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.

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.

Critical behaviour of the Ising ferromagnet confined in quasi-cylindrical pores: a Monte Carlo study.

The critical behaviour of the Ising ferromagnet confined in pores of radius R and length L is studied by means of Monte Carlo computer simulations. Quasi-cylindrical pores are obtained by replicating n-times a triangular lattice disc of radius R, where L = na and a is the spacing between consecutive replications. So, spins placed at the surface of the pores have less nearest-neighbours (NN) as compared to 8 NN for spins in the bulk. These "missing neighbour" effects undergone by surface spins cause a strong suppression of surface ordering, leading to an ordinary surface transition. Also, the effect propagates into the bulk for small tubes (R ≤ 12) and the effective critical temperature of the pores is shifted towards lower values than in the bulk case. By applying the standard finite-size scaling theory, subsequently supported by numerical data, we concluded that data collapse of relevant observables, e.g., magnetization (m), susceptibility, specific heat, etc., can only be observed by comparing simulation results obtained by keeping the aspect ratio C ≡ R∕L constant. Also, by extrapolating "effective" R-dependent critical temperatures to the thermodynamic limit (R → ∞, C fixed), we obtained T(C)(∞) = 6.208(4). As suggested by finite-size scaling arguments, the magnetization is measured at the critical point scales according to [|m|]Tc R(ß/ν) is proportional to [R/L](1/2), where ß and ν are the standard exponents for the order parameter and the correlation length, respectively. Furthermore, it is shown that close to criticality the axial correlation length decreases exponentially with the distance. That result is the signature of the formation of (randomly distributed) alternating domains of different magnetization, which can be directly observed by means of snapshot configurations, whose typical length (ξ) is given by the characteristic length of the exponential decay of correlations. Moreover, we show that at criticality ξ = 0.43(2)R.

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.

Cluster pair correlation function of simple fluids: energetic connectivity criteria.

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick-type integral equation for a velocity-averaged version of Hill's energetic criterion.

Percolation of clusters with a residence time in the bond definition: Integral equation theory.

We consider the clustering and percolation of continuum systems whose particles interact via the Lennard-Jones pair potential. A cluster definition is used according to which two particles are considered directly connected (bonded) at time t if they remain within a distance d, the connectivity distance, during at least a time of duration tau, the residence time. An integral equation for the corresponding pair connectedness function, recently proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved using the orthogonal polynomial approach developed by another of the authors [Phys. Rev. E 55, 426 (1997)]. We compare our results with those obtained by molecular dynamics simulations.

van der Waals equation of state for a fluid in a nanopore.

A generalization of the van der Waals equation of state is presented for a confined fluid in a nanopore. The pressure in the fluid, confined in a narrow pore of infinite length, has tensorial character. From this hypothesis, the Helmholtz free energy is constructed and expressions for the axial and transversal components of the pressure tensor are obtained. The equations predict liquid-vapor equilibria, and a shift of the critical point with respect to that obtained from the van der Waals bulk equation. The results are in good agreement with recent experiments.