Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

Conformation of Circular DNA in 2 Dimensions

The conformation of circular DNA molecules of various lengths adsorbed in a 2D conformation on a mica surface is studied. The results confirm the conjecture that the critical exponent $\nu$ is topologically invariant and equal to the SAW value (in the present case $\nu=3/4$), and that the topology and dimensionality of the system strongly influences the cross-over between the rigid regime and the self-avoiding regime at a scale $L\approx 8 \ell_p$. Additionally, the bond correlation function scales with the molecular length $L$ as predicted. For molecular lengths $L\leq5 \ell_p$, circular DNA behaves like a stiff molecule with approximately elliptic shape.Comment: 4 pages, 5 figure

Probing a non-biaxial behavior of infinitely thin hard platelets

We give a criterion to test a non-biaxial behavior of infinitely thin hard platelets of $D_{2h}$ symmetry based upon the components of three order parameter tensors. We investigated the nematic behavior of monodisperse infinitely thin rectangular hard platelet systems by using the criterion. Starting with a square platelet system, and we compared it with rectangular platelet systems of various aspect ratios. For each system, we performed equilibration runs by using isobaric Monte Carlo simulations. Each system did not show a biaxial nematic behavior but a uniaxial nematic one, despite of the shape anisotropy of those platelets. The relationship between effective diameters by simulations and theoretical effective diameters of the above systems was also determined.Comment: Submitted to JPS

Density-functional study of defects in two-dimensional circular nematic nanocavities

We use density--functional theory to study the structure of two-dimensional defects inside a circular nematic nanocavity. The density, nematic order parameter, and director fields, as well as the defect core energy and core radius, are obtained in a thermodynamically consistent way for defects with topological charge $k=+1$ (with radial and tangential symmetries) and $k=+1/2$. An independent calculation of the fluid elastic constants, within the same theory, allows us to connect with the local free--energy density predicted by elastic theory, which in turn provides a criterion to define a defect core boundary and a defect core free energy for the two types of defects. The radial and tangential defects turn out to have very different properties, a feature that a previous Maier--Saupe theory could not account for due to the simplified nature of the interactions --which caused all elastic constants to be equal. In the case with two $k=+1/2$ defects in the cavity, the elastic r\'egime cannot be reached due to the small radii of the cavities considered, but some trends can already be obtained.Comment: 9 figures. Accepted for publication in liquid crystal

Domains in Melts of Comb-Coil Diblock Copolymers: Superstrong Segregation Regime

Conditions for the crossover from the strong to the superstrong segregation regime are analyzed for the case of comb-coil diblock copolymers. It is shown that the critical interaction energy between the components required to induce the crossover to the superstrong segregation regime is inversely proportional to mb = 1 + n/m, where n is the degree of polymerization of the side chain and m is the distance between successive grafting points. As a result, the superstrong segregation regime, being rather rare in the case of ordinary block copolymers, has a much better chance to be realized in the case of diblock copolymers with combs grafted to one of the blocks.

Exploring the psychosocial and behavioural determinants of household water conservation and intention

Securing urban freshwater supplies is a major challenge for policy makers globally. This study investigated the determinants of household water conservation to identify the relative contribution of psychosocial and behavioural determinants. Using a survey of 1196 households across the UK, we found that attitudes, norms and habits play an important role in determining intention to conserve water, and that habits were the single most important predictor of water conservation intentions and self-reported water bills. Changing ingrained water conservation habits is therefore an important component of managing urban water demand

Bulk phase behaviour of binary hard platelet mixtures from density functional theory

We investigate isotropic-isotropic, isotropic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thickness, continuous rotational degrees of freedom and radial size ratios $\lambda$ up to 5. A fundamental measure density functional theory, previously used for the one-component model, is proposed and results are compared against those from Onsager theory as a benchmark. For $\lambda \leq 1.7$ the system displays isotropic-nematic phase coexistence with a widening of the biphasic region for increasing values of $\lambda$. For size ratios $\lambda \geq 2$, we find demixing into two nematic states becomes stable and an isotropic-nematic-nematic triple point can occur. Fundamental measure theory gives a smaller isotropic-nematic biphasic region than Onsager theory and locates the transition at lower densities. Furthermore, nematic-nematic demixing occurs over a larger range of compositions at a given value of $\lambda$ than found in Onsager theory. Both theories predict the same topologies of the phase diagrams. The partial nematic order parameters vary strongly with composition and indicate that the larger particles are more strongly ordered than the smaller particles

Effective action for the field equations of charged black holes

In this article, we consistently reduce the equations of motion for the bosonic N = 2 supergravity action, using a multi-centered black hole ansatz for the metric. This reduction is done in a general, non-supersymmetric setup, in which we extend concepts of BPS black hole technology. First of all we obtain a more general form of the black hole potential, as part of an effective action for both the scalars and the vectors in the supergravity theory. Furthermore, we show that there are extra constraints specifying the solution, which we calculate explicitly. In the literature, these constraints have already been studied in the one-center case. We also show that the effective action we obtain for non-static metrics, can be linked to the "entropy function" for the spherically symmetric case, as defined by Sen and Cardoso et al.Comment: 18 pages, (v2: small corrections, version to be published in CQG