Acoustofluidics 17: theory and applications of surface acoustic wave devices for particle manipulation

In this paper, number 17 of the thematic tutorial series “Acoustofluidics – exploiting ultrasonic standing waves, forces and acoustic streaming in microfluidic systems for cell and particle manipulation” – we present the theory of surface acoustic waves (SAWs) and some related microfluidic applications. The equations describing SAWs are derived for a solid-vacuum interface before generalisations are made about solid-solid and solid-fluid interfaces. Techniques for SAW generation are discussed before an overview of applications is presented

Topological modular forms with level structure

The cohomology theory known as Tmf, for "topological modular forms," is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to a functorial family of objects corresponding to elliptic curves with level structure and modular forms on them. Along the way, we produce a natural way to restrict to the cusps, providing multiplicative maps from Tmf with level structure to forms of K-theory. In particular, this allows us to construct a connective spectrum tmf_0(3) consistent with properties suggested by Mahowald and Rezk. This is accomplished using the machinery of logarithmic structures. We construct a sheaf of locally even-periodic elliptic cohomology theories, equipped with highly structured multiplication, on the log-\'etale site of the moduli of elliptic curves. Evaluating this sheaf on modular curves produces Tmf with level structure.Comment: 53 pages. Heavily revised, including the addition of a new section on background tools from homotopy theor