Mixing and Un-mixing by Incompressible Flows

We consider the questions of efficient mixing and un-mixing by incompressible flows which satisfy periodic, no-flow, or no-slip boundary conditions on a square. Under the uniform-in-time constraint $\|\nabla u(\cdot,t)\|_p\leq 1$ we show that any function can be mixed to scale $\epsilon$ in time $O(|\log\epsilon|^{1+\nu_p})$, with $\nu_p=0$ for $p<\tfrac{3+\sqrt 5}2$ and $\nu_p\leq \tfrac 13$ for $p\geq \tfrac{3+\sqrt 5}2$. Known lower bounds show that this rate is optimal for $p\in(1,\tfrac{3+\sqrt 5}2)$. We also show that any set which is mixed to scale $\epsilon$ but not much more than that can be un-mixed to a rectangle of the same area (up to a small error) in time $O(|\log\epsilon|^{2-1/p})$. Both results hold with scale-independent finite times if the constraint on the flow is changed to $\|u(\cdot,t)\|_{\dot W^{s,p}}\leq 1$ with some $s<1$. The constants in all our results are independent of the mixed functions and sets.Comment: 37 pages, 5 figure

Production of neutral tone in Mandarin by heritage, native, and second language speakers

This study examined the properties of neutral tone (T0) in Mandarin as produced by three groups: native speakers raised in a Mandarin-speaking environment (L1ers), second language learners raised in an English-speaking environment (L2ers), and heritage language speakers (HLers) exposed to Mandarin from birth but currently dominant in English. T0 production was elicited in both obligatory and non-obligatory contexts, acoustically analyzed, and perceptually evaluated by Mandarin L1ers. Acoustic data indicated little difference among groups in pitch contour, but significant differences in duration, especially in the non-obligatory context. Perceptual data revealed relatively low intelligibility of T0 overall, but also a group difference whereby L2ers tended to outperform HLers in the non-obligatory context; nevertheless, L2ers received the lowest goodness ratings, across both contexts. These results thus suggest that phonetic differences between HLers and L2ers are not unidirectional, but instead vary across aspects of the language in accordance with differences in speakers’ linguistic experience.Accepted manuscriptPublished versio

Characteristics of Pt on zeolite electrocatalyst for direct methanol fuel cell

Characteristics of Platinum (Pt) on zeolite electrocatalysts have been experimentally studied to understand its potentials for direct methanol fuel cell (DMFC) applications. The Y zeolite was chosen as a Pt-supported substrate with 1.5 wt% Pt loading on zeolite. The Pt nanoparticle size and local atomic structure in both electrochemical and gas cell treatments were investigated by using X-ray absorption spectroscopy (XAS), in particular the extended X-ray adsorption fine structure (EXAFS) method, and the electrocatalytic activity of Pt nanoparticle on Y zeolite was determined by cyclic voltammetry (CV). Studies were focused primarily on the observation of hydrogen adsorption and desorption in the hydride region, where the presence of H+ ions was critical for such a process occurred. Analyses have shown that the Pt oxides can be electrochemically reduced, due to a hydrogen ‘spillover’ phenomenon throughout zeolite structures. Based on theoretical estimation and EXAFS data fitting, it was found that the Pt nanoparticle size was 1-1.1 nm from gas cell treatment and 0.7 nm from electrochemical cell treatment. For both scenarios, the number of atoms was estimated 147 and 55 respectively, with 13 atoms at the edge of a Pt cluster for an icosahedron structure. This study demonstrated that the Pt catalytic site on zeolite can be electronically accessible; despite that zeolite is a dc insulator. The Pt/Y zeolite as a new type of electrocatalyst has shown some promises for industrial-scale fuel cell applications, such as reducing higher electrode cost and/or overcoming the difficulty of electrolyte separation