Fractionation effects in phase equilibria of polydisperse hard sphere colloids

The equilibrium phase behaviour of hard spheres with size polydispersity is studied theoretically. We solve numerically the exact phase equilibrium equations that result from accurate free energy expressions for the fluid and solid phases, while accounting fully for size fractionation between coexisting phases. Fluids up to the largest polydispersities that we can study (around 14%) can phase separate by splitting off a solid with a much narrower size distribution. This shows that experimentally observed terminal polydispersities above which phase separation no longer occurs must be due to non-equilibrium effects. We find no evidence of re-entrant melting; instead, sufficiently compressed solids phase separate into two or more solid phases. Under appropriate conditions, coexistence of multiple solids with a fluid phase is also predicted. The solids have smaller polydispersities than the parent phase as expected, while the reverse is true for the fluid phase, which contains predominantly smaller particles but also residual amounts of the larger ones. The properties of the coexisting phases are studied in detail; mean diameter, polydispersity and volume fraction of the phases all reveal marked fractionation. We also propose a method for constructing quantities that optimally distinguish between the coexisting phases, using Principal Component Analysis in the space of density distributions. We conclude by comparing our predictions to perturbative theories for near-monodisperse systems and to Monte Carlo simulations at imposed chemical potential distribution, and find excellent agreement.Comment: 21 pages, 23 figures, 2 table

Incorporation of excluded volume correlations into Poisson-Boltzmann theory

We investigate the effect of excluded volume interactions on the electrolyte distribution around a charged macroion. First, we introduce a criterion for determining when hard-core effects should be taken into account beyond standard mean field Poisson-Boltzmann (PB) theory. Next, we demonstrate that several commonly proposed local density functional approaches for excluded volume interactions cannot be used for this purpose. Instead, we employ a non-local excess free energy by using a simple constant weight approach. We compare the ion distribution and osmotic pressure predicted by this theory with Monte Carlo simulations. They agree very well for weakly developed correlations and give the correct layering effect for stronger ones. In all investigated cases our simple weighted density theory yields more realistic results than the standard PB approach, whereas all local density theories do not improve on the PB density profiles but on the contrary, deviate even more from the simulation results.Comment: 23 pages, 7 figures, 1 tabl

A recurrent neural network with ever changing synapses

A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical study it is found that the fixed points of the dynamics of the net are time dependent, implying that the representation in the brain of a fixed piece of information (e.g., a word to be recognized) is not fixed in time.Comment: 17 pages, LaTeX, 4 figure

Density Functional for Anisotropic Fluids

We propose a density functional for anisotropic fluids of hard body particles. It interpolates between the well-established geometrically based Rosenfeld functional for hard spheres and the Onsager functional for elongated rods. We test the new approach by calculating the location of the the nematic-isotropic transition in systems of hard spherocylinders and hard ellipsoids. The results are compared with existing simulation data. Our functional predicts the location of the transition much more accurately than the Onsager functional, and almost as good as the theory by Parsons and Lee. We argue that it might be suited to study inhomogeneous systems.Comment: To appear in J. Physics: Condensed Matte

Phase separation in mixtures of colloids and long ideal polymer coils

Colloidal suspensions with free polymer coils which are larger than the colloidal particles are considered. The polymer-colloid interaction is modeled by an extension of the Asakura-Oosawa model. Phase separation occurs into dilute and dense fluid phases of colloidal particles when polymer is added. The critical density of this transition tends to zero as the size of the polymer coils diverges.Comment: 5 pages, 3 figure

Effective permittivity of random plasmonic composites

An effective-medium theory (EMT) is developed to predict the effective permittivity \epsilon_eff of dense random dispersions of high optical-conductivity metals such as Ag, Au and Cu. Dependence of \epsilon_eff on the volume fraction \phi, a microstructure parameter \kappa related to the static structure factor and particle radius a is studied. In the electrostatic limit, the upper and lower bounds of \kappa correspond to Maxwell-Garnett and Bruggeman EMTs respectively. Finite size effects are significant when |\beta^2(ka/n)^3| becomes O(1) where \beta, k, and n denote the nanoparticle polarizability, wavenumber and matrix refractive index respectively. The coupling between the particle and effective medium results in a red-shift in the resonance peak, a non-linear dependence of \epsilon_eff on \phi, and Fano resonance in \epsilon_eff.Comment: Manuscript submitted to J. Opt. Soc. Am. B. 33 page

Phase behaviour of a model of colloidal particles with a fluctuating internal state

Colloidal particles are not simple rigid particles, in general an isolated particle is a system with many degrees of freedom in its own right, e.g., the counterions around a charged colloidal particle.The behaviour of model colloidal particles, with a simple phenomenological model to account for these degrees of freedom, is studied. It is found that the interaction between the particles is not pairwise additive. It is even possible that the interaction between a triplet of particles is attractive while the pair interaction is repulsive. When this is so the liquid phase is either stable only in a small region of the phase diagram or absent altogether.Comment: 12 pages including 4 figure

Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow

In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the Chapman-Enskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corresponds to that of the macroscopic dynamical equations for multiphase flow. We extend the 3D MRT LB models developed to represent multiphase flow with reduced compressibility effects. The multiphase models are evaluated by verifying the Laplace-Young relation for static drops and the frequency of oscillations of drops. The results show satisfactory agreement with available data and significant gains in numerical stability.Comment: Accepted for publication in the Journal of Computational Physic

Does self-monitoring reduce blood pressure? Meta-analysis with meta-regression of randomized controlled trials

Introduction. Self-monitoring of blood pressure (BP) is an increasingly common part of hypertension management. The objectives of this systematic review were to evaluate the systolic and diastolic BP reduction, and achievement of target BP, associated with self-monitoring. Methods. MEDLINE, Embase, Cochrane database of systematic reviews, database of abstracts of clinical effectiveness, the health technology assessment database, the NHS economic evaluation database, and the TRIP database were searched for studies where the intervention included self-monitoring of BP and the outcome was change in office/ambulatory BP or proportion with controlled BP. Two reviewers independently extracted data. Meta-analysis using a random effects model was combined with meta-regression to investigate heterogeneity in effect sizes. Results. A total of 25 eligible randomized controlled trials (RCTs) (27 comparisons) were identified. Office systolic BP (20 RCTs, 21 comparisons, 5,898 patients) and diastolic BP (23 RCTs, 25 comparisons, 6,038 patients) were significantly reduced in those who self-monitored compared to usual care (weighted mean difference (WMD) systolic −3.82 mmHg (95% confidence interval −5.61 to −2.03), diastolic −1.45 mmHg (−1.95 to −0.94)). Self-monitoring increased the chance of meeting office BP targets (12 RCTs, 13 comparisons, 2,260 patients, relative risk = 1.09 (1.02 to 1.16)). There was significant heterogeneity between studies for all three comparisons, which could be partially accounted for by the use of additional co-interventions. Conclusion. Self-monitoring reduces blood pressure by a small but significant amount. Meta-regression could only account for part of the observed heterogeneity