Theory and simulations of water flow through carbon nanotubes: prospects and pitfalls.

We study water flow through carbon nanotubes using continuum theory and molecular dynamics simulations. The large slip length in carbon nanotubes greatly enhances the pumping and electrokinetic energy conversion efficiency. In the absence of mobile charges, however, the electro-osmotic flow vanishes. Uncharged nanotubes filled with pure water can therefore not be used as electric field-driven pumps, contrary to some recently ventured ideas. This is in agreement with results from a generalized hydrodynamic theory that includes the angular momentum of rotating dipolar molecules. The electro-osmotic flow observed in simulations of such carbon nanotubes is caused by an imprudent implementation of the Lennard-Jones cutoff. We also discuss the influence of other simulation parameters on the spurious electro-osmotic flow.

Inverted Berezinskii-Kosterlitz-Thouless singularity and high-temperature algebraic order in an Ising model on a scale-free hierarchical-lattice small-world network.

We have obtained exact results for the Ising model on a hierarchical lattice incorporating three key features characterizing many real-world networks--a scale-free degree distribution, a high clustering coefficient, and the small-world effect. By varying the probability p of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a highly clustered, small-world system is studied. Using the self-similar structure of the network, we obtain analytic expressions for the degree distribution P(k) and clustering coefficient C for all p, as well as the average path length l for p = 0 and 1. The ferromagnetic Ising model on this network is studied through an exact renormalization-group transformation of the quenched bond probability distribution, using up to 562,500 renormalized probability bins to represent the distribution. For p < 0.494, we find power-law critical behavior of the magnetization and susceptibility, with critical exponents continuously varying with p, and exponential decay of correlations away from Tc. For p > or = 0.494, in fact where the network exhibits small-world character, the critical behavior radically changes: We find a highly unusual phase transition, namely an inverted Berezinskii-Kosterlitz-Thouless singularity, between a low-temperature phase with nonzero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length, with power-law decay of correlations throughout the phase. Approaching Tc from below, the magnetization and the susceptibility, respectively, exhibit the singularities of exp(-C/square root of Tc - T) and exp(D/square root of Tc - T), with C and D positive constants. With long-range bond strengths decaying with distance, we see a phase transition with power-law critical singularities for all p, and evaluate an unusually narrow critical region and important corrections to power-law behavior that depend on the exponent characterizing the decay of long-range interactions.

Multiplicity of ordered phases in frustrated systems obtained from hard-spin mean-field theory

Random quenched dilution of the triangular-lattice antiferromagnetic Ising model locally relieves frustration, leading to ordering phenomena. We have studied this system, under such dilution of one sublattice, using hard-spin mean-field theory. After a threshold dilution, two sublattices develop nonzero magnetizations of equal magnitude and opposite signs, as all three sublattices exhibit spin-glass order. In this phase, multiple sets of ordered solutions occur. A phase diagram is obtained in dilution fraction and temperature.