate direction implicit (ADI) method, with the main part of the computational work carried out in the GPU computing environment. Efficient and accurate computations allow for simulations on large computational domains in three spatial dimensions (3D) and for long computational times. We apply the methods developed to the particular problem of instabilities of thin fluid films of nanoscale thickness. The large scale of the simulations minimizes the effects of boundaries, and also allows for simulating domains of the size encountered in published experiments. As an outcome, we can analyze the development of instabilities with an unprecedented level of detail. A particular focus is on analyzing the manner in which instability develops, in particular regarding differences between spinodal and nucleation types of dewetting for linearly unstable films, as well as instabilities of metastable films. Simulations in 3D allow for consideration of some recent results that were previously obtained in the 2D geometry (J. Fluid Mech. 841, 925 (2018)). Some of the new results include using Fourier transforms as well as topological invariants (Betti numbers) to distinguish the outcomes of spinodal and nucleation types of instabilities, describing in precise terms the complex processes that lead to the formation of satellite drops, as well as distinguishing the shape of the evolving film front in linearly unstable and metastable regimes. We also discuss direct comparison between simulations and available experimental results for nematic liquid crystal and polymer films.