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We study the temporal evolution of avalanches in the fiber bundle model of disordered solids, when the model is gradually driven towards the critical breakdown point. We use two types of loading protocols: (i) the quasi-static loading, and (ii) loading by a discrete amount. In the quasi-static loading, where the load is increased by the minimum amount needed to initiate an avalanche, the temporal shapes of avalanches are asymmetric away from the critical point and become symmetric as the critical point is approached. A measure of asymmetry follows a universal form $A\sim (\sigma-\sigma_c)^{\theta}$, with $\theta\approx 0.25$, where $\sigma$ is the load per fiber and $\sigma_c$ is the critical load per fiber. This behavior is independent of the disorder present in the system in terms of the individual failure threshold values. Thus it is possible to use this asymmetry measure as a precursor to imminent failure. For the case of discrete loading, the load is always increased by a fixed amount. The dynamics of the model in this case can be solved in the mean field limit. It shows that the avalanche shapes always remain asymmetric. We also present a variable range load sharing version of this case, where the results remain qualitatively similar., Comment: 7 pages, 8 figures

We study the interplay between epidemic dynamics and human decision making for epidemics that involve reinfection risk; in particular, the susceptible-infected-susceptible (SIS) and the susceptible-infected-recovered-infected (SIRI) epidemic models. In the proposed game-theoretic setting, individuals choose whether to adopt protection or not based on the trade-off between the cost of adopting protection and the risk of infection; the latter depends on the current prevalence of the epidemic and the fraction of individuals who adopt protection in the entire population. We define the coupled epidemic-behavioral dynamics by modeling the evolution of individual protection adoption behavior according to the replicator dynamics. For the SIS epidemic, we fully characterize the equilibria and their stability properties. We further analyze the coupled dynamics under timescale separation when individual behavior evolves faster than the epidemic, and characterize the equilibria of the resulting discontinuous hybrid dynamical system for both SIS and SIRI models. Numerical results illustrate how the coupled dynamics exhibits oscillatory behavior and convergence to sliding mode solutions under suitable parameter regimes., Comment: arXiv admin note: text overlap with arXiv:2203.10276

We consider the class of SIS epidemic models in which a large population of individuals chooses whether to adopt protection or to remain unprotected as the epidemic evolves. For a susceptible individual, adopting protection reduces the probability of becoming infected but it comes with a cost that is weighed with the instantaneous risk of becoming infected. An infected individual adopting protection transmits a new infection with a smaller probability compared to an unprotected infected individual. We focus on the replicator evolutionary dynamics to model the evolution of protection decisions by susceptible and infected subpopulations. We completely characterize the existence and local stability of the equilibria of the resulting coupled epidemic and replicator dynamics. We further show how the stability of different equilibrium points gets exchanged as certain parameters change. Finally, we investigate the system behavior under timescale separation between the epidemic and the evolutionary dynamics., Comment: Accepted for publication at the American Control Conference, 2022

In this work, we report the effects of calcination temperature on structural, dielectric, semiconducting and optical properties of YFeO3 nanoparticles prepared by a high energy ball milling process. The structural analysis of the X-ray diffraction data shows that YFeO3 exists in orthorhombic as well as in hexagonal mixed-phase states. The Rietveld analysis confirms that orthorhombic YFeO3 crystallizes into Pnma space group. The optical band gap of YFeO3 reduces from 1.96 eV to 1.68 eV with increasing the calcination temperature of the YFeO3 sample. The bandgap reducing effect might be attributed to the increased crystallite size and decreased lattice strain which is confirmed by the Williamson-Hall plot method. The obtained low bandgap YFeO3 ceramic may provide a new possibility to develop eco-friendly Ferroelectric photovoltaic devices.

We study universality in the kinetics of spinodal phase separation in unstable thin liquid films, via simulations of the thin film equation. It is shown that in addition to morphology and free energy,the number density of local maxima in the film profile can also be used to identify the early, intermediate and late stages of spinodal phase separation. A universal curve between the number density of local maxima and rescaled time describes the kinetics of early stage in d = 2, 3. The Lifshitz-Slyozov exponent of -1/3 describes the kinetics of the late stage in d = 2 even in the absence of coexisting equilibrium phases., Comment: 5 figures