Removing zero Lyapunov exponents in volume-preserving flows

Baraviera and Bonatti proved that it is possible to perturb, in the c^1 topology, a volume-preserving and partial hyperbolic diffeomorphism in order to obtain a non-zero sum of all the Lyapunov exponents in the central direction. In this article we obtain the analogous result for volume-preserving flows.Comment: 10 page

Bayesian optimisation of hexagonal honeycomb metamaterial

Periodic mechanical metamaterials, such as hexagonal honeycombs, have traditionally been designed with uniform cell walls to simplify manufacturing and modelling. However, recent research has suggested that varying strut thickness within the lattice could improve its mechanical properties. To fully explore this design space, we developed a computational framework that leverages Bayesian optimisation to identify configurations with increased uniaxial effective elastic stiffness and plastic or buckling strength. The best topologies found, representative of relative densities with distinct failure modes, were additively manufactured and tested, resulting in a 54% increase in stiffness without compromising the buckling strength for slender architectures, and a 63% increase in elastic modulus and a 88% increase in plastic strength for higher volume fractions. Our results demonstrate the potential of Bayesian optimisation and solid material redistribution to enhance the performance of mechanical metamaterials

Pressure of massless hot scalar theory in the boundary effective theory framework

We use the boundary effective theory (BET) approach to thermal field theory in order to calculate the pressure of a system of massless scalar fields with quartic interaction. The method naturally separates the infrared physics, and is essentially non-perturbative. To lowest order, the main ingredient is the solution of the free Euler-Lagrange equation with non-trivial (time) boundary conditions. We derive a resummed pressure, which is in good agreement with recent calculations found in the literature, following a very direct and compact procedure.Comment: 10 pages, 4 figure

Effective potential in the BET formalism

We calculate the one-loop effective potential at finite temperature for a system of massless scalar fields with quartic interaction $\lambda\phi^4$ in the framework of the boundary effective theory (BET) formalism. The calculation relies on the solution of the classical equation of motion for the field, and Gaussian fluctuations around it. Our result is non-perturbative and differs from the standard one-loop effective potential for field values larger than $T/\sqrt{\lambda}$.Comment: 10 pages, 3 figure

Phase conversion in a weakly first-order quark-hadron transition

We investigate the process of phase conversion in a thermally-driven {\it weakly} first-order quark-hadron transition. This scenario is physically appealing even if the nature of this transition in equilibrium proves to be a smooth crossover for vanishing baryonic chemical potential. We construct an effective potential by combining the equation of state obtained within Lattice QCD for the partonic sector with that of a gas of resonances in the hadronic phase, and present numerical results on bubble profiles, nucleation rates and time evolution, including the effects from reheating on the dynamics for different expansion scenarios. Our findings confirm the standard picture of a cosmological first-order transition, in which the process of phase conversion is entirely dominated by nucleation, also in the case of a weakly first-order transition. On the other hand, we show that, even for expansion rates much lower than those expected in high-energy heavy ion collisions, nucleation is very unlikely, indicating that the main mechanism of phase conversion is spinodal decomposition. Our results are compared to those obtained for a strongly first-order transition, as the one provided by the MIT bag model.Comment: 12 pages, 10 figures; v2: 1 reference added, minor modifications, matches published versio