Title: Chemotactic behavior for a self-phoretic Janus particle near a patch source of fuel

Abstract: Many biological microswimmers are capable of chemotaxis, i.e., they can sense an ambient chemical gradient and adjust their mechanism of motility to move towards or away from the source of the gradient. Synthetic active colloids endowed with chemotactic behavior hold considerable promise for targeted drug delivery and the realization of programmable and reconfigurable materials. Here, we study the chemotactic behavior of a Janus particle, which converts “fuel” molecules, released at an axisymmetric chemical patch located on a planar wall, into “product” molecules at its catalytic cap and moves by self-phoresis induced by the product. The chemotactic behavior is characterized as a function of the interplay between the rates of release (at the patch) and the consumption (at the particle) of fuel, as well as of details of the phoretic response of the particle (i.e., its phoretic mobility). Among other results, we find that, under certain conditions, the particle is attracted to a stable “hovering state” in which it aligns its axis normal to the wall and rests (positions itself) at an activity-dependent distance above the center of the patch.

Speaker: Gioacchino Antonelli,

Room: Keller 302

TITLE: Isoperimetric problems in curved spaces and applications

ABSTRACT: The isoperimetric problem is one of the oldest and fundamental challenges in mathematics, offering a classic example of an optimization problem. Over the last forty years, research has increasingly focused on the connection between the isoperimetric properties of a space and its geometry. In this talk, I will explain how ideas developed to study the relationship between lower curvature bounds and the isoperimetric problem have been applied to resolve a longstanding question in the theory of minimal surfaces: proving that stable minimal hypersurfaces in R^n are flat when n<=6.

Colloquium by Prof. Kjos-Hanssen.

Colloquium by Ritvik Ramkumar (Cornell).