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

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

continuum modelling of semiconductor heteroepitaxy an applied perspective

Semiconductor heteroepitaxy involves a wealth of qualitatively different, competing phenomena. Examples include three-dimensional island formation, injection of dislocations, mixing between film and substrate atoms. Their relative importance depends on the specific growth conditions, giving rise to a very complex scenario. The need for an optimal control over heteroepitaxial films and/or nanostructures is widespread: semiconductor epitaxy by molecular beam epitaxy or chemical vapour deposition is nowadays exploited also in industrial environments. Simulation models can be precious in limiting the parameter space to be sampled while aiming at films/nanostructures with the desired properties. In order to be appealing (and useful) to an applied audience, such models must yield predictions directly comparable with experimental data. This implies matching typical time scales and sizes, while offering a satisfactory description of the main physical driving forces. It is the aim of the present review to show tha..

Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model

We address a three-dimensional, coarse-grained description of dislocation networks at grain boundaries between rotated crystals. The so-called amplitude expansion of the phase-field crystal model is exploited with the aid of finite element method calculations. This approach allows for the description of microscopic features, such as dislocations, while simultaneously being able to describe length scales that are orders of magnitude larger than the lattice spacing. Moreover, it allows for the direct description of extended defects by means of a scalar order parameter. The versatility of this framework is shown by considering both fcc and bcc lattice symmetries and different rotation axes. First, the specific case of planar, twist grain boundaries is illustrated. The details of the method are reported and the consistency of the results with literature is discussed. Then, the dislocation networks forming at the interface between a spherical, rotated crystal embedded in an unrotated crystalline structure, are shown. Although explicitly accounting for dislocations which lead to an anisotropic shrinkage of the rotated grain, the extension of the spherical grain boundary is found to decrease linearly over time in agreement with the classical theory of grain growth and recent atomistic investigations. It is shown that the results obtained for a system with bcc symmetry agree very well with existing results, validating the methodology. Furthermore, fully original results are shown for fcc lattice symmetry, revealing the generality of the reported observations.Comment: 11 pages, 9 figure

Bioinformatics and constraints

This article introduces the topic of bioinformatics to an audience of computer scientists. We discuss the definition of bioinformatics, give a classification of the problem areas which bioinformatics addresses, and illustrate these in detail with examples. We highlight those areas which we believe to be suitable for the application of constraint solving techniques, or where similar techniques are already used. Finally, we give some advice for computer scientists who are considering getting involved in bioinformatics, and provide a resource list and a reading list

Efficient chaining of seeds in ordered trees

We consider here the problem of chaining seeds in ordered trees. Seeds are mappings between two trees Q and T and a chain is a subset of non overlapping seeds that is consistent with respect to postfix order and ancestrality. This problem is a natural extension of a similar problem for sequences, and has applications in computational biology, such as mining a database of RNA secondary structures. For the chaining problem with a set of m constant size seeds, we describe an algorithm with complexity O(m2 log(m)) in time and O(m2) in space