Self-similarity and singularity formation in a coupled system of Yang-Mills-dilaton evolution equations

We study both analytically and numerically a coupled system of spherically symmetric SU(2) Yang-Mills-dilaton equation in 3+1 Minkowski space-time. It has been found that the system admits a hidden scale invariance which becomes transparent if a special ansatz for the dilaton field is used. This choice corresponds to transition to a frame rotated in the $\ln r-t$ plane at a definite angle. We find an infinite countable family of self-similar solutions which can be parametrized by the $N$ - the number of zeros of the relevant Yang-Mills function. According to the performed linear perturbation analysis, the lowest solution with N=0 only occurred to be stable. The Cauchy problem has been solved numerically for a wide range of smooth finite energy initial data. It has been found that if the initial data exceed some threshold, the resulting solutions in a compact region shrinking to the origin, attain the lowest N=0 stable self-similar profile, which can pretend to be a global stable attractor in the Cauchy problem. The solutions live a finite time in a self-similar regime and then the unbounded growth of the second derivative of the YM function at the origin indicates a singularity formation, which is in agreement with the general expectations for the supercritical systems.Comment: 10 pages, 5 figure

Dispersion and collapse of wave maps

We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures. The first conjecture states that singularities which are produced in the evolution of sufficiently large initial data are approached in a universal manner given by the profile of a stable self-similar solution. The second conjecture states that the codimension-one stable manifold of a self-similar solution with exactly one instability determines the threshold of singularity formation for a large class of initial data. Our results can be considered as a toy-model for some aspects of the critical behavior in formation of black holes.Comment: 14 pages, Latex, 9 eps figures included, typos correcte

Trapped surfaces in spherical expanding open universes

Consider spherically symmetric initial data for a cosmology which, in the large, approximates an open $k = -1 ,\Lambda = 0$ Friedmann-Lema{\^\i}tre universe. Further assume that the data is chosen so that the trace of the extrinsic curvature is a constant and that the matter field is at rest at this instant of time. One expects that no trapped surfaces appear in the data if no significant clump of excess matter is to be found. This letter confirms this belief by displaying a necessary condition for the existence of trapped surfaces.This necessary condition, simply stated, says that a relatively large amount of excess matter must be concentrated in a small volume for trapped surfaces to appear.Comment: 8 pages, Late

Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere

In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from $\mathbb{R}^2$ into $S^2$.Comment: 14 pages, 5 figures, final version to be published in Nonlinearit

New Critical Behavior in Einstein-Yang-Mills Collapse

We extend the investigation of the gravitational collapse of a spherically symmetric Yang-Mills field in Einstein gravity and show that, within the black hole regime, a new kind of critical behavior arises which separates black holes formed via Type I collapse from black holes formed through Type II collapse. Further, we provide evidence that these new attracting critical solutions are in fact the previously discovered colored black holes with a single unstable mode.Comment: 13 pages, 4 figure

Coexistence of black holes and a long-range scalar field in cosmology

The exactly solvable scalar hairy black hole model (originated from the modern high-energy theory) is proposed. It turns out that the existence of black holes (BH) is strongly correlated to global scalar field, in a sense that they mutually impose bounds upon their physical parameters like the BH mass (lower bound) or the cosmological constant (upper bound). We consider the same model also as a cosmological one and show that it agrees with recent experimental data; additionally, it provides a unified quintessence-like description of dark energy and dark matter.Comment: 4 pages, 4 figure

Measurement of Indeterminacy in Packings of Perfectly Rigid Disks

Static packings of perfectly rigid particles are investigated theoretically and numerically. The problem of finding the contact forces in such packings is formulated mathematically. Letting the values of the contact forces define a vector in a high-dimensional space enable us to show that the set of all possible contact forces is convex, facilitating its numerical exploration. It is also found that the boundary of the set is connected with the presence of sliding contacts, suggesting that a stable packing should not have more than 2M-3N sliding contacts in two dimensions, where M is the number of contacts and N is the number of particles. These results were used to analyze packings generated in different ways by either molecular dynamics or contact dynamics simulations. The dimension of the set of possible forces and the number of sliding contacts agrees with the theoretical expectations. The indeterminacy of each component of the contact forces are found, as well as the an estimate for the diameter of the set of possible contact forces. We also show that contacts with high indeterminacy are located on force chains. The question of whether the simulation methods can represent a packing's memory of its formation is addressed.Comment: 12 pages, 13 figures, submitted to Phys Rev

Stratified horizontal flow in vertically vibrated granular layers

A layer of granular material on a vertically vibrating sawtooth-shaped base exhibits horizontal flow whose speed and direction depend on the parameters specifying the system in a complex manner. Discrete-particle simulations reveal that the induced flow rate varies with height within the granular layer and oppositely directed flows can occur at different levels. The behavior of the overall flow is readily understood once this novel feature is taken into account.Comment: 4 pages, 6 figures, submitte

Fios de uma hashtag: entextualização de resistência face a desafios políticos e sanitários no Brasil

The scenario for this paper is the combined sanitary and political crisis that Brazil has been facing in these unprecedented times of the COVID-19 pandemic. The country is ideologically polarized and this polarization has been enhanced in the last year and a half in Bolsonaro’s government. A bleak period characterized by a way of governing that Silva (2020) names “pragmatics of chaos” due to denialism (even of the very pandemic) and to the neoliberal values cherished by a radical right-wing that supports the President and backs the discontinuation of important public policies, mainly those directed towards minoritized groups and environmental protection. Having in mind such a scenario, and amidst the societal bewilderment and inaction regarding the President’s contradictory actions towards democracy, we chose to focus on a rare event of direct resistance featured by a migrant of Haitian origin, who told in the face of the president what maybe many Brazilians had not dared to say. What is of interest here is that this performance, recorded on a mobile phone, and posted as a tweet, went viral, and gave rise to a hashtag - #acaboubolsonaro [ItsOverBolsonaro] - that is still alive seven months later. With a focus on the man’s performance of resistance and its entextualization on social media, we analyze his discourse and the impacts of his positioning. In the analysis, we try to retrace some of the threads traversed by the hashtag in two Twitter accounts and some of the reverberations on Instagram. We also discuss how the discursive thread of the postings weaves a metareflexive fabric about the man’s performance. We see this meta-reflection as an acknowledgment of another praxis that we have called ‘pragmatics of resistance’59319661994CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ311870/2015-5O cenário para este artigo é a combinada crise sanitária e política que o Brasil vem enfrentando nesses tempos sem precedentes de pandemia de COVID-19. O país está polarizado ideologicamente e essa polarização aumentou no último ano e meio do governo Bolsonaro. Um período sombrio caracterizado por uma forma de governar que Silva (2020) denomina “pragmática do caos” devido ao negacionismo (até mesmo da própria pandemia) e aos valores neoliberais caros a uma direita radical, que apoia o Presidente e defende a descontinuação de políticas públicas importantes, principalmente as voltadas a grupos minoritários e de proteção ambiental. Tendo em vista tal cenário, e em meio ao espanto e à inação da sociedade em relação às ações contraditórias do Presidente no que concerne à democracia, optamos por nos concentrar em um raro evento de resistência direta protagonizado por um migrante de origem haitiana, que disse na cara do Presidente o que talvez muitos brasileiros não tenham ousado dizer. Essa performance, gravada em um celular e postada como um tweet, viralizou, dando origem a uma hashtag - #acaboubolsonaro [ItsOverBolsonaro] - que continua viva sete meses depois. Focalizando a performance de resistência e sua entextualização nas redes sociais, tentamos reconstituir alguns dos tópicos percorridos pela hashtag em duas contas do Twitter e algumas das reverberações no Instagram. Também discutimos como o fio discursive das postagens delineia um tecido metarreflexivo sobre a performance do Homem. Vemos essa metarreflexão como um reconhecimento de outra práxis, que chamamos de “pragmática da resistência