THE ECONOMICS OF NONLINEAR PRICING: EVIDENCE FROM AIRFARES AND GROCERY PRICES

Quantity discounts, characterised by unit prices falling as the quantity purchased rises, are a proliferate phenomenon that finds root in the economics of packaging. This paper reviews the key economic foundations of nonlinear pricing, introduces new pricing data and conducts an empirical investigation into airfares and grocery prices, which are shown to exhibit quantity discounts of an identical order of magnitude. The constancy of the quantity discount across distinct markets hints at the existence of a common force underlying the determination of prices.

Role of Metastable States in Phase Ordering Dynamics

We show that the rate of separation of two phases of different densities (e.g. gas and solid) can be radically altered by the presence of a metastable intermediate phase (e.g. liquid). Within a Cahn-Hilliard theory we study the growth in one dimension of a solid droplet from a supersaturated gas. A moving interface between solid and gas phases (say) can, for sufficient (transient) supersaturation, unbind into two interfaces separated by a slab of metastable liquid phase. We investigate the criteria for unbinding, and show that it may strongly impede the growth of the solid phase.Comment: 4 pages, Latex, Revtex, epsf. Updated two reference

Weak Mirror Symmetry of Complex Symplectic Algebras

A complex symplectic structure on a Lie algebra \lie h is an integrable complex structure $J$ with a closed non-degenerate $(2,0)$-form. It is determined by $J$ and the real part $\Omega$ of the $(2,0)$-form. Suppose that \lie h is a semi-direct product \lie g\ltimes V, and both \lie g and $V$ are Lagrangian with respect to $\Omega$ and totally real with respect to $J$. This note shows that \lie g\ltimes V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of $\Omega$ and $J$ are isomorphic. The geometry of $(\Omega, J)$ on the semi-direct product \lie g\ltimes V is also shown to be equivalent to that of a torsion-free flat symplectic connection on the Lie algebra \lie g. By further exploring a relation between $(J, \Omega)$ with hypersymplectic algebras, we find an inductive process to build families of complex symplectic algebras of dimension $8n$ from the data of the $4n$-dimensional ones.Comment: 22 page

Polydispersity Effects in Colloid-Polymer Mixtures

We study phase separation and transient gelation in a mixture consisting of polydisperse colloids and non-adsorbing polymers, where the ratio of the average size of the polymer to that of the colloid is approximately 0.063. Unlike what has been reported previously for mixtures with somewhat lower colloid polydispersity, the addition of polymers does not expand the fluid-solid coexistence region. Instead, we find a region of fluid-solid coexistence which has an approximately constant width but an unexpected re-entrant shape. We detect the presence of a metastable gas-liquid binodal, which gives rise to two-stepped crystallization kinetics that can be rationalized as the effect of fractionation. Finally, we find that the separation into multiple coexisting solid phases at high colloid volume fractions predicted by equilibrium statistical mechanics is kinetically suppressed before the system reaches dynamical arrest.Comment: 11 pages, 5 figure

Phase diagram for a mixture of colloids and polymers with equal size

We present the phase diagram of a colloid-polymer mixture in which the radius a of the colloidal spheres is approximately the same as the radius R of a polymer coil (q=R/a1). A three-phase coexistence region is experimentally observed, previously only reported for colloid-polymer mixtures with smaller polymer chains (q0.6). A recently developed generalized free-volume theory (GFVT) for mixtures of hard spheres and non-adsorbing excluded-volume polymer chains gives a quantitative description of the phase diagram. Monte Carlo simulations also agree well with experimen

Using visual analytics to develop situation awareness in astrophysics

We present a novel collaborative visual analytics application for cognitively overloaded users in the astrophysics domain. The system was developed for scientists who need to analyze heterogeneous, complex data under time pressure, and make predictions and time-critical decisions rapidly and correctly under a constant influx of changing data. The Sunfall Data Taking system utilizes several novel visualization and analysis techniques to enable a team of geographically distributed domain specialists to effectively and remotely maneuver a custom-built instrument under challenging operational conditions. Sunfall Data Taking has been in production use for 2 years by a major international astrophysics collaboration (the largest data volume supernova search currently in operation), and has substantially improved the operational efficiency of its users. We describe the system design process by an interdisciplinary team, the system architecture and the results of an informal usability evaluation of the production system by domain experts in the context of Endsley's three levels of situation awareness