Reverse rotations in the circularly driven motion of a rigid body.

We study the dynamical response of a circularly driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and quantitative analysis. A scale-free expression defining the separation between possible spinning regimes is obtained.

Critical behaviour in the optimal generation of multipartite entanglement.

Two systems whose correlations cannot be classically accounted for display the simplest instance of quantum entanglement. Although this two-party association has caused a revolution in the foundations and uses of quantum mechanics, genuine entanglement among several parties unveils a whole new class of phenomena and applications. In this work we suggest a way to prepare Dicke states from a tunable source of bipartite entanglement to investigate foundational issues. The scheme has the following distinctive features: (i) it relies on controlled information loss and unentangled measurements; (ii) irrespective of the source entanglement, whenever a Dicke state is produced, it is ideal; (iii) the optimal entanglement of the bipartite source undergoes a second-order-like transition depending on the parameters of the Dicke state to be produced. These properties lead to asymptotic results on the entanglement between any qubit belonging to a Dicke state and the remaining qubits.

Minimal fragmentation of regular polygonal plates.

Minimal fragmentation models intend to unveil the statistical properties of large ensembles of identical objects, each one segmented in two parts only. Contrary to what happens in the multifragmentation of a single body, minimally fragmented ensembles are often amenable to analytical treatments, while keeping key features of multifragmentation. In this work we present a study on the minimal fragmentation of regular polygonal plates with up to 100 sides. We observe in our model the typical statistical behavior of a solid torn apart by a strong impact, for example. We obtain a robust power law, valid for several decades, in the small mass limit. In the present case we were able to analytically determine the exponent of the cumulative probability distribution to be ½. Less usual, but also reported in a number of experimental and numerical references on impact fragmentation, is the presence of a sharp crossover to a second power-law regime, whose exponent we found to be between ⅓ and 1 depending on the way anisotropy is introduced in the model.

Role of viscous friction in the reverse rotation of a disk.

The mechanical response of a circularly driven disk in a dissipative medium is considered. We focus on the role played by viscous friction in the spinning motion of the disk, especially on the effect called reverse rotation, where the intrinsic and orbital rotations are antiparallel. Contrary to what happens in the frictionless case, where steady reverse rotations are possible, we find that this dynamical behavior may exist only as a transient when dissipation is considered. Whether or not reverse rotations in fact occur depends on the initial conditions and on two parameters, one related to dragging, inertia, and driving, the other associated with the geometric configuration of the system. The critical value of this geometric parameter (separating the regions where reverse rotation is possible from those where it is forbidden) as a function of viscosity is well adjusted by a q-exponential function.

Minimal fragmentation problem.

As an alternative to the paradigmatic fragmentation problem of a single object crushed into a great number of pieces, we survey a large collection of identical bodies, each one randomly split into two fragments only. While some key features of usual fragmentation are preserved, this minimal approach allows for closed analytical results on both shape abundances and mass distributions for the fragments, with robust power-law regimes. All the results are compared to numerical simulations.

Suppression of viscous fluid fingering: a piecewise-constant injection process.

The injection of a fluid into another of larger viscosity in a Hele-Shaw cell usually results in the formation of highly branched patterns. Despite the richness of these structures, in many practical situations such convoluted shapes are quite undesirable. In this Brief Report, we propose an efficient and easily reproducible way to restrain these instabilities based on a simple piecewise-constant pumping protocol. It results in a reduction in the size of the viscous fingers by one order of magnitude.