A fully-nonlocal energy-based formulation and high-performance realization of the quasicontinuum method

The quasicontinuum (QC) method was introduced to coarse-grain crystalline atomic ensembles in order to bridge the scales from individual atoms to the micro- and mesoscales. Though many QC formulations have been proposed with varying characteristics and capabilities, a crucial cornerstone of all QC techniques is the concept of summation rules, which attempt to efficiently approximate the total Hamiltonian of a crystalline atomic ensemble by a weighted sum over a small subset of atoms. In this work we propose a novel, fully-nonlocal, energy-based formulation of the QC method with support for legacy and new summation rules through a general energy-sampling scheme. Our formulation does not conceptually differentiate between atomistic and coarse-grained regions and thus allows for seamless bridging without domain-coupling interfaces. Within this structure, we introduce a new class of summation rules which leverage the affine kinematics of this QC formulation to most accurately integrate thermodynamic quantities of interest. By comparing this new class of summation rules to commonly-employed rules through analysis of energy and spurious force errors, we find that the new rules produce no residual or spurious force artifacts in the large-element limit under arbitrary affine deformation, while allowing us to seamlessly bridge to full atomistics. We verify that the new summation rules exhibit significantly smaller force artifacts and energy approximation errors than all comparable previous summation rules through a comprehensive suite of examples with spatially non-uniform QC discretizations in two and three dimensions. Due to the unique structure of these summation rules, we also use the new formulation to study scenarios with large regions of free surface, a class of problems previously out of reach of the QC method. Lastly, we present the key components of a high-performance, distributed-memory realization of the new method, including a novel algorithm for supporting unparalleled levels of deformation. Overall, this new formulation and implementation allows us to efficiently perform simulations containing an unprecedented number of degrees of freedom with low approximation error.

Turbulent buoyant jets into stratified or flowing ambient fluids

Theoretical and experimental studies were made on two classes of buoyant jet problems, namely:

1) an inclined, round buoyant yet in a stagnant environment with linear density-stratification;

2) a round buoyant jet in a uniform cross stream of homogenous density.

Using the integral technique of analysis, assuming similarity, predictions can be made for jet trajectory, widths, and dilution ratios, in a density-stratified or flowing environment. Such information is of great importance in the design of disposal systems for sewage effluent into the ocean or waste gases into the atmosphere.

The present study of a buoyant jet in a stagnant environment has extended the Morton type of analysis to cover the effect of the initial angle of discharge. Numerical solutions have been presented for a range of initial conditions. Laboratory experiments were conducted for photographic observations of the trajectories of dyed jets. In general the observed jet forms agreed well with the calculated trajectories and nominal half widths when the value of the entrainment coefficient was taken to be α = 0.082, as previously suggested by Morton.

The problem of a buoyant jet in a uniform cross stream was analyzed by assuming an entrainment mechanism based upon the vector difference between the characteristic jet velocity and the ambient velocity. The effect of the unbalanced pressure field on the sides of the jet flow was approximated by a gross drag term. Laboratory flume experiments with sinking jets which are directly analogous to buoyant jets were performed. Salt solutions were injected into fresh water at the free surface in a flume. The jet trajectories, dilution ratios and jet half widths were determined by conductivity measurements. The entrainment coefficient, α, and drag coefficient, C_d, were found from the observed jet trajectories and dilution ratios. In the ten cases studied where jet Froude number ranged from 10 to 80 and velocity ratio (jet: current) K from 4 to 16, α varied from 0.4 to 0.5 and C_d from 1.7 to 0.1. The jet mixing motion for distance within 250D was found to be dominated by the self-generated turbulence, rather than the free-stream turbulence. Similarity of concentration profiles has also been discussed.

The unsteady forces on slender delta wing hydrofoils oscillating in heave

The investigations described herein are both experimental and theoretical. An experimental technique is described by which the models tested could be oscillated sinusoidally in heave. The apparatus used to gather the unsteady lift, drag and pitching moment data is also described.

The models tested were two flat delta wings with apex angles of 15° and 30° and they had sharp leading edges to insure flow separation. The models were fabricated from 0.25 inch aluminum plate and were approximately one foot in length.

Three distinct types of flow were investigated: 1) fully wetted, 2) ventilated and 3) planing. The experimental data are compared with existing theories for steady motions in the case of fully wetted delta wings. Ventilation measurements, made only for the 30° model at 20° angle of attack, of lift and drag are presented.

A correction of the theory proposed by M.P. Tulin for high speed planing of slender bodies is presented and it is extended to unsteady motions. This is compared to the experimental measurements made at 6° and 12° angle of attack for the two models previously described.

This is the first extensive measurement of unsteady drag for any shape wing, the first measurement of unsteady planing forces, the first quantitative documentation of unstable oscillations near a free surface, and the first measurements of the unsteady forces on ventilated delta wings. The results of these investigations, both theoretical and experimental, are discussed and further investigations suggested.

Comparison between empirical formulae of intake vortices

The hydrodynamic properties of free surface vortices at hydraulic intakes were investigated. Based on the axisymmetric Navier-Stokes equations and empirical assumptions, two sets of formulations for the velocity distributions and the free surface profiles are proposed and validated against measurements available in the literature. Compared with previous formulae, the modifications based on Mih's formula are found to greatly improve the agreement with the experimental data. Physical model tests were also conducted to study the intake vortex of the Xiluodu hydroelectric project in China. The proposed velocity distribution formula was applied to the solid boundary as considered by the method of images. A good agreement was again observed between the prediction and the measurements. © 2011 International Association for Hydro-Environment Engineering and Research.

Shallow water equations: Magic and limitations

D Liang from Cambridge University explains the shallow water equations and their applications to the dam-break and other steep-fronted flow modeling. They assume that the horizontal scale of the flow is much greater than the vertical scale, which means the flow is restricted within a thin layer, thus the vertical momentum is insignificant and the pressure distribution is hydrostatic. The left hand sides of the two momentum equations represent the acceleration of the fluid particle in the horizontal plane. If the fluid acceleration is ignored, then the two momentum equations are simplified into the so-called diffusion wave equations. In contrast to the SWEs approach, it is much less convenient to model floods with the Navier-Stokes equations. In conventional computational fluid dynamics (CFD), cumbersome treatments are needed to accurately capture the shape of the free surface. The SWEs are derived using the assumptions of small vertical velocity component, smooth water surface, gradual variation and hydrostatic pressure distribution.

X-ray observation of micro-failures in granular piles approaching an avalanche

An X-ray imaging technique is used to probe the stability of 3-dimensional granular packs in a slowly rotating drum. Well before the surface reaches the avalanche angle, we observe intermittent plastic events associated with collective rearrangements of the grains located in the vicinity of the free surface. The energy released by these discrete events grows as the system approaches the avalanche threshold. By testing various preparation methods, we show that the pre-avalanche dynamics is not solely controlled by the difference between the free surface inclination and the avalanche angle. As a consequence, the measure of the pre-avalanche dynamics is unlikely to serve as a tool for predicting macroscopic avalanches.

Modal stability theory

This article contains a review of modal stability theory. It covers local stability analysis of parallel flows including temporal stability, spatial stability, phase velocity, group velocity, spatio-temporal stability, the linearized Navier-Stokes equations, the Orr-Sommerfeld equation, the Rayleigh equation, the Briggs-Bers criterion, Poiseuille flow, free shear flows, and secondary modal instability. It also covers the parabolized stability equation (PSE), temporal and spatial biglobal theory, 2D eigenvalue problems, 3D eigenvalue problems, spectral collocation methods, and other numerical solution methods. Computer codes are provided for tutorials described in the article. These tutorials cover the main topics of the article and can be adapted to form the basis of research codes. Copyright © 2014 by ASME.

Two opposite gradients of hole density in as-grown and annealed (Ga,Mn)As layers

The depth distribution of the hole density p in 500 nm-thick (Ga,Mn)As layers is investigated. From Raman scattering spectra, it is found that the gradients of p are opposite in the as-grown and annealed layers. At the region around the free surface, with increasing etching depth, p significantly increases in the as-grown layer; however, p decreases distinctly in the annealed layer. Then, in the bulk, p becomes almost homogeneous for both cases. The etching-depth dependence of Curie temperature obtained from magnetic measurements is in agreement with the distribution characterization of p. These results suggest that annealing induces outdiffusion of Mn interstitials towards the free surface, and incomplete outdiffusion during the growth leads to an accumulation of Mn interstitials around the free surface of the as-grown (Ga,Mn)As. (c) 2006 Elsevier B.V. All rights reserved.

Study on the oxygen concentration reduction in heavily Sb-doped silicon

It was determined that oxygen concentration in heavily Sb-doped silicon was about 40% lower than that in the lightly doped Czochralski grown silicon and decreased with increasing content of Sb by means of coincident elastic recoil detection analysis. Through thermodynamic calculation, the oxygen loss by evaporation from the free surface of melt is only due to the formation of SiO, and Sb2O3 evaporation can be neglected. The basic reason for oxygen concentration reduction in heavily Sb-doped CZSi was that oxygen solubility decreased when element Sb with larger radius doped degenerately into silicon crystal. (C) 1999 Elsevier Science B.V. All rights reserved.

Effect of Annealing on Structural and Magnetic Properties of a Thick (Ga,Mn)As Layer

We investigate effects of annealing on magnetic properties of a thick (Ga,Mn)As layer, and find a dramatic increase of the Curie temperature from 65 to 115 K by postgrowth annealing for a 500-nm (Ga,Mn)As layer. Auger electron spectroscopy measurements suggest that the increase of the Curie temperature is mainly due to diffusion of Mn interstitial to the free surface. The double-crystal x-ray diffraction patterns show that the lattice constant of (Ga,Mn)As decreases with increasing annealing temperature. As a result, the annealing induced reduction of the lattice constant is mainly attributed to removal of Mn interstitial.

Thermal effects on Rayleigh-Marangoni-Benard instability in a system of superposed fluid and porous layers

Thermal effects of the heat transfer at free surface (represented by Biot number) on the Rayleigh-Marangoni-Benard instability in a system of liquid-porous layers with top free surface are investigated numerically. The results indicate that this thermal effect can evidently lead to the mode transition of convection, which is overlooked in previous works. (C) 2010 Elsevier Ltd. All rights reserved.

Hole nucleation and growth induced by crystallization and microphase separation of thin semicrystalline diblock copolymer films

We have investigated the hole nucleation and growth induced by crystallization of thin crystalline-coil diblock copolymer films. Semicrystalline rodlike assemblies from neutral/selective binary solvent are used as seeds to nucleate crystallization at temperatures above the glass transition temperature (T-g) but below melting point (T-m). The crystallization of nanorods drives neighboring copolymer chains to diffuse into the growing nanorods. Depletion of copolymer chains yields hole nucleation and growth at the edge of the nanorods. Simultaneously, the polymer chains unassociated into the nanorods were oriented by induction from the free surface and the substrate, leading to limitation of the hole depth to the lamellar spacing, similar to20 nm. The holes, as well as the nanorods, grow as t(alpha), where t is the annealing time and a crossover in the exponent a. is found. The orientation and stretching of the copolymer chains by the surface and interface are believed to accelerate the crystallization, and in turn, the latter accelerates the growth rate of the holes. At T > T-m, the grains melt and the copolymer chains relax and flow into the first layer of the film.

Morphology development of ultrathin symmetric diblock copolymer film via solvent vapor treatment

We have followed the time development of the microdomain structure in symmetric diblock copolymer poly(styrene-b-methyl methacrylate), P(S-b-MMA), ultrathin films via PMMA-selective solvent vapor treatment by atomic force microscopy (AFM). After preparation on a substrate preferentially attracting the PMMA block, PS forms a continuous layer at a film's free surface. With subsequent solvent vapor treatment, the film gradually shows a well-ordered hexagonally packed nanocylinders structure. It is shown that only when the film thickness is less than the 1/2L(0) (lamellar repeat spacing), and exposed to PMMA block selective solvent for an appropriate time, can the well-ordered hexagonally packed nanocylinders form. On an extended solvent vapor treatment, a mixed morphology containing nanocylinders and stripes appears, followed by the striped morphologies. When the annealing time is long enough, the film comes back to the flat surface again, however, with PMMA instead of PS dominating the free surface.

Boundary effect of relief structure on crystallization of diblock copolymer in thin films

In this Letter, crystal growth of a symmetric crystalline-amorphous diblock copolymer, poly(styrene-b-epsilon-caprolactone) (PS-b-PCL), in thin films was investigated by atomic force microscopy (AFM), Relief structures of holes and islands were formed during annealing the film at the molten state, and the in situ observation of subsequent crystal growth at room temperature indicated that the crystals were preferred to occur at the edge of holes or islands and grew into the interior area. It was concluded that the stretched PCL blocks at the edge of relief structures, caused by material transportation or deformation of the interface, could act as nucleation agents during polymer crystallization. The crystal growth rate of individual lamellae varied both from lamellae to lamellae and in time, but the area occupied by crystals increased constantly with time. At 22 degreesC, the growth rate was 1.2 x 10(-2) mum(2)/min with the scan size 2 x 2 mum(2).

Molecular and supramolecular deformations and disclinations in a liquid crystalline copolyether thin films under an electrostatic field

An alignment study of a liquid crystalline copolyether TPP-7/11(5/5) thin films has been carried out in a 10 kV . cm(-1) electrostatic field parallel to the thin film surface normal. This copolyether possesses a negative dielectric anisotropy. The chain molecules are homogeneously aligned in the electric field and they form two-dimensionally ordered lamellae in a tilted columnar phase when the samples were cooled to room temperature. It is observed that the chain molecules are splayed to form bent lamellae and the chain direction is perpendicular to the tangential direction of the lamellar surfaces. These lamellae thus become replicas of the chain orientation, Due to the flexoelectric effect and density fluctuation on the thin film free surface, disclinations having topological strength s = 1, c = pi /4 and defect walls form. These s = 1 disclinations possesses both left- and right-handednesses. Discussion of the defect formations have been attempted.