Tsallis' q index and Mori's q phase transitions at edge of chaos

We uncover the basis for the validity of the Tsallis statistics at the onset of chaos in logistic maps. The dynamics within the critical attractor is found to consist of an infinite family of Mori's $q$-phase transitions of rapidly decreasing strength, each associated to a discontinuity in Feigenbaum's trajectory scaling function $\sigma$. The value of $q$ at each transition corresponds to the same special value for the entropic index $q$, such that the resultant sets of $q$-Lyapunov coefficients are equal to the Tsallis rates of entropy evolution.Comment: Significantly enlarged version, additional figures and references. To be published in Physical Review

The charge shuttle as a nanomechanical ratchet

We consider the charge shuttle proposed by Gorelik {\em et al.} driven by a time-dependent voltage bias. In the case of asymmetric setup, the system behaves as a rachet. For pure AC drive, the rectified current shows a complex frequency dependent response characterized by frequency locking at fracional values of the external frequency. Due to the non-linear dynamics of the shuttle, the rachet effect is present also for very low frequencies.Comment: 4 pages, 4 figure

Gradient porosity poly(dicyclopentadiene)

This article describes the preparation of gradient porosity thermoset polymers. The technique used is based on polymerizing a solution of cross-linkable dicyclopentadiene and 2-propanol. The forming polymer being insoluble in 2-propanol, phase separation occurs. Subsequent drying of the 2-propanol gives porosities up to 80%. An apparatus was built to produce a gradient in 2-propanol concentration in a flask, resulting in polymerized gradient porosity rods. The resulting materials have been characterized by scanning electron microscopy (SEM) and density measurements. A mathematical model which allows prediction of the gradient produced is also presente

Comparison of enzyme kinetics and inhibition of three North American snake venoms

Baseline gelatinase activities of venom from three snake species: Agkistrodon contortrix contortrix (Acc), Crotalus atrox (C. atrox) and Cerastes cerastes (Ccc), were measured using EnzChek® Gelatinase/Collagenase Kit E12055, and found to be similar between Acc and Ccc, while C. atrox venom showed lower baseline activity compared to the other two. Based on Selwyn plots of experimental data, venom from Acc and C. atrox demonstrate enzymatic stability over a wide range of substrate concentrations and reaction times, while Ccc venom demonstrated lower levels of stability under the same conditions. It was also found that the protease inhibitor NNGH inhibits the gelatinase activity of C. atrox venom more than it does for Acc venom. The inhibitory effect on venom gelatinase activity is not affected by enzyme pretreatment with NNGH prior to the gelatinase reaction. The DMSO used in the reaction also has an inhibitory effect, which is greater for C. atrox than for Acc. These results will be useful in understanding reaction kinetics of snake venom enzyme inhibition, which could lead to alternative treatment modalities for envenomation

Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps

Ensemble averages of the sensitivity to initial conditions $\xi(t)$ and the entropy production per unit time of a {\it new} family of one-dimensional dissipative maps, $x_{t+1}=1-ae^{-1/|x_t|^z}(z>0)$, and of the known logistic-like maps, $x_{t+1}=1-a|x_t|^z(z>1)$, are numerically studied, both for {\it strong} (Lyapunov exponent $\lambda_1>0$) and {\it weak} (chaos threshold, i.e., $\lambda_1=0$) chaotic cases. In all cases we verify that (i) both $[\ln_q x \equiv (x^{1-q}-1)/(1-q); \ln_1 x=\ln x]$ and $<S_q > [S_q \equiv (1-\sum_i p_i^q)/(q-1); S_1=-\sum_i p_i \ln p_i]$ {\it linearly} increase with time for (and only for) a special value of $q$, $q_{sen}^{av}$, and (ii) the {\it slope} of $$and that of$$ {\it coincide}, thus interestingly extending the well known Pesin theorem. For strong chaos, $q_{sen}^{av}=1$, whereas at the edge of chaos, $q_{sen}^{av}(z)<1$.Comment: 5 pages, 5 figure

Self-similarities in the frequency-amplitude space of a loss-modulated CO2_2 laser

We show the standard two-level continuous-time model of loss-modulated CO$_2$ lasers to display the same regular network of self-similar stability islands known so far to be typically present only in discrete-time models based on mappings. For class B laser models our results suggest that, more than just convenient surrogates, discrete mappings in fact could be isomorphic to continuous flows.Comment: (5 low-res color figs; for ALL figures high-res PDF: http://www.if.ufrgs.br/~jgallas/jg_papers.html

Fractal geometry, information growth and nonextensive thermodynamics

This is a study of the information evolution of complex systems by geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness of the state number counting at any scale on fractal support, the incomplete normalization $\sum_ip_i^q=1$ is applied throughout the paper, where $q$ is the fractal dimension divided by the dimension of the smooth Euclidean space in which the fractal structure of the phase space is embedded. It is shown that the information growth is nonadditive and is proportional to the trace-form $\sum_ip_i-\sum_ip_i^q$ which can be connected to several nonadditive entropies. This information growth can be extremized to give power law distributions for these non-equilibrium systems. It can also be used for the study of the thermodynamics derived from Tsallis entropy for nonadditive systems which contain subsystems each having its own $q$. It is argued that, within this thermodynamics, the Stefan-Boltzmann law of blackbody radiation can be preserved.Comment: Final version, 10 pages, no figures, Invited talk at the international conference NEXT2003, 21-28 september 2003, Villasimius (Cagliari), Ital

B595: An Illustrated Review of Apple Virus Diseases

The writers have attempted to review the available literature on the subject and to organize it in an orderly fashion. The name, symptomatology, host range, and geographic distribution are given for each virus disease. Where it was possible illustrations of each disorder have also been included. This bulletin addresses the following apple virus diseases: apple mosaic, flat limb, rubbery wood, stem pitting, spy 227 apple reaction, dwarf fruit and decline, chat fruit, chlorotic leaf spot, leaf pucker, dapple apple, false sting and green crinkle, green mottle, ring spot, star cracking, scar skin, rough skin, apple proliferation, rosettehttps://digitalcommons.library.umaine.edu/aes_bulletin/1068/thumbnail.jp

Probability densities for the sums of iterates of the sine-circle map in the vicinity of the quasi-periodic edge of chaos

We investigate the probability density of rescaled sum of iterates of sine-circle map within quasi-periodic route to chaos. When the dynamical system is strongly mixing (i.e., ergodic), standard Central Limit Theorem (CLT) is expected to be valid, but at the edge of chaos where iterates have strong correlations, the standard CLT is not necessarily to be valid anymore. We discuss here the main characteristics of the central limit behavior of deterministic dynamical systems which exhibit quasi-periodic route to chaos. At the golden-mean onset of chaos for the sine-circle map, we numerically verify that the probability density appears to converge to a q-Gaussian with q<1 as the golden mean value is approached.Comment: 7 pages, 7 figures, 1 tabl