Learning PDE to Model Self-Organization of Matter

A self-organization hydrodynamic process has recently been proposed to partially explain the formation of femtosecond laser-induced nanopatterns on Nickel, which have important applications in optics, microbiology, medicine, etc. Exploring laser pattern space is difficult, however, which simultaneously (i) motivates using machine learning (ML) to search for novel patterns and (ii) hinders it, because of the few data available from costly and time-consuming experiments. In this paper, we use ML to predict novel patterns by integrating partial physical knowledge in the form of the Swift-Hohenberg (SH) partial differential equation (PDE). To do so, we propose a framework to learn with few data, in the absence of initial conditions, by benefiting from background knowledge in the form of a PDE solver. We show that in the case of a self-organization process, a feature mapping exists in which initial conditions can safely be ignored and patterns can be described in terms of PDE parameters alone, which drastically simplifies the problem. In order to apply this framework, we develop a second-order pseudospectral solver of the SH equation which offers a good compromise between accuracy and speed. Our method allows us to predict new nanopatterns in good agreement with experimental data. Moreover, we show that pattern features are related, which imposes constraints on novel pattern design, and suggest an efficient procedure of acquiring experimental data iteratively to improve the generalization of the learned model. It also allows us to identify the limitations of the SH equation as a partial model and suggests an improvement to the physical model itself.     

Lateral Deprotometallation-Trapping Reactions on Methylated Pyridines,Quinolines and Quinoxalines Using Lithium Diethylamide

The functionalization of methylated azines and diazines has aroused the interest of chemists given the structural diversity that it affords. Hindered lithium dialkylamides have been used to deprotometallate these substrates chemoselectively. In contrast, it can be observed that, despite some promising work, lithium diethylamide has been used very little for this purpose. Our objective here is on the one hand to make an inventory of what reagents have been used to deprotometallate methylpyridines, -quinolines and -quinoxalines, and on the other hand to describe the results obtained by seeking to functionalize a series of substrates with lithium diethylamide (picolines, 2,4-lutidine, methylquinolines and 2-methylquinoxaline). Our efforts to take advantage of the use of an in-situ trap (a zinc chloride chelate) in these reactions are also described.     

Nanostructured TiO2 as anode material for magnesium-ion batteries

Journal of Solid State Electrochemistry - The nanotubular structure of titanium dioxide (TiO2) is most suitable for creating high-performance energy storage and conversion devices. This paper...