Shear Jamming and Fragility of Suspensions in a Continuum Model with Elastic Constraints.

Under an applied traction, highly concentrated suspensions of solid particles in fluids can turn from a state in which they flow to a state in which they counteract the traction as an elastic solid: a shear-jammed state. Remarkably, the suspension can turn back to the flowing state simply by inverting the traction. A tensorial model is presented and tested in paradigmatic cases.

Interplay of different environments in open quantum systems: Breakdown of the additive approximation.

We analyze an open quantum system under the influence of more than one environment: a dephasing bath and a probability-absorbing bath that represents a decay channel, as encountered in many models of quantum networks. In our case, dephasing is modeled by random fluctuations of the site energies, while the absorbing bath is modeled with an external lead attached to the system. We analyze under which conditions the effects of the two baths can enter additively the quantum master equation.

Continuum balances from extended Hamiltonian dynamics.

The classical procedure devised by Irving and Kirkwood in 1950 and completed slightly later by Noll produces counterparts of the basic balance laws of standard continuum mechanics starting from an ordinary Hamiltonian description of the dynamics of a system of material points. Post-1980 molecular dynamics simulations of the time evolution of such systems use extended Hamiltonians such as those introduced by Andersen, Nosé, and Parrinello and Rahman. The additional terms present in these extensions affect the statistical properties of the system so as to capture certain target phenomenologies that would otherwise be beyond reach.

Solution of the Kirchhoff-Plateau Problem.

The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. We establish the existence of an equilibrium shape that minimizes the total energy of the system under the physical constraint of noninterpenetration of matter, but allowing for points on the surface of the bounding loop to come into contact. In our treatment, the bounding loop retains a finite cross-sectional thickness and a nonvanishing volume, while the liquid film is represented by a set with finite two-dimensional Hausdorff measure.

Collective couplings: Rectification and supertransmittance.

We investigate heat transport between two thermal reservoirs that are coupled via a large spin composed of N identical two-level systems. One coupling implements the dissipative Dicke superradiance. The other coupling is locally of the pure-dephasing type and requires to go beyond the standard weak-coupling limit by employing a Bogoliubov mapping in the corresponding reservoir.

Optimal efficiency of quantum transport in a disordered trimer.

Disordered quantum networks, such as those describing light-harvesting complexes, are often characterized by the presence of peripheral ringlike structures, where the excitation is initialized, and inner structures and reaction centers (RCs), where the excitation is trapped and transferred. The peripheral rings often display distinguished coherent features: Their eigenstates can be separated, with respect to the transfer of excitation, into two classes of superradiant and subradiant states. Both are important to optimize transfer efficiency.

Predicting Ageing: On the Mathematical Modelization of Ageing Muscle Tissue.

The ageing of biological tissues can be accelerated by many factors, mainly of physiological and nutritional nature. In the case of skeletal muscle tissue, one of the main consequences of ageing is a progressive loss of muscle mass and a worsening of the quality of muscle tissue, termed "sarcopenia". The correlation between the deterioration of muscle tissue and what we usually refer to as the "lifestyle", although being the subject of several studies, up to now has been considered only from a clinical and a statistical viewpoint.