Polymer scaling and dynamics in steady-state sedimentation at infinite Péclet number

We consider the static and dynamical behavior of a flexible polymer chain under steady-state sedimentation using analytic arguments and computer simulations. The model system comprises a single coarse-grained polymer chain of N segments, which resides in a Newtonian fluid as described by the Navier-Stokes equations. The chain is driven into nonequilibrium steady state by gravity acting on each segment. The equations of motion for the segments and the Navier-Stokes equations are solved simultaneously using an immersed boundary method, where thermal fluctuations are neglected. To characterize the chain conformation, we consider its radius of gyration RG(N). We find that the presence of gravity explicitly breaks the spatial symmetry leading to anisotropic scaling of the components of RG with N along the direction of gravity RG,∥ and perpendicular to it RG,⊥, respectively. We numerically estimate the corresponding anisotropic scaling exponents ν∥≈0.79 and ν⊥≈0.45, which differ significantly from the equilibrium scaling exponent νe=0.588 in three dimensions. This indicates that on the average, the chain becomes elongated along the sedimentation direction for large enough N. We present a generalization of the Flory scaling argument, which is in good agreement with the numerical results. It also reveals an explicit dependence of the scaling exponents on the Reynolds number. To study the dynamics of the chain, we compute its effective diffusion coefficient D(N), which does not contain Brownian motion. For the range of values of N used here, we find that both the parallel and perpendicular components of D increase with the chain length N, in contrast to the case of thermal diffusion in equilibrium. This is caused by the fluid-driven fluctuations in the internal configuration of the polymer that are magnified as polymer size becomes larger.Peer reviewe

Phase-field-crystal models and mechanical equilibrium

Phase-field-crystal (PFC) models constitute a field theoretical approach to solidification, melting, and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain elastic excitations associated with strain in crystalline bodies. However, instabilities that are diffusively driven towards equilibrium are often orders of magnitude slower than the dynamics of the elastic excitations, and are thus not included in the standard PFC model dynamics. We derive a method to isolate the time evolution of the elastic excitations from the diffusive dynamics in the PFC approach and set up a two-stage process, in which elastic excitations are equilibrated separately. This ensures mechanical equilibrium at all times. We show concrete examples demonstrating the necessity of the separation of the elastic and diffusive time scales. In the small-deformation limit this approach is shown to agree with the theory of linear elasticity.Peer reviewe

Thermodynamics of bcc metals in phase-field-crystal models

We examine the influence of different forms of the free-energy functionals used in the phase-field-crystal (PFC) model, and compare them with the second-order density-functional theory (DFT) of freezing, by using bcc iron as an example case. We show that there are large differences between the PFC and the DFT and it is difficult to obtain reasonable parameters for existing PFC models directly from the DFT. Therefore, we propose a way of expanding the correlation function in terms of gradients that allows us to incorporate the bulk modulus of the liquid as an additional parameter in the theory. We show that this functional reproduces reasonable values for both bulk and surface properties of bcc iron, and therefore it should be useful in modeling bcc materials. As a further demonstration, we also calculate the grain boundary energy as a function of misorientation for a symmetric tilt boundary close to the melting transition.Peer reviewe

Phase diagram of pinned lattices in the phase field crystal model

We study the phase diagram and the commensurate-incommensurate phase transitions of a two-dimensional phase field crystal model for adsorbed layers. The model allows for both elastic and plastic deformations on atomic and diffusive time-scales, and provides a continuum description of lattice systems, such as adsorbed atomic layers or two-dimensional vortex lattices. Analytically, mode expansion analysis and numerical minimization of the free energy are used to determine the ground states as a function of the pinning potential and lattice mismatch parameter. The results show a rich phase diagram with several different types of commensurate and incommensurate phases.Peer reviewe

Modeling self-organization of thin strained metallic overlayers from atomic to micron scales

A computational study of the self-organization of heteroepitaxial ultrathin metal films is presented. By means of a continuum complex field model, the relationship of the equilibrium surface patterns of the film to the adsorbate-substrate adhesion energy, as well as to the mismatch between the adsorbate and the substrate bulk lattice parameters, are obtained in both the tensile and the compressive regimes. Our approach captures pattern periodicities over large length scales, up to several hundreds of nm, retaining atomistic resolution. Thus, the results can be directly compared with experimental data, in particular for systems such as Cu/Ru(0001) and Ag/Cu(111). Three nontrivial, stable superstructures for the overlayer, namely, stripe, honeycomb, and triangular, are identified that closely resemble those observed experimentally. Simulations in nonequilibrium conditions are performed as well to identify metastable structural configurations and the dynamics of ordering of the overlayer.Peer reviewe

Patterning of Heteroepitaxial Overlayers from Nano to Micron Scales

Thin heteroepitaxial overlayers have been proposed as templates to generate stable, self-organized nanostructures at large length scales, with a variety of important technological applications. However, modeling strain-driven self-organization is a formidable challenge due to different length scales involved. In this Letter, we present a method for predicting the patterning of ultrathin films on micron length scales with atomic resolution. We make quantitative predictions for the type of superstructures (stripes, honeycomb, triangular) and length scale of pattern formation of two metal-metal systems, Cu on Ru(0001) and Cu on Pd(111). Our findings are in excellent agreement with previous experiments and call for future experimental investigations of such systems.Peer reviewe

Common Variant Burden Contributes to the Familial Aggregation of Migraine in 1,589 Families

© 2018 Elsevier Inc. Complex traits, including migraine, often aggregate in families, but the underlying genetic architecture behind this is not well understood. The aggregation could be explained by rare, penetrant variants that segregate according to Mendelian inheritance or by the sufficient polygenic accumulation of common variants, each with an individually small effect, or a combination of the two hypotheses. In 8,319 individuals across 1,589 migraine families, we calculated migraine polygenic risk scores (PRS) and found a significantly higher common variant burden in familial cases (n = 5,317, OR = 1.76, 95% CI = 1.71–1.81, p = 1.7 × 10−109) compared to population cases from the FINRISK cohort (n = 1,101, OR = 1.32, 95% CI = 1.25–1.38, p = 7.2 × 10−17). The PRS explained 1.6% of the phenotypic variance in the population cases and 3.5% in the familial cases (including 2.9% for migraine without aura, 5.5% for migraine with typical aura, and 8.2% for hemiplegic migraine). The results demonstrate a significant contribution of common polygenic variation to the familial aggregation of migraine. Gormley et al. use polygenic risk scores to show that common variation, captured by genome-wide association studies, in combination contributes to the aggregation of migraine in families. The results may have similar implications for other complex traits in general

Consistent Hydrodynamics for Phase Field Crystals

We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to the well-known macroscopic theories in appropriate limits, including compressible Navier-Stokes and wave equations. Moreover, we show that the dynamics proposed allows for long wavelength phonon modes and demonstrate the theory numerically showing that the elastic excitations in the system are relaxed through phonon emission.Peer reviewe