Inertial effects in three dimensional spinodal decomposition of a symmetric binary fluid mixture: A lattice Boltzmann study

The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamicaly consistent lattice Boltzmann method. We combine results from simulations with different numerical parameters to obtain an unprecendented range of length and time scales when expressed in reduced physical units. Using eight large (256^3) runs, the resulting composite graph of reduced domain size l against reduced time t covers 1 < l < 10^5, 10 < t < 10^8. Our data is consistent with the dynamical scaling hypothesis, that l(t) is a universal scaling curve. We give the first detailed statistical analysis of fluid motion, rather than just domain evolution, in simulations of this kind, and introduce scaling plots for several quantities derived from the fluid velocity and velocity gradient fields.Comment: 49 pages, latex, J. Fluid Mech. style, 48 embedded eps figs plus 6 colour jpegs for Fig 10 on p.2

Entropy-induced smectic phases in rod-coil copolymers

We present a self-consistent field theory (SCFT) of semiflexible (wormlike) diblock copolymers, each consisting of a rigid and a flexible part. The segments of the polymers are otherwise identical, in particular with regard to their interactions, which are taken to be of an Onsager excluded-volume type. The theory is developed in a general three-dimensional form, as well as in a simpler one-dimensional version. Using the latter, we demonstrate that the theory predicts the formation of a partial-bilayer smectic-A phase in this system, as shown by profiles of the local density and orientational distribution functions. The phase diagram of the system, which includes the isotropic and nematic phases, is obtained in terms of the mean density and rigid-rod fraction of each molecule. The nematic-smectic transition is found to be second order. Since the smectic phase is induced solely by the difference in the rigidities, the onset of smectic ordering is shown to be an entropic effect and therefore does not have to rely on additional Flory-Huggins-type repulsive interactions between unlike chain segments. These findings are compared with other recent SCFT studies of similar copolymer models and with computer simulations of several molecular models.Comment: 13 pages, 8 figure

Hard-core Yukawa model for two-dimensional charge stabilized colloids

The hyper-netted chain (HNC) and Percus-Yevick (PY) approximations are used to study the phase diagram of a simple hard-core Yukawa model of charge-stabilized colloidal particles in a two-dimensional system. We calculate the static structure factor and the pair distribution function over a wide range of parameters. Using the statics correlation functions we present an estimate for the liquid-solid phase diagram for the wide range of the parameters.Comment: 7 pages, 9figure

Collective dynamics of colloids at fluid interfaces

The evolution of an initially prepared distribution of micron sized colloidal particles, trapped at a fluid interface and under the action of their mutual capillary attraction, is analyzed by using Brownian dynamics simulations. At a separation \lambda\ given by the capillary length of typically 1 mm, the distance dependence of this attraction exhibits a crossover from a logarithmic decay, formally analogous to two-dimensional gravity, to an exponential decay. We discuss in detail the adaption of a particle-mesh algorithm, as used in cosmological simulations to study structure formation due to gravitational collapse, to the present colloidal problem. These simulations confirm the predictions, as far as available, of a mean-field theory developed previously for this problem. The evolution is monitored by quantitative characteristics which are particularly sensitive to the formation of highly inhomogeneous structures. Upon increasing \lambda\ the dynamics show a smooth transition from the spinodal decomposition expected for a simple fluid with short-ranged attraction to the self-gravitational collapse scenario.Comment: 13 pages, 12 figures, revised, matches version accepted for publication in the European Physical Journal

Tests of Dynamical Scaling in 3-D Spinodal Decomposition

We simulate late-stage coarsening of a 3-D symmetric binary fluid. With reduced units l,t (with scales set by viscosity, density and surface tension) our data extends two decades in t beyond earlier work. Across at least four decades, our own and others' individual datasets (< 1 decade each) show viscous hydrodynamic scaling (l ~ a + b t), but b is not constant between runs as this scaling demands. This betrays either the unexpected intrusion of a discretization (or molecular) lengthscale, or an exceptionally slow crossover between viscous and inertial regimes.Comment: Submitted to Phys. Rev.

Analysis of a spatial Lotka-Volterra model with a finite range predator-prey interaction

We perform an analysis of a recent spatial version of the classical Lotka-Volterra model, where a finite scale controls individuals' interaction. We study the behavior of the predator-prey dynamics in physical spaces higher than one, showing how spatial patterns can emerge for some values of the interaction range and of the diffusion parameter.Comment: 7 pages, 7 figure

3D Spinodal Decomposition in the Inertial Regime

We simulate late-stage coarsening of a 3D symmetric binary fluid using a lattice Boltzmann method. With reduced lengths and times l and t respectively (scales set by viscosity, density and surface tension) our data sets cover 1 < l 100 we find clear evidence of Furukawa's inertial scaling (l ~ t^{2/3}), although the crossover from the viscous regime (l ~ t) is very broad. Though it cannot be ruled out, we find no indication that Re is self-limiting (l ~ t^{1/2}) as proposed by M. Grant and K. R. Elder [Phys. Rev. Lett. 82, 14 (1999)].Comment: 4 pages, 3 eps figures, RevTex, minor changes to bring in line with published version. Mobility values added to Table

Shape programming for narrow ribbons of nematic elastomers

Using the theory of Γ-convergence, we derive from three-dimensional elasticity new one-dimensional models for non-Euclidean elastic ribbons, i.e., ribbons exhibiting spontaneous curvature and twist. We apply the models to shape-selection problems for thin films of nematic elastomers with twist and splay-bend texture of the nematic director. For the former, we discuss the possibility of helicoid-like shapes as an alternative to spiral ribbons

Beyond Species Richness for Biological Conservation

Recent global policy developments have highlighted the need for straightforward, robust, and meaningful biodiversity metrics. However, much of conservation science is dominated by the use of a single metric, species richness, despite several known limitations. Here, we review and synthesize why species richness (i.e., the number of species in a local area) is a poor metric for a variety of topical‐ and policy‐relevant conservation problems. We identify the following three key issues: (1) increasing evidence emphasizes that species richness is often not a robust metric for identifying biodiversity change, (2) species richness ignores species identity and so may often not reflect impacts on species of concern, and (3) species richness does not provide information needed on the persistence of biodiversity or the provision of ecosystem services. We highlight the unappreciated practical outcomes of these limitations with examples from three ongoing conservation debates: whether local biodiversity is declining, how habitat fragmentation affects biodiversity, and the extent to which land sharing or sparing is more beneficial for biodiversity conservation. To address these limitations, we offer a set of guidelines for the use of biodiversity metrics in conservation policy and practice