ORALS

A. Fluid Dynamical point of view. My initial reaction, after reading this report, was that it was a conjecture on a very topical subject with small chance of success. In fact, I thought that writing a report on it would be somehow a straightforward affair. It has proven though, upon closer examination, that this application is anything but trivial, and deserves special attention. In this talk I will provide my view, as to how combining theoretical approaches from fluid dynamics can be combined with pattern formation in solids to form a universal theory of approaching turbulence, that is applicable to both these rather distinct phases. In order to understand how this is possible it is necessary to understand and subsequently combine two concepts. The first is the array of computational techniques, such as spectral element and Galerkin spectral collocation-tau methods, Zenolli patching, finite difference and other iterative methods, that I have developed over the past decades, and their application to puzzling experimental results and observations in fluids. These methods have had applications in non-trivial solution with impact on both basic science and modern engineering. The figure included in his application, in particular, explains how the proposed sequence of bifurcations approach (SBA) can, in a fully deterministic manner, explain the beginning of a/approach to the phenomenon that is aperiodic/chaotic and which we term as ‘turbulence’. It is based on Ref [1]. The second concept is described extensively in Ref [2] of the application, where a detailed account is presented of the author’s internal length gradient (ILG) mechanics framework. It is based on the assignment of internal lengths (ILs) (associated with the local geometry/topology of material substructures) as scalar multipliers of extra Laplacian terms that are introduced to account for heterogeneity effects and weak nonlocality. This pioneering new concept clearly paves the way to understand hydro- and solid- dynamics under one umbrella, by incorporating, relatively simple extensions to the fluid constitutive equations, when describing pattern formation in fluids. If we combine the ILG framework with the computational ability of the proprietary software of the PI, it is not difficult to conclude that the theoretical concepts, such as classical laws for solids (Hooke) and fluids (Navier–Stokes) can be unified under one unified banner. This new view of solids, as a type of fluid, coupled with the aid of the tried SBA based and developed proprietary software, will allow the probing of the structure of the pattern formation. B. Physics point of view. 1. The work of the team member Elias C. Aifantis on gradient theory has rejuvenated the field of engineering based on Hooke’s law and has provided new avenues for considering size effects and stability of solid materials and structures. The main aspect of this work will be on extending the methodology used for extending Hooke’s equation for elastic motion to the extension of the Navier-Stokes equations for Newtonian fluids and points out the similarities in addressing flow and instabilities of polymer based materials and plastics. This will be a very useful tool for developing protocol and design criteria for recycling, with great benefits to environmental and renewable energy sectors. 2. Of particular importance is the proposed transfer of new ideas and novel techniques recently developed for fluid flow and turbulence to describe plastic flow and spatio-temporal instabilities in plastic processing. The success of the methodology is proven for Newtonian fluids (see recent publication [1]), which have been numerically implemented for stability and turbulence, will open up a new field of rheological materials, such as plastics. In particular, I will explain the direct connection of this work with LAMMPS, The Large-scale Atomic/Molecular Massively Parallel Simulator, that deals with calculations at the molecular level. This proposal has already started work in the direction with the Horizon 2020 Research and Innovation Staff Exchange (RISE) award, ATM2BT – Atomistic to Molecular To Bulk Turbulence - which am leading and in which Professor Aifantis is a critical member. This association will ensure close interaction of the fluid and solids communities. The result will be a unifying framework for treating the higher order terms in fluids and solids within the same footing.

References:
1. Akinaga, T., Generalis, S. C. & Busse, F. H. Tertiary and Quaternary States in the Taylor-Couette System. Chaos, Solitons & Fractals 109, 107–117 (2018).
2. Aifantis, E. C. Internal Length Gradient (ILG) Material Mechanics Across Scales and Disciplines. Advances in Applied Mechanics, Volume 49, 1-110(2016)