Denise Josino Soares

Preferential attachment growth model and nonextensive statistical mechanics

We introduce a two-dimensional growth model where every new site is located, at a distance r from the barycenter of the pre-existing graph, according to the probability law 1/r2 + αG (αG > 0), and is attached to (only) one pre-existing site with a probability ki/riαA (αA ≥ 0; ki is the number of links of the i-th site of the pre-existing graph, and ri its distance to the new site). Then we numerically determine that the probability distribution for a site to have k links is asymptotically given, for all values of αG, by P(k) eq−k/κ, where eqx ≡ [1 + (1 − q)x]1/(1 − q) is the function naturally emerging within nonextensive statistical mechanics. The entropic index is numerically given (at least for αA not too large) by q = 1 + (1/3)e−0.526 αA, and the characteristic number of links by κ 0.1 + 0.08 αA. The αA = 0 particular case belongs to the same universality class to which the Barabasi-Albert model belongs. In addition to this, we have numerically studied the rate at which the average number of links ki increases with the scaled time t/i; asymptotically, ki (t/i)β, the exponent being close to β = ½(1 − αA) for 0 ≤ αA ≤ 1, and zero otherwise. The present results reinforce the conjecture that the microscopic dynamics of nonextensive systems typically build (for instance, in Gibbs Γ-space for Hamiltonian systems) a scale-free network.

Prevalent fatty acids in cashew nuts obtained from conventional and organic cultivation in different stages of processing

Brazil is one of the three largest producers of fruits in the world, and among those fruit trees, the cashew tree stands out due to the high nutritional and commercial value of its products. During its fruit processing, there are losses in some compounds and few studies address this issue. Over the last decade the conventional system of food production has been substituted for the organic cultivation system, which is a promising alternative source of income given the global demand for healthy food. Therefore, this research aimed to characterize and quantify the prevalent fatty acids found in cashew nuts obtained from conventional and organic cultivation during various stages of processing. The prevalent fatty acids found were palmitic, linoleic, oleic, and stearic acid. The average of these fatty acids were 6.93 ± 0.55; 16.99 ± 0.61; 67.62 ± 1.00 and 8.42 ± 0.55 g/100 g, respectively. There was no reduction in the palmitic, oleic and stearic fatty acid contents during processing. Very little difference was observed between the nuts obtained from conventional and organic cultivation, indicating that the method of cultivation used has little or no influence on the content of cashew nut fatty acids.