Scaling dependence on time and distance in nonlinear fractional diffusion equations and possible applications to the water transport in soils

Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different physical systems like: amorphous semicondutors, polymers, composite heterogeneous films and porous media. They have also been used to calculate the heat load intensity change in blast furnace walls, to solve problems of control theory \ and dynamic problems of linear and nonlinear hereditary mechanics of solids. In this work, we investigate the scaling properties related to the nonlinear fractional diffusion equations and indicate the possibilities to the applications of these equations to simulate the water transport in unsaturated soils. Usually, the water transport in soils with anomalous diffusion, the dependence of concentration on time and distance may be expressed in term of a single variable given by $\lambda _{q}=x/t^{q}.$ In particular, for $q=1/2$ the systems obey Fick's law and Richards' equation for water transport. We show that a generalization of Richards' equation via fractional approach can incorporate the above property.Comment: 9 page

On the dynamics of bubbles in boiling water

We investigate the dynamics of many interacting bubbles in boiling water by using a laser scattering experiment. Specifically, we analyze the temporal variations of a laser intensity signal which passed through a sample of boiling water. Our empirical results indicate that the return interval distribution of the laser signal does not follow an exponential distribution; contrariwise, a heavy-tailed distribution has been found. Additionally, we compare the experimental results with those obtained from a minimalist phenomenological model, finding a good agreement.Comment: Accepted for publication in Chaos, Solitons & Fractal

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

director profile of a nematic between two concentric cylinders with inhomogeneous boundary conditions

The tilt angle profile in a nematic cell limited by two concentric cylindrical surfaces with inhomogeneous distribution of easy axes is investigated in the one-constant approximation. The results are presented in terms of the Green function approach by considering the strong anchoring case and the presence of an external electric field for small distortions

Nuclear alpha-clustering, superdeformation, and molecular resonances

Nuclear alpha-clustering has been the subject of intense study since the advent of heavy-ion accelerators. Looking back for more than 40 years we are able today to see the connection between quasimolecular resonances in heavy-ion collisions and extremely deformed states in light nuclei. For example superdeformed bands have been recently discovered in light N=Z nuclei such as $^{36}$Ar, $^{40}$Ca, $^{48}$Cr, and $^{56}$Ni by $\gamma$-ray spectroscopy. The search for strongly deformed shapes in N=Z nuclei is also the domain of charged-particle spectroscopy, and our experimental group at IReS Strasbourg has studied a number of these nuclei with the charged particle multidetector array {\sc Icare} at the {\sc Vivitron} Tandem facility in a systematical manner. Recently the search for $\gamma$-decays in $^{24}$Mg has been undertaken in a range of excitation energies where previously nuclear molecular resonances were found in $^{12}$C+$^{12}$C collisions. The breakup reaction $^{24}$Mg$+^{12}$C has been investigated at E$_{lab}$($^{24}$Mg) = 130 MeV, an energy which corresponds to the appropriate excitation energy in $^{24}$Mg for which the $^{12}$C+$^{12}$C resonance could be related to the breakup resonance. Very exclusive data were collected with the Binary Reaction Spectrometer in coincidence with {\sc Euroball IV} installed at the {\sc Vivitron}.Comment: 10 pages, 4 eps figures included. Invited Talk 10th Nuclear Physics Workshop Marie and Pierre Curie, Kazimierz Dolny Poland, Sep. 24-28, 2003; To be published in International Journal of Modern Physics