Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: microscopic derivations and attractors

We derive and investigate several hydrodynamic formalisms that emerge from a system of classical, ultra-relativistic scalar particles self-interacting via a quartic potential. The specific form of the total cross-section enables the analytical computation of all transport coefficients that appear in Navier-Stokes (NS), Bemfica-Disconzi-Noronha-Kovtun (BDNK), and second-order transient hydrodynamic theories. We solve all these formalisms in a Bjorken flow scenario and show that NS and BDNK theories display unphysical features when gradients become sufficiently large. This implies that these hydrodynamic approaches may not be suitable to describe the early stages of heavy ion collisions.Comment: 30 pages, 8 figure

Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: causality and stability

We investigate the causality and stability of three different relativistic dissipative fluid-dynamical formulations emerging from a system of classical, ultra-relativistic scalar particles self-interacting via a quartic potential. For this particular interaction, all transport coefficients of Navier-Stokes, Bemfica-Disconzi-Noronha-Kovtun and second-order transient theories can be computed in analytical form. We first show that Navier-Stokes theory is acausal and unstable regardless of the matching conditions. On the other hand, BDNK theory can be linearly causal and stable for a particular set of matching choices that does not contain the so-called exotic Eckart prescription. In particular, using the Li\'enard-Chipart criterion, we obtain a set of sufficient conditions that guarantee the stability of the theory. Last, second-order transient hydrodynamic theory in Landau matching is shown to be linearly causal and stable.Comment: 21 pages, 5 figure

Spinor Fields Classification in Arbitrary Dimensions and New Classes of Spinor Fields on 7-Manifolds

A classification of spinor fields according to the associated bilinear covariants is constructed in arbitrary dimensions and metric signatures, generalizing Lounesto's 4D spinor field classification. In such a generalized classification a basic role is played by the geometric Fierz identities. In 4D Minkowski spacetime the standard bilinear covariants can be either null or non-null -- with the exception of the current density which is invariably different from zero for physical reasons -- and sweep all types of spinor fields, including Dirac, Weyl, Majorana and more generally flagpoles, flag-dipoles and dipole spinor fields. To obtain an analogous classification in higher dimensions we use the Fierz identities, which constrain the covariant bilinears in the spinor fields and force some of them to vanish. A generalized graded Fierz aggregate is moreover obtained in such a context simply from the completeness relation. We analyze the particular and important case of Riemannian 7-manifolds, where the Majorana spinor fields turn out to have a quite special place. In particular, at variance with spinor fields in 4D Minkowski spacetime that are classified in six disjoint classes, spinors in Riemannian 7-manifolds are shown to be classified, according to the bilinear covariants: (a) in just one class, in the real case of Majorana spinors; (b) in four classes, in the most general case. Much like new classes of spinor fields in 4D Minkowski spacetime have been evincing new possibilities in physics, we think these new classes of spinor fields in seven dimensions are, in particular, potential candidates for new solutions in the compactification of supergravity on a seven-dimensional manifold and its exotic versions.Comment: 15 page

Produção de ácidos orgânicos das silagens de sete genótipos de sorgo (Sorghum bicolor (L.) Moench).

Foi avaliada a qualidade das silagens de sete genotipos de sorgo, que variam quanto ao porte e suculencia do colmo, abertas apos sete, 14, 28 e 56 dias de fermentacao, quanto a producao de acidos organicos. Aos 56 dias os niveis de acido latico variaram de 2,8 a 8,5%, sendo que, apenas as silagens dos sorgos de porte medio nao foram classificados como de "muito boa" qualidade. Os teores de acido acetico e de acido butirico variaram, respectivamente, de 0,6 a 1,9% e de zero a 0,34, indicando uma boa preservacao dos materiais ensilados