arXiv subjects

Peter K. Liaw

Publications and source records attributed to Peter K. Liaw.

21 records · Page 2Linked to original sources

arXiv2018

On the Study of Chaos and Memory Effects in the Bonhoeffer-van der Pol Oscillator with a Non-Ideal Capacitor

In this paper, the voltage fluctuations of the Bonhoeffer van der pol oscillator system with a non-ideal capacitor were investigated. Here, the capacitor was modeled, using a fractional differential equation in which the order of the fractional derivative is also a measure of the memory in the dielectric. The governing fractional differential equation was derived using two methods, namely a differential and integral approach. The former method utilized a hierarchical resistor-capacitor (RC) ladder model while the latter utilized the theory of the universal dielectric-response. The dynamical behavior of the potential across the capacitor was found to be affected by this parameter, and, therefore, the memory of the system. Additionally, findings indicate that an increase in the memory parameter was associated with an increase in the energy stored in the dielectric. It was found that oscillation death resulted in a higher amount of stored energy in the dielectric over time, as compared to behavior, which displayed relaxation oscillations or chaotic fluctuations. The relatively-lower stored energy resulting from the latter types of dynamical behavior appeared to be a consequence of the memory effect, where present accumulations of energy in the capacitor are affected by previous decreases in the potential. Hence, in this type of scenario, the dielectric material can be thought of as remembering the past behavior of the voltage, which leads to either a decrease, or an enhancement in the stored energy. The non-ideal capacitor was also found to have a transitory nature, where it behaves more like a resistor as α approaches 0, and conversely, more like a capacitor as α goes to 1. Here, a decrease in α was linked to an enhanced metallic character of the dielectric.

physics.data-an↗

arXiv2017

Complexity Analysis of Chaos and Other Fluctuating Phenomena

The refined composite multiscale-entropy algorithm was applied to the time-dependent behavior of the Weierstrass functions, colored noise, and Logistic map to provide fresh insight into the dynamics of these fluctuating phenomena. For the Weierstrass function, the complexity of fluctuations was found to increase with respect to the fractional dimension, D, of the graph. Additionally, the sample-entropy curves increased in an exponential fashion with increasing D. This increase in the complexity was found to correspond to a rising amount of irregularities in the oscillations. In terms of the colored noise, the complexity of the fluctuations was found to be highest for the 1/f noise (f is the frequency of the generated noise), which is in agreement with findings in the literature. Moreover, the sample-entropy curves exhibited a decreasing trend for noise when the spectral exponent, β, was less than 1 and obeyed an increasing trend when β> 1. Importantly, a direct relationship was observed between the power-law exponents for the curves and the spectral exponents of the noise. For the logistic map, a correspondence was observed between the complexity maps and its bifurcation diagrams. Specifically, the map of the sample-entropy curves was negligible when the bifurcation parameter, R, varied between 3 - 3.5. Beyond these values, the curves attained non-zero values that increased with increasing R, in general.

physics.data-an↗

arXiv2017

First-principles prediction of high-entropy-alloy stability

High entropy alloys (HEAs) are multicomponent compounds whose high configurational entropy allows them to solidify into a single phase, with a simple crystal lattice structure. Some HEA's exhibit desirable properties, such as high specific strength, ductility, and corrosion resistance, while challenging the scientist to make confident predictions in the face of multiple competing phases. We demonstrate phase stability in the multicomponent alloy system of Cr-Mo-Nb-V, for which some of its binary subsystems are subject to phase separation and complex intermetallic-phase formation. Our first-principles calculation of free energy predicts that the configurational entropy stabilizes a single body-centered cubic (BCC) phase from T = 1,700K up to melting, while precipitation of a complex intermetallic is favored at lower temperatures. We form the compound experimentally and confirm that it forms as a single BCC phase from the melt, but that it transforms reversibly at lower temperatures.

cond-mat.mtrl-sci↗