Photoacoustic Spectroscopy Applied To The Study Of Clay Soils

The study of clay soils using photoacoustic spectroscopy was presented. The observation of the photoacoustic spectra showed the transition bands associated with Fe3+ ions in octahedral or tetrahedral symmetry. Rietveld refinements showed that the Al3+ cations were partially substituted by the Fe3+ cations in the octahedral states of kaolinite structure.741 II355357Alexandre, J., Saboya, F., Marques, B.C., Ribeiro, M.L.P., Salles, C., Da Silva, M.G., Sthel, M.S., Vargas, H., (1999) Analyst, 124, p. 1209Ambikadevi, V.R., Lalithambika, M., (2000) Appl. Clay Sci., 16, p. 133Mehra, O.P., Jackson, M.L., (1960) Clays Clay Miner., 7, p. 317Young, R.A., Sakthivel, A., Moss, T.S., Paiva-Santos, C.O., (1995) J. Appl. Crystallogr., 28, p. 366Sugano, S., Tunabe, Y., Kamimura, H., (1970) Multiplets of Transition-Metal Ions in Crystals, , Academic, New YorkAbritta, T., De Souza Barros, F., (1988) J. Lumin., 40, p. 187Abritta, T., Cella, N., Vargas, H., (1989) Chem. Phys. Lett., 161, p. 12Lima, G.A.R., Baesso, M.L., Arguello, Z.P., Da Silva, E.C., Vargas, H., (1987) Phys. Rev. B, 36, p. 9812Rosencwaig, A., Gersho, A., (1976) J. Appl. Phys., 47, p. 64Baesso, M.L., Mansanares, A.M., Da Silva, E.C., Vargas, H., (1989) Phys. Rev. B, 40, p. 188

Analytical results for coupled map lattices with long-range interactions

We obtain exact analytical results for lattices of maps with couplings that decay with distance as $r^{-\alpha}$. We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements are piecewise linear maps, we get an algebraic expression for the Lyapunov spectrum. When the local dynamics is given by a nonlinear map, the Lyapunov spectrum for a completely synchronized state is analytically obtained. The critical lines characterizing the synchronization transition are determined from the expression for the largest transversal Lyapunov exponent. In particular, it is shown that in the thermodynamical limit, such transition is only possible for sufficiently long-range interactions, namely, for $\alpha\le alpha_c<d$, where $d$ is the lattice dimension.Comment: 4 pages, 2 figures, corrections included. Phys. Rev. E 68, 045202(R) (2003); correction in pres