Cutoff profile of ASEP on a segment

This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length N. Our main result is that for particle densities in (0, 1), the total-variation cutoff window of ASEP is $$N^{1/3}$$ N 1 / 3 and the cutoff profile is $$1-F_{\mathrm {GUE}},$$ 1 - F GUE , where $$F_{\mathrm {GUE}}$$ F GUE is the Tracy-Widom distribution function. This also gives a new proof of the cutoff itself, shown earlier by Labbé and Lacoin. Our proof combines coupling arguments, the result of Tracy–Widom about fluctuations of ASEP started from the step initial condition, and exact algebraic identities coming from interpreting the multi-species ASEP as a random walk on a Hecke algebra.

Solid phase behavior of mixture systems based on tripalmitoyl glycerol and monounsaturated triacylglycerols forming a molecular compound

Differential scanning calorimetry and X-ray diffraction were used to investigate the mixing behavior of triacylglycerol (TAG) mixtures of PPP/PPO (tripalmitoyl glycerol/1,2-dipalmitoyl-3-oleoyl-rac-glycerol) and PPP/MCPOP/PPO (being MCPOP/PPO the equimolecular blend of 1,3-dipalmitoyl-2-oleoyl-glycerol...

Effects of Impeller Rotational Speed and Immersion Depth on Flow Pattern, Mixing and Interface Characteristics for Kanbara Reactors using VOF-SMM Simulations

The Kanbara Reactor (KR) is a primary desulfurization technology in the hot metal pretreatment refining process that is widely employed in the modern steelmaking industry. The operating parameters of KR impeller immersion depth (IID) and rotation speed (IRS) have a crucial impact on the process performance and the desulfurization effect. Still, their influences have not been fully understood. This study systematically investigated the effects of IID and IRS on the flow pattern, mixing behavior, vortex core depth, and free surface characteristics for KR processes based on a 3D Volume of Fluid (VOF) model coupled with the sliding mesh method (SMM). The model was validated via scale-down water model experiments and then applied to the KR process, and simulations found that IID and IRS have different impacts on the flow pattern. Specifically, the discharge flow location moves downward with IID increasing, but the discharge strength and mean velocity hardly changes. Comparatively, the rise of IRS significantly increases the mean velocity, but few changes occur to the discharge flow position. Increasing IRS improves bath hydrodynamics, strengthens recirculation, and efficiently shortens mixing time, but IID has a neglectable effect on these features. The minimum mixing time is 55 s at a maximum IRS of 260 rpm. Moreover, the vortex core depth and free surface velocity visibly increase with the increase of IRS. Comparatively, IID has a limited effect on the flow and mixing behavior but directly impacts the distribution of recirculation regions at the axial direction and the velocity gradient on the free surface at the radial direction. Furthermore, the correlation equations of these critical parameters as a function of the operating parameters were obtained. The results from this study may provide references for operating optimizations and industrial practices of KRs.