Irreversible processes and the accelerated-decelerated phases of the Universe

A model for the Universe is proposed where it is considered as a mixture of scalar and matter fields. The particle production is due to an irreversible transfer of energy from the gravitational field to the matter field and represented by a non-equilibrium pressure. This model can simulate three distinct periods of the Universe: (a) an accelerated epoch where the energy density of the scalar field prevails over the matter field, (b) a past decelerated period where the energy density of the matter field becomes more predominant than the scalar energy density, and (c) a present acceleration phase where the scalar energy density overcomes the energy density of the matter field.Comment: 6 pages, 2 figures, to be published in Brazilian Journal of Physic

The fully kinetic Biermann battery and associated generation of pressure anisotropy

The dynamical evolution of a fully kinetic, collisionless system with imposed background density and temperature gradients is investigated analytically. The temperature gradient leads to the generation of temperature anisotropy, with the temperature along the gradient becoming larger than that in the direction perpendicular to it. This causes the system to become unstable to pressure anisotropy driven instabilities, dominantly to electron Weibel. When both density and temperature gradients are present and non-parallel to each other, we obtain a Biermann-like linear in time magnetic field growth. Accompanying particle in cell numerical simulations are shown to confirm our analytical results.Comment: 5 pages, 2 figures, + Supplementary materials (4 pages, 2 figures

Damage-based fracture with electro-magnetic coupling

Acoupled elastic and electro-magnetic analysis is proposed including finite displacements and damage-based fracture. Piezo-electric terms are considered and resulting partial differential equations include a non-classical wave equation due to the specific constitutive law. The resulting wave equation is constrained and, in contrast with the traditional solutions of the decoupled classical electromagnetic wave equations, the constraint is directly included in the analysis. The absence of free current density allows the expression of the magnetic field rate as a function of the electric field and therefore, under specific circumstances, removal of the corresponding magnetic degrees-offreedom. A Lagrange multiplier field is introduced to exactly enforce the divergence constraint, forming a three-field variational formulation (required to include thewave constraint). No vector-potential is required or mentioned, eliminating the need for gauges. The classical boundary conditions of electromagnetism are specialized and a boundary condition involving the electric field is obtained. The spatial discretization makes use of mixed bubble-based (of the MINI type) finite elementswith displacement, electric field and Lagrange multiplier degrees-of-freedom. Three verification examples are presented with very good qualitative conclusions and mesh-independence

Universality class for bootstrap percolation with m=3m=3 on the cubic lattice

We study the $m=3$ bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with probability $p$ or $1-p$, respectively. Occupied sites with less than $m$ occupied first-neighbours are then rendered unoccupied; this culling process is repeated until a stable configuration is reached. We evaluate the percolation critical probability, $p_c$, and both scaling powers, $y_p$ and $y_h$, and, contrarily to previous calculations, our results indicate that the model belongs to the same universality class as usual percolation (i.e., $m=0$). The critical spanning probability, $R(p_c)$, is also numerically studied, for systems with linear sizes ranging from L=32 up to L=480: the value we found, $R(p_c)=0.270 \pm 0.005$, is the same as for usual percolation with free boundary conditions.Comment: 11 pages; 4 figures; to appear in Int. J. Mod. Phys.

Meson decay in a corrected 30P3^P_0 model

Extensively applied to both light and heavy meson decay and standing as one of the most successful strong decay models is the $3^P_0$ model, in which $q\bar{q}$ pair production is the dominant mechanism. The pair production can be obtained from the non-relativistic limit of a microscopic interaction Hamiltonian involving Dirac quark fields. The evaluation of the decay amplitude can be performed by a diagrammatic technique for drawing quark lines. In this paper we use an alternative approach which consists in a mapping technique, the Fock-Tani formalism, in order to obtain an effective Hamiltonian starting from same microscopic interaction. An additional effect is manifest in this formalism associated to the extended nature of mesons: bound-state corrections. A corrected $3^P_0$ is obtained and applied, as an example, to $b_{1}\to\omega\pi$ and $a_{1}\to\rho\pi$ decays.Comment: 3 figures. To appear in Physical Review

Leptonic Invariants, Neutrino Mass-Ordering and the Octant of θ23\theta_{23}

We point out that leptonic weak-basis invariants are an important tool for the study of the properties of lepton flavour models. In particular, we show that appropriately chosen invariants can give a clear indication of whether a particular lepton flavour model favours normal or inverted hierarchy for neutrino masses and what is the octant of $\theta_{23}$. These invariants can be evaluated in any conveniently chosen weak-basis and can also be expressed in terms of neutrino masses, charged lepton masses, mixing angles and CP violation phases.Comment: 10 pages, no figure

Non-Factorizable Phases, Yukawa Textures and the Size of sin (2 beta)

We emphasize the crucial r\^ ole played by non-factorizable phases in the analysis of the Yukawa flavour structure performed in weak bases with Hermitian mass matrices and with vanishing $(1,1)$ entries. We show that non-factorizable phases are important in order to generate a sufficiently large $\sin 2 \beta$. A method is suggested to reconstruct the flavour structure of Yukawa couplings from input experimental data both in this Hermitian basis and in a non-Hermitian basis with a maximal number of texture zeros. The corresponding Froggatt--Nielsen patterns are presented in both cases.Comment: 15 pages, 3 figure