A simple view of the heavy-tailed sales distributions and application to the box-office grosses of U.S. movies

This letter treats of the power-law distribution of the sales of items. We propose a simple stochastic model which expresses a selling process of an item. This model produces a stationary power-law distribution, whose power-law exponent is analytically derived. Next we compare the model with an actual data set of movie income. We focus on the return on investment (ROI), defined as the gross income divided by the production budget. We confirm that the power-law exponent of ROI distribution can be estimated from the ratios of income between two adjoining weeks, as predicted by the model analysis. Moreover, exponential decay of weekly income is observed both in the model and actual income. Therefore, the proposed model is simple enough, but it can quantitatively describe the power-law sales distribution.Comment: 5 pages, 6 figure

Sectorial sift, inverted U-shaped fertility dynamics, and growth

This paper constructs a small open two-sector overlapping-generations model with the subsistence level of consumption of agricultural goods and explains the following key stylized facts in the process of economic development: increases followed by declines in fertility rate, increases in human capital investment for children, and a sectorial shift in labor from agriculture to manufacture.Demographic transition Sectorial sift Economic development

Concentration-adjustable micromixer using droplet injection into a microchannel

A novel micromixing technique that exploit a thrust of droplets into the mixing interface is developed. The technique enhances the mixing by injecting immiscible droplets in a mixing channel and the methodology enables a control of the mixing level simply by changing the droplet injection frequency. We experimentally characterize the mixing performance with various droplet injection frequencies, channel geometries, and diffusion coefficients. Consequently, it is revealed that the mixing level increases with the injection frequency, the droplet-diameter-to-channel-width ratio, and the diffusion coefficient. Moreover, the mixing level is found to be a linear function of the droplet volume fraction in the mixing section. The results suggest that the developed technique can produce a large amount of sample solution whose concentration is arbitrary and precisely controllable with a simple and stable operation.Comment: 12 + 3 pages, 6 + 4 figure