Critical phase behavior in multi-component fluid mixtures: Complete scaling analysis

We analyze the critical gas-liquid phase behavior of arbitrary fluid mixtures in their coexistence region. We focus on the setting relevant for polydisperse colloids, where the overall density and composition of the system are being controlled, in addition to temperature. Our analysis uses the complete scaling formalism and thus includes pressure mixing effects in the mapping from thermodynamic fields to the effective fields of 3D Ising criticality. Because of fractionation, where mixture components are distributed unevenly across coexisting phases, the critical behavior is remarkably rich. We give scaling laws for a number of important loci in the phase diagram. These include the cloud and shadow curves, which characterise the onset of phase coexistence, a more general set of curves defined by fixing the fractional volumes of the coexisting phases to arbitrary values, and conventional coexistence curves of the densities of coexisting phases for fixed overall density. We identify suitable observables (distinct from the Yang-Yang anomalies discussed in the literature) for detecting pressure mixing effects. Our analytical predictions are checked against numerics using a set of mapping parameters fitted to simulation data for a polydisperse Lennard-Jones fluid, allowing us to highlight crossovers where pressure mixing becomes relevant close to the critical point.Comment: 21 pages, 7 captioned figure

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

New insights into phase separation in colloidal suspensions are provided via a new dynamical theory based on the Polydisperse Lattice-Gas model. The model gives a simplified description of polydisperse colloids, incorporating a hard-core repulsion combined with polydispersity in the strength of the attraction between neighbouring particles. Our mean-field equations describe the local concentration evolution for each of an arbitrary number of species, and for an arbitrary overall composition of the system. We focus on the predictions for the dynamics of colloidal gas-liquid phase separation after a quench into the coexistence region. The critical point and the relevant spinodal curves are determined analytically, with the latter depending only on three moments of the overall composition. The results for the early-time spinodal dynamics show qualitative changes as one crosses a 'quenched' spinodal that excludes fractionation and so allows only density fluctuations at fixed composition. This effect occurs for dense systems, in agreement with a conjecture by Warren that, at high density, fractionation should be generically slow because it requires inter-diffusion of particles. We verify this conclusion by showing that the observed qualitative changes disappear when direct particle-particle swaps are allowed in the dynamics. Finally, the rich behaviour beyond the spinodal regime is examined, where we find that the evaporation of gas bubbles with strongly fractionated interfaces causes long-lived composition heterogeneities in the liquid phase; we introduce a two-dimensional density histogram method that allows such effects to be easily visualized for an arbitrary number of particle species.Comment: 20 pages; accepted for publication in Physical Chemistry Chemical Physic

Almost complete and equable heteroclinic networks

Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems with flow-invariant spaces. In this paper we examine the relation between the heteroclinic network as a flow-invariant set and directed graphs of possible connections between nodes. We consider realizations of a large class of transitive digraphs as robust heteroclinic networks and show that although robust realizations are typically not complete (i.e. not all unstable manifolds of nodes are part of the network), they can be almost complete (i.e. complete up to a set of zero measure within the unstable manifold) and equable (i.e. all sets of connections from a node have the same dimension). We show there are almost complete and equable realizations that can be closed by adding a number of extra nodes and connections. We discuss some examples and describe a sense in which an equable almost complete network embedding is an optimal description of stochastically perturbed motion on the network

A highly distorted turbulent free shear layer

Imperial Users onl

Collaborative Researchers or Cold Warriors? The Origins, Activities, and Legacy of the Smithsonian’s Institute of Social Anthropology

International research collaboration is increasingly popular, providing many scholarly and practical benefits. These collaborative endeavors also encounter obstacles and costs, including ones involving issues of power and professional ethics. My study seeks to widen our understanding of international collaborative social science research by examining the complex origins, diverse activities, and clouded legacy of the Smithsonian Institution’s Institute of Social Anthropology (ISA). The ISA was an innovative collaborative teaching and research program founded by Julian Steward during World War II to meet many goals, including increasing social science capacity in Latin America, expanding knowledge about contemporary cultural change, strengthening area expertise among U.S. scholars, and promoting closer relations among the peoples of the Americas. The ISA provided career-enhancing opportunities for U.S. and Latin American scholars, while helping to pioneer applied medical anthropology. I take issue with recent analysts who portray the ISA as promoting, including through covert research, U.S. hegemonic interests seeking to control rural Latin America

Spectroscopic Analysis in the Virtual Observatory Environment with SPLAT-VO

SPLAT-VO is a powerful graphical tool for displaying, comparing, modifying and analyzing astronomical spectra, as well as searching and retrieving spectra from services around the world using Virtual Observatory (VO) protocols and services. The development of SPLAT-VO started in 1999, as part of the Starlink StarJava initiative, sometime before that of the VO, so initial support for the VO was necessarily added once VO standards and services became available. Further developments were supported by the Joint Astronomy Centre, Hawaii until 2009. Since end of 2011 development of SPLAT-VO has been continued by the German Astrophysical Virtual Observatory, and the Astronomical Institute of the Academy of Sciences of the Czech Republic. From this time several new features have been added, including support for the latest VO protocols, along with new visualization and spectra storing capabilities. This paper presents the history of SPLAT-VO, it's capabilities, recent additions and future plans, as well as a discussion on the motivations and lessons learned up to now.Comment: 15 pages, 6 figures, accepted for publication in Astronomy & Computin

Direct perturbations of aggregate excess demand

We establish that an exchange economy, i.e., preferences and endowments, that generates a giiven aggregate excess demand (AED) function is close to the economy generating the AED obtained by an arbitrary perturbation of the original one.Arrow-Debreu, transversality, exchange economy.

Ferguson, J. Give a Man a Fish: Reflections on the New Politics of Distribution. Durham and London: Duke University Press, 2015.

Book review

Existence and Uniqueness for a Variational Hyperbolic System without Resonance

In this paper, we study the existence of weak solutions of the problem □u + ∇G(u) = f(t,x) ; (t,x) є Ω ≡ (0,π)x(0,π) u(t,x) = 0 ; (t,x) є ∂Ω where □ is the wave operator ∂2/∂t2 - ∂2/∂x2, G: Rn→R is a function of class C2 such that ∇G(0) = 0 and f:Ώ→R^n is a continuous function having first derivative with respect to t in (L2,(Ω))n and satisfying f(0,x) = f(π,x) = 0 for all x є [0,π]