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

Una comparación de algoritmos basados en trayectoria granular para el problema de localización y ruteo con flota heterogénea (LRPH)

Indexación: Scopus.We consider the Location-Routing Problem with Heterogeneous Fleet (LRPH) in which the goal is to determine the depots to be opened, the customers to be assigned to each open depot, and the corresponding routes fulfilling the demand of the customers and by considering a heterogeneous fleet. We propose a comparison of granular approaches of Simulated Annealing (GSA), of Variable Neighborhood Search (GVNS) and of a probabilistic Tabu Search (pGTS) for the LRPH. Thus, the proposed approaches consider a subset of the search space in which non-favorable movements are discarded regarding a granularity factor. The proposed algorithms are experimentally compared for the solution of the LRPH, by taking into account the CPU time and the quality of the solutions obtained on the instances adapted from the literature. The computational results show that algorithm GSA is able to obtain high quality solutions within short CPU times, improving the results obtained by the other proposed approaches.https://revistas.unal.edu.co/index.php/dyna/article/view/55533/5896

Note on a q-modified central limit theorem

A q-modified version of the central limit theorem due to Umarov et al. affirms that q-Gaussians are attractors under addition and rescaling of certain classes of strongly correlated random variables. The proof of this theorem rests on a nonlinear q-modified Fourier transform. By exhibiting an invariance property we show that this Fourier transform does not have an inverse. As a consequence, the theorem falls short of achieving its stated goal.Comment: 10 pages, no figure

Diseño y Optimización del tamaño de grano triturado para alimentación avícola para criaderos y suministro de balanceado/Design and Optimization of crushed grain size for poultry feed for hatcheries and supply of balanced

En la investigación se diseñó, modeló y mejoró un molino de martillo económico y accesible aplicando métodos lógicos deductivos, la máquina provee un tamaño de grano ideal, que sirve como alimentación directa para aves, o también se puede utilizar como un componente para balanceado en la producción avícola, acorde a los requerimientos de las distintas pymes ya sea para consumo cárnico, producción de huevos, entre otros. Por esta razón es necesario definir distintos parámetros como el tamaño adecuado del tamiz teniendo una variedad desde los 2mm hasta los 5 mm, cuchillas, selección adecuada del motor dependiendo de la cantidad de horas por día, para esto se realizó un análisis mecánico y dinámico de los distintos elementos de la máquina mediante simulación en el software Solidworks free students, luego de tener el dimensionamiento óptimo bajo parámetros ingenieriles de cada una de las partes de la máquina, se realizó una cotización de los materiales bajo consideración económica en el que fue necesario realizar una correcta selección de los mismo elementos basados en catálogos nacionales para que la maquina sea rentable y accesible a los micro productores así como a los mayoristas, una vez considerado todo el procedimiento se construyó la máquina con un costo final de 355,39 dólares americanos, siendo esta de fácil desmontaje, mantenimiento y aplicación para la sociedad, el cual permite la reducción de costos, tiempos de producción y aumenta la eficiencia en la obtención grano triturado para el consumo el sector avícola. In the research an economical and accessible hammer mill was designed, modeled and improved by applying deductive logical methods, the machine provides an ideal grain size, which serves as direct feed for birds, or it can also be used as a component for balanced in the poultry production, according to the requirements of the different SMEs, whether for meat consumption, egg production, among others. For this reason, it is necessary to define different parameters such as the appropriate size of the sieve having a variety from 2mm to 5 mm, blades, suitable engine selection depending on the number of hours per day, for this a mechanical and dynamic analysis of the different elements of the machine by means of simulation in the software Solidworks free students, after having the optimal dimensioning under engineering parameters of each one of the parts of the machine, a quotation of the materials was made under economic consideration in which it was necessary to carry out a correct selection of the same elements based on national catalogs so that the machine is profitable and accessible to the micro producers as well as to the wholesalers. Once the entire procedure was considered, the machine was built with a final cost of US $ 355.39. being this easy to disassembly, maintenance and application for society, which allows the reduction of costs, production times and increases the efficiency in obtaining crushed grain for consumption in the poultry sector. Palabras clave: diseño, producción avícola, grano, balanceado, molino, grano triturado. Keywords: design, poultry production, grain, balanced, mill, crushed grain

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

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

When do generalized entropies apply? How phase space volume determines entropy

We show how the dependence of phase space volume $\Omega(N)$ of a classical system on its size $N$ uniquely determines its extensive entropy. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a {\em generalized} (non-additive) form. We show that generalized entropies can only exist when the dynamically (statistically) relevant fraction of degrees of freedom in the system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen and is practically statistically inactive. Systems governed by generalized entropies are therefore systems whose phase space volume effectively collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for binomial processes and argue that generalized entropies could be relevant for self organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.Comment: 5 pages, 2 figure

On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al

In the present paper we refute the criticism advanced in a recent preprint by Figueiredo et al [1] about the possible application of the $q$-generalized Central Limit Theorem (CLT) to a paradigmatic long-range-interacting many-body classical Hamiltonian system, the so-called Hamiltonian Mean Field (HMF) model. We exhibit that, contrary to what is claimed by these authors and in accordance with our previous results, $q$-Gaussian-like curves are possible and real attractors for a certain class of initial conditions, namely the one which produces nontrivial longstanding quasi-stationary states before the arrival, only for finite size, to the thermal equilibrium.Comment: 2 pages, 2 figures. Short version of the paper, accepted for publication in Europhysics Letters, (2009) in pres