Lattice Model Results for Pattern Formation in a Mixture with Competing Interactions.

A monolayer consisting of two types of particles, with energetically favored alternating stripes of the two components, is studied by Monte Carlo simulations and within a mesoscopic theory. We consider a triangular lattice model and assume short-range attraction and long-range repulsion between particles of the same kind, as well as short-range repulsion and long-range attraction for the cross-interaction. The structural evolution of the model upon increasing temperature is studied for equal chemical potentials of the two species. We determine the structure factor, the chemical potential-density isotherms, the specific heat, and the compressibility, and show how these thermodynamic functions are associated with the spontaneous formation of stripes with varying degrees of order.

Structural characterization of systems with competing interactions confined in narrow spherical shells.

Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. In fact, confinement has been proven to be a good strategy to induce the formation of novel ordered microphases that might be appealing to the development of functional nanomaterials. Using Grand Canonical Monte Carlo (GCMC) simulations, we study a model colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions under which the hexagonal phase is stable in bulk. We observe the formation of three parent ordered structures formed by toroidal clusters and two spherical clusters (Type I), toroidal clusters and one spherical cluster (Type II), and toroidal clusters alone (Type III), depending on the radius of the confining shell, that can often coexist with other related structures derived from these parent ones by a simple transformation, in which the system is divided into two hemispheres that are rotated with respect to each other by a given angle. We propose a general method to characterize and predict the structures obtained under confinement in spherical shells in systems able to self-assemble into a hexagonal phase in bulk. We also show that deforming the spherical shells into ellipsoidal ones affects the structure of the system in such a way that helical structures are favoured by prolate ellipsoids and toroidal structures by oblate ellipsoids.

Pattern Formation in Two-Component Monolayers of Particles with Competing Interactions.

Competing interactions between charged inclusions in membranes of living organisms or charged nanoparticles in near-critical mixtures can lead to self-assembly into various patterns. Motivated by these systems, we developed a simple triangular lattice model for binary mixtures of oppositely charged particles with additional short-range attraction or repulsion between like or different particles, respectively. We determined the ground state for the system in contact with a reservoir of the particles for the whole chemical potentials plane, and the structure of self-assembled conglomerates for fixed numbers of particles. Stability of the low-temperature ordered patterns was verified by Monte Carlo simulations. In addition, we performed molecular dynamics simulations for a continuous model with interactions having similar features, but a larger range and lower strength than in the lattice model. Interactions with and without symmetry between different components were assumed. We investigated both the conglomerate formed in the center of a thin slit with repulsive walls, and the structure of a monolayer adsorbed at an attractive substrate. Both models give the same patterns for large chemical potentials or densities. For low densities, more patterns occur in the lattice model. Different phases coexist with dilute gas on the lattice and in the continuum, leading to different patterns in self-assembled conglomerates ('rafts').

Self-Assembly of Optimally Packed Cylindrical Clusters inside Spherical Shells.

Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. Using grand canonical Monte Carlo simulations, we study a colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions at which the hexagonal phase of cylindrical clusters is stable in bulk. We observe spontaneous formation of different ordered structures. The results of the simulations are in a very good agreement with the predictions of a simple mathematical model based on the geometry and optimal packing of colloidal clusters. The results of the simulations and the explanation provided by a relatively simple geometric model may be helpful in manufacturing copolymer nanocapsules and may indicate possible ways of coiling DNA strands on spherical objects.

Hyperuniformity on spherical surfaces.

We study and characterize local density fluctuations of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to date few works have dealt with the problem of hyperuniformity in curved spaces. Indeed, some systems that display disordered hyperuniformity, like the spatial distribution of photoreceptors in avian retina, actually occur on curved surfaces. Here we will focus on the local particle number variance and its dependence on the size of the sampling window (which we take to be a spherical cap) for regular and uniform point distributions, as well as for equilibrium configurations of fluid particles interacting through Lennard-Jones, dipole-dipole, and charge-charge potentials. We show that the scaling of the local number variance as a function of the window size enables one to characterize hyperuniform and nonhyperuniform point patterns also on spherical surfaces.

First insights into the functional role of vasicentric tracheids and parenchyma in eucalyptus species with solitary vessels: do they contribute to xylem efficiency or safety?

The relationship between hydraulic specific conductivity (ks) and vulnerability to cavitation (VC) with size and number of vessels has been studied in many angiosperms. However, few of the studies link other cell types (vasicentric tracheids (VT), fibre-tracheids, parenchyma) with these hydraulic functions. Eucalyptus is one of the most important genera in forestry worldwide. It exhibits a complex wood anatomy, with solitary vessels surrounded by VT and parenchyma, which could serve as a good model to investigate the functional role of the different cell types in xylem functioning. Wood anatomy (several traits of vessels, VT, fibres and parenchyma) in conjunction with maximum ks and VC was studied in adult trees of commercial species with medium-to-high wood density (Eucalyptus globulus Labill., Eucalyptus viminalis Labill. and Eucalyptus camaldulensis Dehnh.). Traits of cells accompanying vessels presented correlations with functional variables suggesting that they contribute to both increasing connectivity between adjacent vessels-and, therefore, to xylem conduction efficiency-and decreasing the probability of embolism propagation into the tissue, i.e., xylem safety. All three species presented moderate-to-high resistance to cavitation (mean P50 values = -2.4 to -4.2 MPa) with no general trade-off between efficiency and safety at the interspecific level. The results in these species do not support some well-established hypotheses of the functional meaning of wood anatomy.

A magnetosome chain viewed as a bio-elastic magnet.

In light of the coarse-grained Monte Carlo numerical simulation method, the magnetosome chain stability of magnetotactic bacteria is analysed and discussed. This discrete chain of magnetic nanoparticles, encapsulated in a lipid membrane and flanked by filaments, orients bacteria in the geomagnetic field as a compass needle. Each magnetosome is a magnetite or greigite nanocrystal encapsulated in a soft lipid shell. This structure is modelled by a hard core with a magnetic dipole embedded and a cloud of electric dipoles which are able to move and rotate over the magnetic spherical core. In the present paper, some of the many possibilities of the model by varying the control parameters of the system are explored. Magnetic particles arrange in long linear clusters when the coating is removed. However, linear but twisted chains of magnetic particles emerge when there are electric dipoles in the coating shell. A unique linear and straight chain is not observed in any 3D numerical simulation; this result is in agreement with a real living system of bacteria in a geomagnetic field when proteins that form the filament are absent. Finally, the stability and magnetization of a magnetosome chain of 30 beads in one dimension set up are discussed resembling a real chain. The results suggest that a magnetosome chain not only orients bacteria but also should be considered as a potential storage of elastic energy.

Self-organization of plants in a dryland ecosystem: Symmetry breaking and critical cluster size.

Periodical patterns of vegetation in an arid or semiarid ecosystem are described using statistical mechanics and Monte Carlo numerical simulation technique. Plants are characterized by the area that each individual occupies and a facilitation-competition pairwise interaction. Assuming that external resources (precipitation, solar radiation, nutrients, etc.) are available to the ecosystem, it is possible to obtain the persistent configurations of plants compatible with an equitable distribution of resources maximizing the Shannon entropy. Variation of vegetation patterns with density, critical cluster size, and facilitation distance are predicted. Morphological changes of clusters are shown to be a function of the external resources. As a final remark, it is proposed that an early warning of desertification could be detected from the coefficient of variation of the mean cluster size together with the distribution of cluster sizes.

Geometrical and physicochemical considerations of the pit membrane in relation to air seeding: the pit membrane as a capillary valve.

A theoretical treatment of some of the factors influencing air seeding at the pit membranes of xylem vessels is given. Pit membrane structure, viewed as a three-dimensional mesh of intercrossing fibrils, and vulnerability to water-stress-induced air seeding are examined in the context of the Young-Laplace equation. Simple geometrical considerations of the porous membrane show that the vapor-liquid interface curvature radius is a function of fiber-fiber distance, fiber radius, wetting angle and position of the wetting line. Air seeding (maximum pressure) occurs at the minimum curvature radius, therefore air seeding is not simply determined by the fiber-fiber distance but is a function of the geometry of the pit membrane and of physicochemical quantities like surface tension and wetting angle. As a consequence of considering a wetting angle different from zero, the minimum curvature radius becomes larger than half the fiber-fiber distance. The present model considers that, for a given pressure difference at the pit membrane, all local interface curvatures are the same. In this sense, pit membranes work as variable capillary valves that allow or prevent air seeding by adjusting local curvatures and interface positions relative to the pore-forming fibers, following the pressure differences across the membranes. The theoretical prediction for the air seeding threshold is consistent with recent experimental data for angiosperm trees.