Modified Gravity in Clusters of Galaxies

For the last century, General Relativity (GR) has been successful in explaining several phenomena which were not explained before, for instance, the perihelion precession of Mercury, the bending of light due to the gravitational field, and the prediction of Gravitational Waves (GWs). Nevertheless, GR fails to explain some of the most important phenomena in the universe, namely the Dark Energy (DE) component, and inflation. Therefore, an extension to its original framework should be adop...

Massive black holes from single and binary stars

The first direct detection of gravitational waves in 2015 ushered in a new era for studying compact objects. Upcoming detectors like the Einstein Telescope are expected to contribute thousands of binary coalescence events to the existing data pool. However, uncertainties in the nature of stellar remnants from core-collapse supernovae and binary stellar evolution hinder our theoretical understanding of compact objects binaries. In the first part of my work, we examined the properties of stell...

Advances in lattice thermal transport in crystals and glasses

Thermal conductivity is a fundamental property for describing the non-equilibrium phenomenon of thermal transport. In solid insulators, whether disordered or crystalline, heat is primarily carried by lattice vibrations, emphasizing the need to accurately understand and compute the lattice thermal conductivity. This computation remains a central challenge in condensed matter physics, and lattice dynamical approaches have long been favored for this purpose. Despite being limited to (quasi-) har...

On Thermodynamics of Driven Quantum Systems: Novel Results and Perspectives

Driven quantum systems are systems in which a set of parameters obeys a time-dependent protocol, both periodic and non-periodic. The study of these systems bridges theoretical advances with experimental realizations in a variety of platforms—these range from quantum dot arrays to molecular junctions to trapped ions. The theoretical study is challenging due to the inherent non-equilibrium nature of the problem. These systems offer an interesting playground for quantum thermodynamics. They ...

Dielectric and dynamical properties of supercooled water

Water's anomalies have long intrigued scientists across various disciplines due to their profound implications for understanding fundamental properties of matter. Despite significant efforts from experimental, theoretical, and computational fronts, a consensus on the microscopic origins of water's anomalies remains elusive, fostering an open and active area of research. In the first part of this work we propose a simulation protocol, based on the Green-Kubo theory of linear response, that...

Thermoelectric effects in polar liquids and ionic conductors

Transport theory describes non-equilibrium conditions. The Onsager equations set a linear relationship between thermodynamic forces and macroscopic currents. When a temperature gradient is applied, it can generate heat and ions diffusion. Similarly, an electric field can induce electric currents and heat transport. The off-diagonal elements of the Onsager matrix address coupled, e.g. thermoelectric, effects. In the 1950s, Green and Kubo developed a sound equilibrium framework for transport ph...

Destabilising subvarieties for partial differential equations in complex geometry

In this thesis, we consider the set of destabilising subvarieties associated to various geometric partial differential equations (PDEs) of Monge-Ampère type arising in complex geometry, including the $J$-equation, the deformed Hermitian Yang-Mills equation and certain generalised Monge-Ampère equations. Each of these PDEs has an associated Nakai-Moishezon type criterion characterising their solvability in terms of a certain stability condition involving subvarieties. We show that the set of s...

Understanding the Role of SERPINA3/SerpinA3n in Prion Diseases

Machine-Learning Integration of Single-cell Multi-omics Data