Giulio Giusteri's Web Page

My research focuses on developing and applying mathematical theories to describe and understand basic physical phenomena, ranging from the mechanical behavior of soft matter to the dynamics in disordered quantum networks to general systems of interactions. Answering questions like "What's the best mathematics for talking about this phenomenon?", I want to enhance our understanding of nature.

I am currently involved in three main projects (detailed below) and keep an interest in many other problems.

[1] Rheology of suspensions

Local velocity fields in different types of planar flow.

I am interested in developing a rheometric framework that is applicable beyond the clessical setting of viscometric flows. This is important if one wishes to consistently describe the material response of complex fluids in real flows, where the typical local flow type is not viscometric.

The first context in which such a framework proves to be useful is the study of dense suspensions. Here, the microstructure which is built under different flow conditions heavily affects the behavior of the mixture. This needs to be taken into account when developing effective continuum models for such out-of-equilibrium systems.

[2] Stability and reshaping of elastic loops spanned by liquid films

Elastic loop bent by a soap film

I study the interplay between the elastic properties of a filament, closed to form a simple loop, and those of a liquid film that spans such a loop. I am particularly interested in understanding the relation between bending and torsional rigidities of the filament and the dominant shape deformations induced by the action of surface tension, which is a characteristic of the liquid film.

In an effort to build a mathematical model that captures the essential physical properties of such systems, I am exploring how to blend rod theory, differential geometry, and the theory of Radon measures into novel theoretical and computational tools.

Experimental observations involving polypropylene loops spanned by a soap film evidenced that the presence of intrinsic curvature of the filament and the shape of its cross-sections strongly affect the deformation induced by the presence of the soap film. I established a quantitative link between those features and the form of the perturbation which is amplified during a dynamic destabilization of the flat circular configuration.

This research provides important directions for the design of structures with improved stability with respect to particular mechanical perturbations and would also be essential in designing microstructures that can be dynamically reshaped by exploiting surface tension effects at liquid interfaces.

[3] Efficiency of quantum transport in disordered systems

Efficiency landscape in a disordered trimer

The first stages of photosynthesis take place within the light-harvesting complexes constituted by aggregates of chlorophyll molecules in cells. The main task of such complexes is to funnel solar energy towards the reaction centers where conversion and storage take place. Two seemingly incompatible features characterize these complexes: the nanometric dimensions of these natural optical devices make quantum effects of paramount importance, while the degree of disorder and thermal disturbances, which would normally hinder quantum effects, is relatively high.

I investigated theoretically and computationally what are, in some paradigmatic models, the optimal conditions in which the competition between coherent quantum effects and structural and dynamic disorder can become helpful in sustaining the transport properties of light-harvesting complexes. I also studied the limit of validity of some models commonly used in describing those systems, showing that it is not uncommon to find real systems operating outside those limits.

These studies not only provide a basic step in understanding the links between structure and function of natural complexes, but also elucidate important principles that could be exploited to design quantum devices that can operate in the presence of disorder and thermal disturbances.

Past research

During my gaduate studies I developed the mathematical theory of second-gradient linear isotropic liquids. After framing it within a general theory of higher-gradient continua, I proved the well-posedness of fluid-structure interaction problems, involving one-dimensional immersed bodies. I also showed how higher-gradient models can capture concentrated effects that would be otherwise ignored by using classical fluid models. In the subsequent years, I further studied the mathematics of free-falling slender bodies in such liquids.