Equation of state for active matter.

We characterize the steady states of a suspension of two-dimensional active Brownian particles (ABPs). By approximating the first-order correction to the steady-state probability distribution to lowest order in Peclet number, we show that macroscopic quantities can be calculated in analogous way to equilibrium systems using this probability distribution. We then derive expressions for the macroscopic pressure and position-orientation correlation functions. We check our results by direct comparison with extensive numerical simulations. A key finding is the importance of many-body effective interactions even at very low densities.

Polymorphism of stable collagen fibrils.

Collagen fibrils are versatile self-assembled structures that provide mechanical integrity within mammalian tissues. The radius of collagen fibrils vary widely depending on experimental conditions in vitro or anatomical location in vivo. Here we explore the variety of thermodynamically stable fibril configurations that are available. We use a liquid crystal model of radial collagen fibril structure with a double-twist director field. Using a numerical relaxation method we show that two dimensionless parameters, the ratio of saddle-splay to twist elastic constants k24/K22 and the ratio of surface tension to chiral strength [small gamma, Greek, tilde] ≡ γ/(K22q), largely specify both the scaled fibril radius and the associated surface twist of equilibrium fibrils. We find that collagen fibrils are the stable phase with respect to the cholesteric phase only when the reduced surface tension is small, [small gamma, Greek, tilde] ⪅ 0.2. Within this stable regime, collagen fibrils can access a wide range of radii and associated surface twists. Remarkably, we find a maximal equilibrium surface twist of 0.33 rad (19°). Our results are compatible with corneal collagen fibrils, and we show how the large surface twist can explain the narrow distribution of corneal fibril radii. Conversely, we show how small surface twist is required for the thermodynamic stability of tendon fibrils in the face of considerable polydispersity of radius.

What can be measured in dating data: comment on Vaillant (2006).

Vaillant's 2006 paper presents data from a marriage bureau to give evidence on partner-seeking behavior. Three questions may be asked about the nature and usefulness of such work, whether it can (i) measure the efficiency of such bureaux, (ii) indicate the volume of resources devoted to partner search from commercially sourced dating data, and (iii) be used to test hypotheses about preference formation.

Artists' suicides as a public good.

This Commentary suggests that it is possible, from an economic perspective, that any individual artist/celebrity suicide may be of net benefit to society. Sales of the artist's products and associated merchandise may increase after the suicide, and people, including those who were not even born at the time of the suicide, may derive value from its iconic rectification, not to mention the higher value they derive from some private goods. A case study of Kurt Cobain is given to illustrate this phenomenon.