Normativity: A Unit of

This entry discusses the notion of a unit of normativity. This notion may be understood in two distinct ways. One way to understand a unit of normativity is as some particular type of assignment of normative status, e.g., a requirement, an ought, a reason, or a permission. A second way to understand a unit of normativity is as a measure of a quantity of normativity, perhaps associated with the numerical assignment given to the strength of reasons. This entry outlines some basic differences among units of normativity in the first sense, noting that they vary slightly depending on whether one is talking about normativity in a more general or more robust sense. This entry also discusses in more detail the question of whether there might be a unit of normativity in the second sense. It discusses the relevant metaphysical questions. It also provides an explanation of why reasons can be assigned numerical strengths, even if there are no units of normativity in the sense of measurements of quantities of normativity

Dynamics of capillary spreading along hydrophilic microstripes

We have studied the capillary spreading of a Newtonian liquid along hydrophilic microstripes that are chemically defined on a hydrophobic substrate. The front of the spreading film advances in time according to a power law x=Bt1/2. This exponent of 1/2 is much larger than the value 1/10 observed in the axisymmetric spreading of a wetting droplet. It is identical to the exponent found for wicking in open or closed microchannels. Even though no wicking occurs in our system, the influence of surface curvature induced by the lateral confinement of the liquid stripe also leads to an exponent of 1/2 but with a strongly modified prefactor B. We obtain excellent experimental agreement with the predicted time dependence of the front location and the dependence of the front speed on the stripe width. Additional experiments and simulations reveal the influence of the reservoir volume, liquid material parameters, edge roughness, and nonwetting defects. These results are relevant to liquid dosing applications or microfluidic delivery systems based on free-surface flow

Local minimality of the volume-product at the simplex

It is proved that the simplex is a strict local minimum for the volume product, P(K)=min(vol(K) vol(K^z)), K^z is the polar body of K with respect to z, the minimum is taken over z in the interior of K, in the Banach-Mazur space of n-dimensional (classes of ) convex bodies. Linear local stability in the neighborhood of the simplex is proved as well. The proof consists of an extension to the non-symmetric setting of methods that were recently introduced by Nazarov, Petrov, Ryabogin and Zvavitch, as well as proving results of independent interest, concerning stability of square order of volumes of polars of non-symmetric convex bodies.Comment: Mathematika, accepte