Carolina Brito

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The jamming transition of non-spherical particles is fundamentally different from the spherical case. Non-spherical particles are hypostatic at their jamming points, while isostaticity is ensured in the case of the jamming of spherical particles. This structural difference implies that the presence of asphericity affects the critical exponents related to the contact number and the vibrational density of states. Moreover, while the force and gap distributions of isostatic jamming present power-law behaviors, even an infinitesimal asphericity is enough to smooth out these singularities. In a recent work (Brito et al 2018 Proc. Natl Acad. Sci. 115 11736–41), we have used a combination of marginal stability arguments and the replica method to explain these observations. We argued that systems with internal degrees of freedom, like the rotations in ellipsoids, or the variation of the radii in the case of the breathing particles fall in the same universality class. In this paper, we review comprehensively the results about the jamming with internal degrees of freedom in addition to the translational degrees of freedom. We use a variational argument to derive the critical exponents of the contact number, shear modulus, and the characteristic frequencies of the density of states. Moreover, we present additional numerical data supporting the theoretical results, which were not shown in the previous work.

Brazil’s presidential system is characterized by the existence of many political parties that are elected for the Chamber of Deputies and unite in legislative coalitions to form a majority. Since the re-democratization in 1985, Brazil has had 8 direct presidential elections, among which there were two impeachments of the elected presidents. In this work we identify clear differences between stable presidential periods and Legislative terms with an impeachment by analyzing the votes that took place in the Chamber of Deputies from 1991 to 2019. Our statistical analysis are blind to the content of the bills. We start by measuring the cohesion of the parties and the congress for each bill. We then quantify the agreement between the votes of congressmen and observe that there is a stronger polarization among congressmen during legislative periods where there was no impeachment, referred here as stable legislative periods. Using clustering algorithms, we are able to associate these polarized groups observed during the stable periods with the opposition to the government and government base. For periods with an impeachment, the data shows that the congress split up in more than two groups. To characterize the impeachment of Collor and Dilma Rousseff (in 1992 and 2016, respectively) we analyze how the agreement between congressmen and the government evolved over time and we also propose a division of the congressmen in three groups. We identified that, in periods with an impeachment, the third group aligns itself against the president.