Symbolic Sequences and Tsallis Entropy

We address this work to investigate symbolic sequences with long-range correlations by using computational simulation. We analyze sequences with two, three and four symbols that could be repeated $l$ times, with the probability distribution $p(l)\propto 1/ l^{\mu}$. For these sequences, we verified that the usual entropy increases more slowly when the symbols are correlated and the Tsallis entropy exhibits, for a suitable choice of $q$, a linear behavior. We also study the chain as a random walk-like process and observe a nonusual diffusive behavior depending on the values of the parameter $\mu$.Comment: Published in the Brazilian Journal of Physic

The Contribution of the Smectic-Nematic Interface to the Surface Energy

The contribution of the smectic-nematic interface to the surface energy of a nematic liquid crystal sample is analyzed. By means of a simple model it is shown that the surface energy depends on the thickness of the region over which the transition smectic-nematic takes place. For perfectly flat substrates this thickness is of the order of the correlation length entering in the transition. An estimate of this contribution shows that it is greater than the one arising from the nematic-substrate interaction. Moreover, it is also shown that the surface energy determined in this way presents a non-monotonic behavior with the temperature.Comment: 10 pages, revte

Geometry, stochastic calculus and quantum fields in a non-commutative space-time

The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic quantum mechanics algebra is also unstable. Its stabilization requires the non-commutativity of the space-time coordinates and the existence of a fundamental length constant. The new relativistic quantum mechanics algebra has important consequences on the geometry of space-time, on quantum stochastic calculus and on the construction of quantum fields. Some of these effects are studied in this paper.Comment: 36 pages Latex, 1 eps figur

AN OBJECTIVE EXPLICIT FORMULATION BASED ON THE OLDROYD-B CONSTITUTIVE EQUATION

In the present paper is shown how to obtain an objective explicit algebraic extra-stress model (AESM) based on differential constitutive equations for viscoelastic flows (Oldroyd B, White-Metzner, Phan-Thien-Tanner, etc). The formulation is developed for three-dimensional time-dependent flows. In a previous work, Mompean, 1998 obtained a non-objective algebraic model. This inconsistency is now removed introducing the relative-rate-ofrotation tensor making the model frame-invariant. A new generalized objective time derivative is also introduced, giving flexibility to the model. Calculations are performed with an Oldroyd B based AESM for a 4:1 contraction flow, showing good agreement with the original constitutive differential model. Several results with particular derivatives are obtained and an analysis guided by a flow type classifier is given. This formulation is able to include a prediction, not present in the Oldroyd B model, the viscometric second normal stress difference, N2

Soft singularity and the fundamental length

It is shown that some regular solutions in 5D Kaluza-Klein gravity may have interesting properties if one from the parameters is in the Planck region. In this case the Kretschman metric invariant runs up to a maximal reachable value in nature, i.e. practically the metric becomes singular. This observation allows us to suppose that in this situation the problems with such soft singularity will be much easier resolved in the future quantum gravity then by the situation with the ordinary hard singularity (Reissner-Nordstr\"om singularity, for example). It is supposed that the analogous consideration can be applied for the avoiding the hard singularities connected with the gauge charges.Comment: 5 page