Proof of the volume conjecture for Whitehead chains

We prove the volume conjecture for an infinite family of links called Whitehead chains that generalizes both the Whitehead link and the Borromean rings.Comment: 11 pages, 1 figure. See also http://www.science.uva.nl/~riveen/papers.html New in version two is a computation for the constant term in the asymptotic expansion. The proof of lemma 5 has been omitted because it is almost the same as that of lemma

Periodic solutions to a mean-field model for electrocortical activity

We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic inputs. The coupling of these components is represented by sigmoidal and quadratic nonlinearities. We consider these equations on a square domain with periodic boundary conditions, in the vicinity of the primary transition from a stable equilibrium to time-periodic motion through an equivariant Hopf bifurcation. We compute part of a family of standing wave solutions, emanating from this point.Comment: 9 pages, 5 figure

How micropatterns and air pressure affect splashing on surfaces

We experimentally investigate the splashing mechanism of a millimeter-sized ethanol drop impinging on a structured solid surface, comprised of micro-pillars, through side-view and top-view high speed imaging. By increasing the impact velocity we can tune the impact outcome from a gentle deposition to a violent splash, at which tiny droplets are emitted as the liquid sheet spreads laterally. We measure the splashing threshold for different micropatterns and find that the arrangement of the pillars significantly affects the splashing outcome. In particular, directional splashing in direction in which air flow through pattern is possible. Our top-view observations of impact dynamics reveal that an trapped air is responsible for the splashing. Indeed by lowering the pressure of the surrounding air we show that we can suppress the splashing in the explored parameter regime.Comment: 7 pages, 9 figure