Multifractal analysis of nonhyperbolic coupled map lattices: Application to genomic sequences

Symbolic sequences generated by coupled map lattices (CMLs) can be used to model the chaotic-like structure of genomic sequences. In this study it is shown that diffusively coupled Chebyshev maps of order 4 (corresponding to a shift of 4 symbols) very closely reproduce the multifractal spectrum $D_q$ of human genomic sequences for coupling constant $\alpha =0.35\pm 0.01$ if $q>0$. The presence of rare configurations causes deviations for $q<0$, which disappear if the rare event statistics of the CML is modified. Such rare configurations are known to play specific functional roles in genomic sequences serving as promoters or regulatory elements.Comment: 7 pages, 6 picture

A Peculiar Velocity Pattern in and near the Leading Sunspot of NOAA 10781: Wave Refraction by Large-Scale Magnetic Fields?

I report observations of unusually strong photospheric and chromospheric velocity oscillations in and near the leading sunspot of NOAA 10781 on 03 July 2005. I investigate an impinging wave as a possible origin of the velocity pattern, and the changes of the wave after the passage through the magnetic fields of the sunspot. The wave pattern found consists of a wave with about 3 Mm apparent wavelength that propagates towards the sunspot. This wave seems to trigger oscillations inside the sunspot's umbra, which originate from a location inside the penumbra on the side of the impinging wave. The wavelength decreases and the velocity amplitude increases by an order of magnitude in the chromospheric layers inside the sunspot. On the side of the sunspot opposite to the impinging plane wave, circular wave fronts centered on the umbra are seen propagating away from the sunspot outside its outer white-light boundary. They lead to a peculiar ring structure around the sunspot, which is visible in both velocity and intensity maps. The fact that only weak photospheric velocity oscillations are seen in the umbra - contrary to the chromosphere where they peak there - highlights the necessity to include the upper solar atmosphere in calculations of wave propagation through spatially and vertically extended magnetic field concentrations like sunspots.Comment: 16 pages, 12 figures, accepted by Solar Physics. The final publication is available at springerlink.co

An uncombed inversion of multi-wavelength observations reproducing the Net Circular Polarization in a sunspots' penumbra

I derived a geometrical model of the penumbral magnetic field topology from an uncombed inversion setup that aimed at reproducing the NCP of simultaneous spectra in near-IR (1.56 mu) and VIS (630 nm) spectral lines. I inverted the spectra of five photospheric lines with a model that mimicked vertically interlaced magnetic fields with two components, labeled background field and flow channels. The flow channels were modeled as a perturbation of the background field with a Gaussian shape using the SIRGAUS code. The location and extension of the Gaussian perturbation in the optical depth scale was then converted to a geometrical height scale. I investigated the relative amount of magnetic flux in the flow channels and the background field atmosphere. The uncombed model is able to reproduce the NCP well on the limb side of the spot and worse on the center side; the VIS lines are better reproduced than the near-IR lines. The Evershed flow happens along nearly horizontal field lines close to the solar surface. The magnetic flux that is related to the flow channels makes up about 20-50% of the total magnetic flux in the penumbra. The gradients obtainable by a Gaussian perturbation are too small for a perfect reproduction of the NCP in the IR lines with their small formation height range. Two peculiarities of the observed NCP, a sign change of the NCP of the VIS lines on the center side and a ring structure around the umbra in the Ti line at 630.37nm and the FeI line at 1565.2nm deserve closer attention. The large fraction of magnetic flux related to the flow channel component could allow to replenish the penumbral radiative losses in the flux tube picture.Comment: 12 pages, 14 figures + 4 pages Appendix, 5 figures, accepted by Astronomy & Astrophysic

Competition between quasi-molecular resonances and fusion-fission in light dinuclear systems

The results presented in this paper clearly suggest that a coherent framework may exist which connects the topics of heavy-ion molecular resonances, hyperdeformation effects, and fission shape isomerism. New data on particle-particle-$\gamma$ triple coincidences of the $^{28}$Si+$^{28}$Si reaction at a beam energy corresponding to the population of a conjectured J$^{\pi}$ = 38$^{+}$ resonance in $^{56}$Ni are presented. The absence of alignment of the spins of the outgoing fragments with respect to the orbital angular momentum is found to be in contrast with the alignment as measured for the $^{24}$Mg+$^{24}$Mg resonances. A molecular-model picture is presented to suggest a "butterfly" motion of two oblate $^{28}$Si nuclei interacting in a equator-to-equator molecular configuration.Comment: 10 pages standard REVTeX file, 7 ps and eps Figures included -- Talk given at the International Conference ``Nuclear Physics close to the Barrier", Warsaw, Poland, June 30- July 4, 1998 (Proceedings to be published in Acta Physica Polonica A, fall 1998) -

The entropy in finite NN-unit nonextensive systems: the ordinary average and qq-average

We have discussed the Tsallis entropy in finite $N$-unit nonextensive systems, by using the multivariate $q$-Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the $q$-average ($q$: the entropic index). The Tsallis entropy obtained by the $q$-average has an exponential $N$ dependence: $S_q^{(N)}/N \simeq \:e^{(1-q)N \:S_1^{(1)}}$ for large $N$ ($\gg \frac{1}{(1-q)} >0$). In contrast, the Tsallis entropy obtained by the normal average is given by $S_q^{(N)}/N \simeq [1/(q-1)N]$ for large $N$ ($\gg \frac{1}{(q-1)} > 0)$. $N$ dependences of the Tsallis entropy obtained by the $q$- and normal averages are generally quite different, although the both results are in fairly good agreement for $\vert q-1 \vert \ll 1.0$. The validity of the factorization approximation to PDFs which has been commonly adopted in the literature, has been examined. We have calculated correlations defined by $C_m= \langle (\delta x_i \:\delta x_j)^m \rangle -\langle (\delta x_i)^m \rangle\: \langle (\delta x_j)^m \rangle$ for $i \neq j$ where $\delta x_i=x_i -\langle x_i \rangle$, and the bracket $\langle \cdot \rangle$ stands for the normal and $q$-averages. The first-order correlation ($m=1$) expresses the intrinsic correlation and higher-order correlations with $m \geq 2$ include nonextensivity-induced correlation, whose physical origin is elucidated in the superstatistics.Comment: 23 pages, 5 figures: the final version accepted in J. Math. Phy

Superstatistics

We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the statistical properties of the fluctuations, we obtain different effective statistical mechanics descriptions. Tsallis statistics is one, but other classes of generalized statistics are obtained as well. We show that for small variance of the fluctuations all these different statistics behave in a universal way.Comment: 12 pages /a few more references and comments added in revised versio