Molecular random tilings as glasses

We have recently shown [Blunt et al., Science 322, 1077 (2008)] that p-terphenyl-3,5,3',5'-tetracarboxylic acid adsorbed on graphite self-assembles into a two-dimensional rhombus random tiling. This tiling is close to ideal, displaying long range correlations punctuated by sparse localised tiling defects. In this paper we explore the analogy between dynamic arrest in this type of random tilings and that of structural glasses. We show that the structural relaxation of these systems is via the propagation--reaction of tiling defects, giving rise to dynamic heterogeneity. We study the scaling properties of the dynamics, and discuss connections with kinetically constrained models of glasses.Comment: 5 pages, 5 figure

Macroscopic Equations of Motion for Two Phase Flow in Porous Media

The established macroscopic equations of motion for two phase immiscible displacement in porous media are known to be physically incomplete because they do not contain the surface tension and surface areas governing capillary phenomena. Therefore a more general system of macroscopic equations is derived here which incorporates the spatiotemporal variation of interfacial energies. These equations are based on the theory of mixtures in macroscopic continuum mechanics. They include wetting phenomena through surface tensions instead of the traditional use of capillary pressure functions. Relative permeabilities can be identified in this approach which exhibit a complex dependence on the state variables. A capillary pressure function can be identified in equilibrium which shows the qualitative saturation dependence known from experiment. In addition the new equations allow to describe the spatiotemporal changes of residual saturations during immiscible displacement.Comment: 15 pages, Phys. Rev. E (1998), in prin

Microwave characterization of two Ba 0.6 Sr 0.4 TiO 3 dielectric thin films with out-of-plane and in-plane electrode structures

Ferroelectric (FE) thin films have recently attracted renewed interest in research due to their great potential for designing novel tunable electromagnetic devices such as large intelligent surfaces (LISs). However, the mechanism of how a polar structure in the FE thin films contributes to desired tunable performance, especially within the microwave frequency range, which is the most widely used frequency range of electromagnetics, has not been illustrated clearly. In this paper, we described several straightforward and cost-effective methods to fabricate and characterize Ba0.6Sr0.4TiO3 (BST) thin films at microwave frequencies. The prepared BST thin films here exhibit homogenous structures and great tunability (η) in a wide frequency and temperature range when the applied field is in the out-of-plane direction. The high tunability can be attributed to high concentration of polar nanoclusters. Their response to the applied direct current (DC) field was directly visualized using a novel non-destructive near-field scanning microwave microscopy (NSMM) technique. Our results have provided some intriguing insights into the application of the FE thin films for future programmable high-frequency devices and systems.</p

Broken symmetry and the variation of critical properties in the phase behaviour of supramolecular rhombus tilings

The degree of randomness, or partial order, present in two-dimensional supramolecular arrays of isophthalate tetracarboxylic acids is shown to vary due to subtle chemical changes such as the choice of solvent or small differences in molecular dimensions. This variation may be quantified using an order parameter and reveals a novel phase behaviour including random tiling with varying critical properties as well as ordered phases dominated by either parallel or non-parallel alignment of neighbouring molecules, consistent with long-standing theoretical studies. The balance between order and randomness is driven by small differences in the intermolecular interaction energies, which we show, using numerical simulations, can be related to the measured order parameter. Significant variations occur even when the energy difference is much less than the thermal energy highlighting the delicate balance between entropic and energetic effects in complex self-assembly processes

Nonequilibrium dynamics of fully frustrated Ising models at T=0

We consider two fully frustrated Ising models: the antiferromagnetic triangular model in a field of strength, $h=H T k_B$, as well as the Villain model on the square lattice. After a quench from a disordered initial state to T=0 we study the nonequilibrium dynamics of both models by Monte Carlo simulations. In a finite system of linear size, $L$, we define and measure sample dependent "first passage time", $t_r$, which is the number of Monte Carlo steps until the energy is relaxed to the ground-state value. The distribution of $t_r$, in particular its mean value, $$, is shown to obey the scaling relation, $\sim L^2 \ln(L/L_0)$, for both models. Scaling of the autocorrelation function of the antiferromagnetic triangular model is shown to involve logarithmic corrections, both at H=0 and at the field-induced Kosterlitz-Thouless transition, however the autocorrelation exponent is found to be $H$ dependent.Comment: 7 pages, 8 figure

Simulating temporal evolution of pressure in two-phase flow in porous media

We have simulated the temporal evolution of pressure due to capillary and viscous forces in two-phase drainage in porous media. We analyze our result in light of macroscopic flow equations for two-phase flow. We also investigate the effect of the trapped clusters on the pressure evolution and on the effective permeability of the system. We find that the capillary forces play an important role during the displacements for both fast and slow injection rates and both when the invading fluid is more or less viscous than the defending fluid. The simulations are based on a network simulator modeling two-phase drainage displacements on a two-dimensional lattice of tubes.Comment: 12 pages, LaTeX, 14 figures, Postscrip

Pipe network model for scaling of dynamic interfaces in porous media

We present a numerical study on the dynamics of imbibition fronts in porous media using a pipe network model. This model quantitatively reproduces the anomalous scaling behavior found in imbibition experiments [Phys. Rev. E {\bf 52}, 5166 (1995)]. Using simple scaling arguments, we derive a new identity among the scaling exponents in agreement with the experimental results.Comment: 13 pages, 3 figures, REVTeX, to appear in Phys. Rev. Let