Labyrinthine pathways towards supercycle attractors in unimodal maps

We uncover previously unknown properties of the family of periodic superstable cycles in unimodal maps characterized each by a Lyapunov exponent that diverges to minus infinity. Amongst the main novel properties are the following: i) The basins of attraction for the phases of the cycles develop fractal boundaries of increasing complexity as the period-doubling structure advances towards the transition to chaos. ii) The fractal boundaries, formed by the preimages of the repellor, display hierarchical structures organized according to exponential clusterings that manifest in the dynamics as sensitivity to the final state and transient chaos. iii) There is a functional composition renormalization group (RG) fixed-point map associated to the family of supercycles. iv) This map is given in closed form by the same kind of $q$-exponential function found for both the pitchfork and tangent bifurcation attractors. v) There is a final stage ultra-fast dynamics towards the attractor with a sensitivity to initial conditions that decreases as an exponential of an exponential of time.Comment: 8 pages, 13 figure

On the diffusive anomalies in a long-range Hamiltonian system

We scrutinize the anomalies in diffusion observed in an extended long-range system of classical rotors, the HMF model. Under suitable preparation, the system falls into long-lived quasi-stationary states presenting super-diffusion of rotor phases. We investigate the diffusive motion of phases by monitoring the evolution of their probability density function for large system sizes. These densities are shown to be of the $q$-Gaussian form, $P(x)\propto (1+(q-1)[x/\beta]^2)^{1/(1-q)}$, with parameter $q$ increasing with time before reaching a steady value $q\simeq 3/2$. From this perspective, we also discuss the relaxation to equilibrium and show that diffusive motion in quasi-stationary trajectories strongly depends on system size.Comment: 5 pages, 5 figures. References added and correcte

Sweet Wines Produced by an Innovative Winemaking Procedure: Colour, Active Odorants and Sensory Profile

The colour, aroma-active compounds and sensory properties of sweet wines from Pedro Ximenez grapes produced by means of an innovative winemaking procedure, based on controlled chamber-drying of grapes, partial fermentation of the must (to 4% or 8% vol ethanol) and subsequent accelerated ageing by contact with oak chips, were studied. Fermentation made the musts less brown and more yellow, whereas ageing made them darker and increased their brown, reddish and yellowish hues. Overall, the musts fermented to 8% vol ethanol exhibited higher odour activity values (OAVs). In addition, the musts aged with oak chips were slightly different from those without chips. Expert tasters gave the highest scores to the musts fermented to 8% (v/v) ethanol with 2 g/L of oak chips added. The winemaking process studied would allow the existing range of sweet wines from dried grapes to be expanded by using a fast, flexible, hygienic procedure

Dynamics towards the Feigenbaum attractor

We expose at a previously unknown level of detail the features of the dynamics of trajectories that either evolve towards the Feigenbaum attractor or are captured by its matching repellor. Amongst these features are the following: i) The set of preimages of the attractor and of the repellor are embedded (dense) into each other. ii) The preimage layout is obtained as the limiting form of the rank structure of the fractal boundaries between attractor and repellor positions for the family of supercycle attractors. iii) The joint set of preimages for each case form an infinite number of families of well-defined phase-space gaps in the attractor or in the repellor. iv) The gaps in each of these families can be ordered with decreasing width in accord to power laws and are seen to appear sequentially in the dynamics generated by uniform distributions of initial conditions. v) The power law with log-periodic modulation associated to the rate of approach of trajectories towards the attractor (and to the repellor) is explained in terms of the progression of gap formation. vi) The relationship between the law of rate of convergence to the attractor and the inexhaustible hierarchy feature of the preimage structure is elucidated.Comment: 8 pages, 12 figure

Boltzmann-Gibbs thermal equilibrium distribution for classical systems and Newton law: A computational discussion

We implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs $\Gamma$-space. Using paradigmatic first-neighbor models, namely, the inertial XY ferromagnet and the Fermi-Pasta-Ulam $\beta$-model, we show that at intermediate energies the Boltzmann-Gibbs equilibrium distribution is a consequence of Newton second law (${\mathbf F}=m{\mathbf a}$). At higher energies we discuss partial agreement between time and ensemble averages.Comment: New title, revision of the text. EPJ latex, 4 figure

Chromatography-Olfactometry Study of the Aroma of Fino Sherry Wines

The aroma of Fino sherry wines produced by industrial biological aging for 0, 1.5, 2.5, 4.5, and 6 years in the Montilla-Moriles region (southern Spain) was studied by gas chromatography-olfactometry. The aroma sensations detected by 3 trained sniffers were classified according to their odor descriptors into 8 odorant series (fruity, empyreumatic, chemical, fatty, balsamic, vegetable, floral, and spicy), describing the aroma profile of the studied wines. The results showed 47 detected odors in the unaged wines, 50 in the 1.5-years-old wines and 59, 61 and 69 in the wines aged 2.5, 4.5, and 6 years, respectively. According to the frequency of the perceived aromas, the fruity and empyreumatic series were the most characteristic odorant series. By exception of chemical, floral and balsamic series without changes during aging of the wines, the remainder series increased their participation during the aging, mainly the fruity, empyreumatic, and fatty series

Extraction of phenolic compounds in controlled macerations of Pedro Ximenez grapes

Crushed grapes of cv. Pedro Ximenez were macerated together with their must for 4, 16, 24 and 48 h at temperatures of 10, 15 and 25°C. The musts obtained after pressing were used for the determination of 14 phenolic compounds from the following fractions: hydroxybenzoic acids, hydroxycinnamic acids, other nonflavonoids, flavan-3-ols and flavonols. The temperature was found not to exert a marked influence on the extraction of the phenolic compounds in the first 16 h of maceration. After that time, however, it had a significant effect, so maceration times longer than 16 h are inadvisable unless subsequent oxidation is applied. The analytical results obtained showed that the flavan-3-ols, catechin and epicatechin were extracted at the highest rates, related with maceration temperature, followed by hydroxbenzoic acids, other nonflavonoids, hydroxycinnamic acids and flavonols. The flavan-3-ol fraction was also extracted in higher proportions under the different conditions assayed, through very closely followed by that of hydroxybenzoic acids

Flavour in "Pedro Ximénez" grape musts subjected to maceration processes

Crushed grapes of  Vitis vinifera cv. Pedro Ximenez were macerated at 10, 15 and 25°C for 4, 16, 24 and 48 hours. The musts obtained after pressing were used for the determination of higher alcohols, esters and terpene compounds. The data was subjected to discriminant analysis, obtaining three functions of difficult interpretation. A fruitiness index (SIGMA favourable aromas/SIGMA unfavourable aromas) x 100 and the total of phenolic compounds were subjected to variance and multiple range analyses which revealed significant differences (p<0.01) for maceration times and temperatures. Taking into account the fruitiness index and phenolic compound values, as well as the significant differences obtained by multifactorial (time-temperature) variance analysis, the 24 h-10°C, 4 h-15°C, 16 h-15°C and 24 h-15°C were the best condition