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This study employs the discrete element method (DEM) to investigate the impact of the widths of lognormal particle size distributions (PSDs) with the same mean particle diameter on hopper discharge behaviors, namely, discharge rate, particle velocities, and size‐segregation. Results reveal that (i) the hopper discharge rate decreases as PSD width increases; (ii) the mean discharge rates are constant with time, but the fluctuations increase as the PSD width increases; (iii) the overall size‐segregation increases with PSD width; (iv) the overall mean particle diameters of the narrower PSDs do not exceed the initial mean of 5 mm, whereas that of wider ones do; (v) the relationship between PSD width and particle velocities is non‐monotonic with no consistent trends; and (vi) no direct correlation exists between particle velocity and size‐segregation. The results here provide valuable insights on the behavior of the prevalent polydisperse mixtures in hoppers. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1174–1190, 2018

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Travel time is a vital performance index in assessing transportation network performance. Vehicle speeds along any network route fluctuate, and route travel times are essentially random. This technical note first examines travel time modeling and estimation with the random modeling of speeds, and then a general approach is presented for travel time estimation based on speed distributions. Because normal and lognormal distributions are commonly employed for speed modeling in traffic engineering, travel time estimation is further discussed concerning distributions. Most probability distributions (including normal and lognormal) assume that a modeled random variable spreads over the whole or half-range of the real number axis, but in practice, any traffic quantity of interest makes sense only within a limited value range. The concept of truncated distributions is introduced, and specifically, the probability features of truncated normal and lognormal distributions are explored concerning the discussed travel time estimation issue.