Lifetime of dynamical heterogeneity in a highly supercooled liquid

We numerically examine dynamical heterogeneity in a highly supercooled three-dimensional liquid via molecular-dynamics simulations. To define the local dynamics, we consider two time intervals, $\tau_\alpha$ and $\tau_{\text{ngp}}$. $\tau_\alpha$ is the $\alpha$ relaxation time, and $\tau_{\text{ngp}}$ is the time at which non-Gaussian parameter of the van Hove self-correlation function is maximized. We determine the lifetimes of the heterogeneous dynamics in these two different time intervals, $\tau_{\text{hetero}}(\tau_\alpha)$ and $\tau_{\text{hetero}}(\tau_{\text{ngp}})$, by calculating the time correlation function of the particle dynamics, i.e., the four-point correlation function. We find that the difference between $\tau_{\text{hetero}}(\tau_\alpha)$ and $\tau_{\text{hetero}}(\tau_{\text{ngp}})$ increases with decreasing temperature. At low temperatures, $\tau_{\text{hetero}}(\tau_\alpha)$ is considerably larger than $\tau_{\alpha}$, while $\tau_{\text{hetero}}(\tau_{\text{ngp}})$ remains comparable to $\tau_{\alpha}$. Thus, the lifetime of the heterogeneous dynamics depends strongly on the time interval.Comment: 4pages, 6figure

Dynamical heterogeneity in a highly supercooled liquid: Consistent calculations of correlation length, intensity, and lifetime

We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length $\xi_4$, intensity $\chi_4$, and lifetime $\tau_{\text{hetero}}$. We evaluated all three quantities consistently from a single order parameter. In a previous study (H. Mizuno and R. Yamamoto, Phys. Rev. E {\bf 82}, 030501(R) (2010)), we examined the lifetime $\tau_{\text{hetero}}(t)$ in two time intervals $t=\tau_\alpha$ and $\tau_{\text{ngp}}$, where $\tau_\alpha$ is the $\alpha$-relaxation time and $\tau_{\text{ngp}}$ is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime $\tau_{\text{hetero}}(t)$, we evaluated the correlation length $\xi_4(t)$ and the intensity $\chi_4(t)$ from the same order parameter used for the lifetime $\tau_{\text{hetero}}(t)$. We found that as the temperature decreases, the lifetime $\tau_{\text{hetero}}(t)$ grows dramatically, whereas the correlation length $\xi_4(t)$ and the intensity $\chi_4(t)$ increase slowly compared to $\tau_{\text{hetero}}(t)$ or plateaus. Furthermore, we investigated the lifetime $\tau_{\text{hetero}}(t)$ in more detail. We examined the time-interval dependence of the lifetime $\tau_{\text{hetero}}(t)$ and found that as the time interval $t$ increases, $\tau_{\text{hetero}}(t)$ monotonically becomes longer and plateaus at the relaxation time of the two-point density correlation function. At the large time intervals for which $\tau_{\text{hetero}}(t)$ plateaus, the heterogeneous dynamics migrate in space with a diffusion mechanism, such as the particle density.Comment: 12pages, 13figures, to appear in Physical Review

Comparing technical efficiency of organic and conventional coffee farms in Nepal using data envelopment analysis (DEA) approach

Data Envelopment Analysis (DEA) approach used to estimate technical efficiency and followed by regressing the technical efficiency scores to farm specific characters under tobit regression model. Primary data was collected from random samples of 240 (120 from each) coffee famers. Mean technical efficiency score was 0.89 and 0.83 in organic and conventional coffee farming respectively. Farms operating under CRS, DRS and IRS were 31.67, 3.83 and 37.5% respectively in organic coffee and 29.17, 25 and 45.83% respectively in conventional farming areas. Tobit regression showed the variation in technical efficiency was related education, farm experience and training/extension services and excess to credit.Production frontier, Resource use, Technical efficiency, Organic, Altitude, Productivity Analysis,