arXiv subjects

J. Farjas

Publications and source records attributed to J. Farjas.

9 recordsLinked to original sources

arXiv2021

Unphysical source of dynamic order for the natural world

The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the scientific debate due to the lack of candidates for a proper answer. Here we propose a general explanation based on the oscillatory possibilities of the dynamical systems, as demonstrated with a family of differential equations exhibiting self-sustained oscillations of unbounded complexity: complex evolutions by nonlinear mixing of an arbitrarily large number of oscillation modes, in which the different modes describe specific dynamical activities and their combination articulates the interactive conjunction of such activities into the whole functioning. The dynamical scenario is rather generic since it is exclusively based on the reiterative occurrence of the two most standard mechanisms of nonlinear dynamics: the saddle-node and Hopf bifurcations, and its extraordinary richness makes feasible the well-defined occurrence of ordered features over enormously complex dynamical activities as simply arising from the proper structure of dynamical relations among the system components, i.e., without requiring any other physical cause than those involved in such relations.

nlin.AO↗

arXiv2021

Nonlinear oscillatory mixing in the generalized Landau scenario

We present a set of phase-space portraits illustrating the extraordinary oscillatory possibilities of the dynamical systems through the so-called generalized Landau scenario. In its simplest form the scenario develops in N dimensions around a saddle-node pair of fixed points experiencing successive Hopf bifurcations up to exhausting their stable manifolds and generating N-1 different limit cycles. The oscillation modes associated with these cycles extend over a wide phase-space region by mixing ones within the others and by affecting both the transient trajectories and the periodic orbits themselves. A mathematical theory covering the mode-mixing mechanisms is lacking, and our aim is to provide an overview of their main qualitative features in order to stimulate research on it.

nlin.AO↗

arXiv2021

Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits

We have found a way for penetrating the space of the dynamical systems towards systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which extraordinarily complex time evolutions arise. The system design is based on assuring the occurrence of a number of Hopf bifurcations in a set of fixed points of a relatively generic system of ordinary differential equations, in which the main peculiarity is that the nonlinearities appear through functions of a linear combination of the system variables. The paper presents the design procedure and a selection of numerical simulations with a variety of designed systems whose dynamical behaviors are really rich and full of unknown features. For concreteness, the presentation is focused to illustrating the oscillatory mixing effects on the periodic orbits, through which the harmonic oscillation born in a Hopf bifurcation becomes successively enriched with the intermittent incorporation of other oscillation modes of higher frequencies while the orbit remains periodic and without necessity of bifurcating instabilities. Even in the absence of a proper mathematical theory covering the nonlinear mixing mechanisms we find enough evidence to expect that the oscillatory scenario be truly scalable concerning the phase space dimension, the multiplicity of involved fixed points and the range of time scales, so that extremely complex but ordered dynamical behaviors could be sustained through it.

nlin.AO↗

arXiv2010

Relaxation and derelaxation of pure and hydrogenated amorphous silicon during thermal annealing experiments

The structural relaxation of pure amorphous silicon (a-Si) and hydrogenated amorphous silicon (a-Si:H) materials, that occurs during thermal annealing experiments, has been analysed by Raman spectroscopy and differential scanning calorimetry. Unlike a-Si, the heat evolved from a-Si:H cannot be explained by relaxation of the Si-Si network strain, but it reveals a derelaxation of the bond angle strain. Since the state of relaxation after annealing is very similar for pure and hydrogenated materials, our results give strong experimental support to the predicted configurational gap between a-Si and crystalline silicon.

cond-mat.mtrl-sci↗

arXiv2008

Kinetic study of the oxide-assisted catalyst-free synthesis of silicon nitride nanowires

The synthesis of Si3N4 nanowires from the reaction of silicon nanoparticles with N2 in the 1200-1440 C temperature range is reported. The nitridation conditions are such that the reaction with nitrogen is favoured by the presence of silicon oxide in the particles and by the active oxidation of silicon without a catalyst. It is shown that the Si to Si3N4 conversion rate depends on the amount of silicon particles used in the experiments and that, in general, the reaction slows down for greater amounts. This trend is explained by particle stacking, which restricts the exchange of gases between the furnace atmosphere and the atmosphere around the inner particles. In a first stage, local oxygen partial pressure increases around the inner particles and inhibits nitridation locally. If the amount of reactant Si nanoparticles is small enough, this extrinsic effect is avoided and the intrinsic nitridation kinetics can be measured. Experiments show that intrinsic kinetics does not depend on temperature.

cond-mat.mtrl-sci↗

arXiv2008

Si3N4 single-crystal nanowires grown from silicon micro and nanoparticles near the threshold of passive oxidation

A simple and most promising oxide-assisted catalyst-free method is used to prepare silicon nitride nanowires that give rise to high yield in a short time. After a brief analysis of the state of the art, we reveal the crucial role played by the oxygen partial pressure: when oxygen partial pressure is slightly below the threshold of passive oxidation, a high yield inhibiting the formation of any silica layer covering the nanowires occurs and thanks to the synthesis temperature one can control nanowire dimensions.

cond-mat.mtrl-sci↗

arXiv2008

Numerical model of solid phase transformations governed by nucleation and growth. Microstructure development during isothermal crystallization

A simple numerical model which calculates the kinetics of crystallization involving randomly distributed nucleation and isotropic growth is presented. The model can be applied to different thermal histories and no restrictions are imposed on the time and the temperature dependencies of the nucleation and growth rates. We also develop an algorithm which evaluates the corresponding emerging grain size distribution. The algorithm is easy to implement and particularly flexible making it possible to simulate several experimental conditions. Its simplicity and minimal computer requirements allow high accuracy for two- and three-dimensional growth simulations. The algorithm is applied to explore the grain morphology development during isothermal treatments for several nucleation regimes. In particular, thermal nucleation, pre-existing nuclei and the combination of both nucleation mechanisms are analyzed. For the first two cases, the universal grain size distribution is obtained. The high accuracy of the model is stated from its comparison to analytical predictions. Finally, the validity of the Kolmogorov-Johnson-Mehl-Avrami model is verified for all the cases studied.

cond-mat.mtrl-sci↗

arXiv2008

Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors.Concerning the kinetics, it is shown that the extended volume evolves with time according to alpha_ex=[exp(kappa Ct)]^m+1, where t' is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters.

cond-mat.mtrl-sci↗

arXiv2008

Quantification of the bond-angle dispersion by Raman spectroscopy and the strain energy of amorphous silicon

A thorough critical analysis of the theoretical relationships between the bond-angle dispersion in a-Si and the width of the transverse optical (TO) Raman peak is presented. It is shown that the discrepancies between them are drastically reduced when unified definitions for these magnitudes are used. This reduced dispersion in the predicted values of the bond-angle dispersion together with the broad agreement with its scarce direct determinations is then used to analyze the strain energy in partially relaxed pure a-Si. It is concluded that defect annihilation does not contribute appreciably to reducing the a-Si energy during structural relaxation. In contrast, it can account for half of the crystallization energy, which can be as low as 7 kJ/mol in defect-free a-Si.

cond-mat.mtrl-sci↗