Development of an Optimization-Based Atomistic-to-Continuum Coupling Method

Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the efficiency of a continuum model. In this note we extend the optimization-based AtC, formulated in arXiv:1304.4976 for linear, one-dimensional problems to multi-dimensional settings and arbitrary interatomic potentials. We conjecture optimal error estimates for the multidimensional AtC, outline an implementation procedure, and provide numerical results to corroborate the conjecture for a 1D Lennard-Jones system with next-nearest neighbor interactions.Comment: 12 pages, 3 figure

Effective pair potentials for spherical nanoparticles

An effective description for spherical nanoparticles in a fluid of point particles is presented. The points inside the nanoparticles and the point particles are assumed to interact via spherically symmetric additive pair potentials, while the distribution of points inside the nanoparticles is taken to be spherically symmetric and smooth. The resulting effective pair interactions between a nanoparticle and a point particle, as well as between two nanoparticles, are then given by spherically symmetric potentials. If overlap between particles is allowed, the effective potential generally has non-analytic points, but for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential. Effective potentials for hollow nanoparticles (appropriate e.g. for buckyballs) are also considered, and shown to be related to those for solid nanoparticles. Finally, explicit expressions are given for the effective potentials derived from basic pair potentials of power law and exponential form, as well as from the commonly used London-Van der Waals, Morse, Buckingham, and Lennard-Jones potential. The applicability of the latter is demonstrated by comparison with an atomic description of nanoparticles with an internal face centered cubic structure.Comment: 27 pages, 12 figures. Unified description of overlapping and nonoverlapping particles added, as well as a comparison with an idealized atomic descriptio

Dislocation Emission around Nanoindentations on a (001) fcc Metal Surface Studied by STM and Atomistic Simulations

We present a combined study by Scanning Tunneling Microscopy and atomistic simulations of the emission of dissociated dislocation loops by nanoindentation on a (001) fcc surface. The latter consist of two stacking-fault ribbons bounded by Shockley partials and a stair-rod dislocation. These dissociated loops, which intersect the surface, are shown to originate from loops of interstitial character emitted along the directions and are usually located at hundreds of angstroms away from the indentation point. Simulations reproduce the nucleation and glide of these dislocation loops.Comment: 10 pages, 4 figure

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

We present a systematic study of the effect of crack blunting on subsequent crack propagation and dislocation emission. We show that the stress intensity factor required to propagate the crack is increased as the crack is blunted by up to thirteen atomic layers, but only by a relatively modest amount for a crack with a sharp 60$^\circ$ corner. The effect of the blunting is far less than would be expected from a smoothly blunted crack; the sharp corners preserve the stress concentration, reducing the effect of the blunting. However, for some material parameters blunting changes the preferred deformation mode from brittle cleavage to dislocation emission. In such materials, the absorption of preexisting dislocations by the crack tip can cause the crack tip to be locally arrested, causing a significant increase in the microscopic toughness of the crack tip. Continuum plasticity models have shown that even a moderate increase in the microscopic toughness can lead to an increase in the macroscopic fracture toughness of the material by several orders of magnitude. We thus propose an atomic-scale mechanism at the crack tip, that ultimately may lead to a high fracture toughness in some materials where a sharp crack would seem to be able to propagate in a brittle manner. Results for blunt cracks loaded in mode II are also presented.Comment: 12 pages, REVTeX using epsfig.sty. 13 PostScript figures. Final version to appear in Phys. Rev. B. Main changes: Discussion slightly shortened, one figure remove

Renormalization group approach to multiscale modelling in materials science

Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. The phase field approach of Langer, enhanced by optimal asymptotic methods and adaptive mesh refinement, copes with this range of scales, and provides an effective way to move phase boundaries. However, it fails to preserve memory of the underlying crystallographic anisotropy, and thus is ill-suited for problems involving defects or elasticity. The phase field crystal (PFC) equation-- a conserving analogue of the Hohenberg-Swift equation --is a phase field equation with periodic solutions that represent the atomic density. It can natively model elasticity, the formation of solid phases, and accurately reproduces the nonequilibrium dynamics of phase transitions in real materials. However, the PFC models matter at the atomic scale, rendering it unsuitable for coping with the range of length scales in problems of serious interest. Here, we show that a computationally-efficient multiscale approach to the PFC can be developed systematically by using the renormalization group or equivalent techniques to derive appropriate coarse-grained coupled phase and amplitude equations, which are suitable for solution by adaptive mesh refinement algorithms

Coupled surface polaritons and the Casimir force

The Casimir force between metallic plates made of realistic materials is evaluated for distances in the nanometer range. A spectrum over real frequencies is introduced and shows narrow peaks due to surface resonances (plasmon polaritons or phonon polaritons) that are coupled across the vacuum gap. We demonstrate that the Casimir force originates from the attraction (repulsion) due to the corresponding symmetric (antisymmetric) eigenmodes, respectively. This picture is used to derive a simple analytical estimate of the Casimir force at short distances. We recover the result known for Drude metals without absorption and compute the correction for weakly absorbing materials.Comment: revised version submitted to Phys. Rev. A, 06 November 200

Eleanor Davies and the New Jerusalem

Eleanor Davies was a great believer in historical moments. In her first work—A Warning to the Dragon and All His Angels of 1625-she told readers that “The Lord is at the Dore.”1 This immanence of God made her watchful and purposeful, reading the signs in her daily life, counting days, weeks, and years because she believed that Christ would come again. His arrival had been predestined from the beginning of the world: “from the going forth of the Commandement, which is the beginning of the Creation to the building of the New Jerusalem, the second comming of Messiah, the Prince the Sonne of God, it shall be Seaven Weekes or Seaven Moneths.”2 For Davies, time was elastic, but history was absolute. What the biblical prophets (in this case Ezekiel) said would come to pass, really would come to pass, but their promises were oracular; they had complete authority but were also elusive. Davies accepted this. She knew that she was living in the latter days, but when it came to God’s final judgment, “the daye and houre knoweth no man.”3 God could not be known as such and what she called knowledge was a spiritual transformation that took place when “He powreth out his Spirit upon his hand-maidens,” like herself.4 This essay uses A Warning to the Dragon and Davies’ works of the 1630s and 1640s to examine her theology

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

Development of a distributed international patient data registry for hairy cell leukemia

Hairy cell leukemia (HCL) is a rare lymphoproliferative disorder, comprising only 2% of all leukemias. The Hairy Cell Leukemia Foundation (HCLF) has developed a patient data registry to enable investigators to better study the clinical features, treatment outcomes, and complications of patients with HCL. This system utilizes a centralized registry architecture. Patients are enrolled at HCL Centers of Excellence (COE) or via a web-based portal. All data are de-identified, which reduces regulatory burden and increases opportunities for data access and re-use. To date, 579 patients have been enrolled in the registry. Efforts are underway to engage additional COE’s to expand access to patients across the globe. This international PDR will enable researchers to study outcomes in HCL in ways not previously possible due to the rarity of the disease and will serve as a platform for future prospective research