Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt

The nucleation of a droplet of stable cylinder phase from a metastable lamellar phase is examined within the single-mode approximation to the mean-field Landau–Brazovskii model for diblock copolymer melts. By employing a variational ansatz for the droplet interfacial profile, an analytic expression for the interfacial free energy of an interface of arbitrary orientation between cylinders and lamellae is found. The interfacial free energy is anisotropic and is lower when the cylinder axis is perpendicular to the interface than when the cylinders lie along the interface. Consequently, the droplet shape computed via the Wulff construction is lens like, being flattened along the axis of the cylinders. The size of the critical droplet and the nucleation barrier are determined within classical nucleation theory. Near the lamellar–cylinder phase boundary, where classical nucleation theory is applicable, critical droplets of size 30–400 cylinders across with aspect ratios of 4–10 and nucleation barriers of (30–40)kBT are typically found. The general trend is to larger critical droplets, higher aspect ratios, and smaller nucleation barriers as the mean-field critical point is approached

A simple model for the anomalous intrinsic viscosity of dendrimers

The intrinsic viscosity of dendrimers in solution shows several anomalous behaviors that have hitherto not been explained within the existing theoretical frameworks of either Zimm or Rouse. Here we propose a simple two-zone model based on the radial segmental density profile of the dendrimers and combine a non-draining core with a free-draining outer region description, to arrive at a simple formula that captures most of the main features in the intrinsic viscosity data obtained in experiments

Defense Expenditure and Economic Growth under External Predation

This paper develops a growth model of a country under a Hobbesian environment with international conflicts where national defense is the only way to prevent external predation. The long run growth path is determined by the equilibrium of a dynamic game with three players, the external predator, the government and the family. The equilibrium growth path has three phases, submissive equilibrium, tolerant equilibrium and full-protected equilibrium. Different defense strategies result in different growth prospects and sustainable growth will endogenously induce adjustment of defense strategies.economic growth; predate; defense expenditure

Heterogeneity in structurally arrested hard spheres

When cooled or compressed sufficiently rapidly, a liquid vitrifies into a glassy amorphous state. Vitrification in a dense liquid is associated with jamming of the particles. For hard spheres, the density and degree of order in the final structure depend on the compression rate: simple intuition suggests, and previous computer simulation demonstrates, that slower compression results in states that are both denser and more ordered. In this work, we use the Lubachevsky-Stillinger algorithm to generate a sequence of structurally arrested hard-sphere states by varying the compression rate. We find that while the degree of order, as measured by both bond-orientation and translation order parameters, increases monotonically with decreasing compression rate, the density of the arrested state first increases, then decreases, then increases again, as the compression rate decreases, showing a minimum at an intermediate compression rate. Examination of the distribution of the local order parameters and the distribution of the root-mean-square fluctuation of the particle positions, as well as direct visual inspection of the arrested structures, reveal that they are structurally heterogeneous, consisting of disordered, amorphous regions and locally ordered crystal-like domains. In particular, the low-density arrested states correspond with many interconnected small crystal clusters that form a polycrystalline network interspersed in an amorphous background, suggesting that jamming by the domains may be an important mechanism for these states

Effects of Geometrical Symmetry on the Vortex Nucleation and Penetration in Mesoscopic Superconductors

We investigate how the geometrical symmetry affects the penetration and arrangement of vortices in mesoscopic superconductors using self-consistent Bogoliubov-de Gennes equations. We find that the entrance of the vortex happens when the current density at the hot spots reaches the depairing current density. Through determining the spatial distribution of hot spots, the geometrical symmetry of the superconducting sample influences the nucleation and entrance of vortices. Our results propose one possible experimental approach to control and manipulate the quantum states of mesoscopic superconductors with their topological geometries, and they can be easily generalized to the confined superfluids and Bose-Einstein condensates