A phase-field-crystal approach to critical nuclei

We investigate a phase-field-crystal model for homogeneous nucleation. Instead of solving the time evolution of a density field towards equilibrium we use a String Method to identify saddle points in phase space. The saddle points allow to obtain the nucleation barrier and the critical nucleus. The advantage of using the phase-field-crystal model for this task is its ability to resolve atomistic effects. The obtained results indicate different properties of the critical nucleus compared with bulk crystals and show a detailed description of the nucleation process.Comment: 12 pages, 5 figures, submitte

Relaxation of curvature induced elastic stress by the Asaro-Tiller-Grinfeld instability

A two-dimensional crystal on the surface of a sphere experiences elastic stress due to the incompatibility of the crystal axes and the curvature. A common mechanism to relax elastic stress is the Asaro-Tiller-Grinfeld (ATG) instability. With a combined numerical and analytical approach we demonstrate, that also curvature induced stress in surface crystals can be relaxed by the long wave length ATG instability. The numerical results are obtained using a surface phase-field crystal (PFC) model, from which we determine the characteristic wave numbers of the ATG instability for various surface coverages corresponding to different curvature induced compressions. The results are compared with an analytic expression for the characteristic wave number, obtained from a continuum approach which accounts for hexagonal crystals and intrinsic PFC symmetries. We find our numerical results in accordance with the analytical predictions.Comment: 6 pages, 5 figure

Regular path expressions in feature logic

We examine the existential fragment of a feature logic, which is extended by regular path expressions. A regular path expression is a subterm relation, where the allowed paths for the subterms are restricted to any given regular language. We will prove that satisfiability is decidable. This is achieved by setting up a quasi-terminating rule system

Grain growth beyond the Mullins model, capturing the complex physics behind universal grain size distributions

Grain growth experiments on thin metallic films have shown the geometric and topological characteristics of the grain structure to be universal and independent of many experimental conditions. The universal size distribution, however, is found to differ both qualitatively and quantitatively from the standard Mullins curvature driven model of grain growth; with the experiments exhibiting an excess of small grains (termed an "ear") and an excess of very large grains (termed a "tail") compared with the model. While a plethora of extensions of the Mullins model have been proposed to explain these characteristics, none have been successful. In this work, large scale simulations of a model that resolves the atomic scale on diffusive time scales, the phase field crystal model, is used to examine the complex phenomena of grain growth. The results are in remarkable agreement with the experimental results, recovering the characteristic "ear" and "tail" features of the experimental grain size distribution. The simulations also indicate that while the geometric and topological characteristics are universal, the dynamic growth exponent is not.Comment: 4 pages, 5 figure

A Complete and Recursive Feature Theory

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions considered in this paper are the possibly quantified first-order formulae obtained from a signature of binary and unary predicates called features and sorts, respectively. We establish a first-order theory FT by means of three axiom schemes, show its completeness, and construct three elementarily equivalent models. One of the models consists of so-called feature graphs, a data structure common in computational linguistics. The other two models consist of so-called feature trees, a record-like data structure generalizing the trees corresponding to first-order terms. Our completeness proof exhibits a terminating simplification system deciding validity and satisfiability of possibly quantified feature descriptions.Comment: Short version appeared in the 1992 Annual Meeting of the Association for Computational Linguistic

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model

One of the major difficulties in employing phase field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.Comment: 14 pages, 9 figure

FLASH: ultra-fast protocol to identify RNA-protein interactions in cells

Determination of the in vivo binding sites of RNA-binding proteins (RBPs) is paramount to understanding their function and how they affect different aspects of gene regulation. With hundreds of RNA-binding proteins identified in human cells, a flexible, high-resolution, high-throughput, highly multiplexible and radioactivity-free method to determine their binding sites has not been described to date. Here we report FLASH (Fast Ligation of RNA after some sort of Affinity Purification for High-throughput Sequencing), which uses a special adapter design and an optimized protocol to determine protein-RNA interactions in living cells. The entire FLASH protocol, starting from cells on plates to a sequencing library, takes 1.5 days. We demonstrate the flexibility, speed and versatility of FLASH by using it to determine RNA targets of both tagged and endogenously expressed proteins under diverse conditions in vivo