Numerical representations of fluid mixing

The work contained within this thesis is concerned with a theoretical investigatiop of both laminar and thermally driven types of cavity flow, together with an analysis of their associated mixing processes which find applications to Industrial mixing and also to the environment. The mixing efficiency has been viewed from two perspectives namely the tracking of a selection of fluid particles, and also the simulation of the dispersive mixing of a coloured fluid element as carried along by the flow. This thesis also incorporates features of both Newtonian and a wide range of non-Newtonian fluids

Competition between transport phenomena in a Reaction-Diffusion-Convection system

This doctoral dissertation consists of three main parts. In part one, a general overview of the basic concepts of nonlinear science, nonlinear analysis and non-equilibrium thermodynamics is presented. Kinetics of chemical oscillations and the well known Belousov-Zhabotinsky reaction are also illustrated. In part two, a Reaction-Diffusion-Convection (RDC) model is introduced as a convenient framework for studying instability scenarios by which chemical oscillators are driven to chaos, along with its translation to an opportune code for numerical simulations. In part three, we report the methods and the data obtained. We observe that distinct bifurcation points are found in the oscillating patterns as Diu-sion coecients (di) or Grashof numbers (Gri) vary. Singularly there emerge peculiar bifurcation paths, inscribed in a general scenario of the RTN type, in which quasi{periodicity transmutes into a period-doubling sequence to chemical chaos. The opposite influence exhibited by the two parameters in these transitions clearly indicate that diusion of active species and natural convection are in `competition` for the stability of ordered dynamics. Moreover, a mirrored behavior between chemical oscillations and spatio-temporal dynamics is observed, suggesting that the emergence of the two observables are a manifestation of the same phenomenon. The interplay between chemical and transport phenomena instabilities is at the general origin of chaos for these systems. Further, a molecular dynamics study has been carried out for the calculation of diusion coecients of active species in the Belousov-Zhabotinsky reaction, namely HBrO2 and Ce(III), by means of mean square displacement and velocity autocorrelation function. These data have been used for a deeper comprehension of the hydrodynamic competition observed between diusion and convective motions for the stability of the system.</br

Evidence for the dynamical relevance of relative periodic orbits in turbulence

Despite a long and rich history of scientific investigation, fluid turbulence remains one of the most challenging problems in science and engineering. One of the key outstanding questions concerns the role of coherent structures that describe frequently observed patterns embedded in turbulence. It has been suggested, but not proven, that coherent structures correspond to unstable, recurrent solutions of the governing equations of fluid dynamics. In this thesis, I present the first experimental evidence that three-dimensional turbulent flow mimics the spatial and temporal structure of multiple such solutions episodically but repeatedly. These results provide compelling evidence that coherent structures, grounded in the governing equations, can be harnessed to predict how turbulent flows evolve.Ph.D

New Trends in Statistical Physics of Complex Systems

A topical research activity in statistical physics concerns the study of complex and disordered systems. Generally, these systems are characterized by an elevated level of interconnection and interaction between the parts so that they give rise to a rich structure in the phase space that self-organizes under the control of internal non-linear dynamics. These emergent collective dynamics confer new behaviours to the whole system that are no longer the direct consequence of the properties of the single parts, but rather characterize the whole system as a new entity with its own features, giving rise to the birth of new phenomenologies. As is highlighted in this collection of papers, the methodologies of statistical physics have become very promising in understanding these new phenomena. This volume groups together 12 research works showing the use of typical tools developed within the framework of statistical mechanics, in non-linear kinetic and information geometry, to investigate emerging features in complex physical and physical-like systems. A topical research activity in statistical physics concerns the study of complex and disordered systems. Generally, these systems are characterized by an elevated level of interconnection and interaction between the parts so that they give rise to a rich structure in the phase space that self-organizes under the control of internal non-linear dynamics. These emergent collective dynamics confer new behaviours to the whole system that are no longer the direct consequence of the properties of the single parts, but rather characterize the whole system as a new entity with its own features, giving rise to the birth of new phenomenologies. As is highlighted in this collection of papers, the methodologies of statistical physics have become very promising in understanding these new phenomena. This volume groups together 12 research works showing the use of typical tools developed within the framework of statistical mechanics, in non-linear kinetic and information geometry, to investigate emerging features in complex physical and physical-like systems