Can pure polymer liquids be represented at two different resolutions simultaneously?

Can Musicians Track Two Different Beats Simultaneously?

Multiple Cracks Propagate Simultaneously in Polymer Liquids in Tension.

Understanding the mechanism of fracture is essential for material and process design. While the initiation of fracture in brittle solids is generally associated with the preexistence of material imperfections, the mechanism for initiation of fracture in viscoelastic fluids, e.g., polymer melts and solutions, remains an open question. We use high speed imaging to visualize crack propagation in e...

How Different Can Two Intersecting Families Be?

To measure the difference between two intersecting families F ,G ⊆ 2[n] we introduce the quantity D(F ,G) = |{(F,G) : F ∈ F , G ∈ G, F ∩ G = ∅}|. We prove that if F is k-uniform and G is l-uniform, then for large enough n and for any i 6= j Fi = {F ⊆ [n] : i ∈ F, |F | = k} and Fj = {F ⊆ [n] : j ∈ F, |F | = l} form an optimal pair of families (that is D(F ,G) ≤ D(Fi,Fj) for all uniform and inter...

Lcm Lattices Supporting Pure Resolutions

We characterize the lcm lattices that support a monomial ideal with a pure resolution. Given such a lattice, we provide a construction that yields a monomial ideal with that lcm lattice and whose minimal free resolution is pure.

Can two streams of auditory information be processed simultaneously ? Evidence from the gleaning bat

A tenet of auditory scene analysis is that we can fully process only one stream of auditory information at a time. We tested this assumption in a gleaning bat, the pallid bat (Antrozous pallidus) because this bat uses echolocation for general orientation, and relies heavily on prey-generated sounds to detect and locate its prey. It may therefore encounter situations in which the echolocation an...