Adaptive Embedded LES of the NASA Hump

A scheme for adaptive embedded LES is proposed which automatically determines boundaries for LES regions in a hybrid LES-RANS computation, with the goal of minimizing the LES part of the computation for maximum accuracy with minimum cost. The model-invariant hybrid formulation enables this scheme through greater flexibility in the placement of RANS-LES transitions. An adaptive embedded large-eddy simulation is carried out for the NASA hump test case and adaptive meshing is added to show how additional adaptive features may be controlled by the adaptive hybrid scheme

A scanning tunnelling microscopy study of C and N adsorption phases on the vicinal Ni(100) surfaces Ni(810) and Ni(911)

The influence of N and C chemisorption on the morphology and local structure of nominal Ni(810) and Ni(911) surfaces, both vicinal to (100) but with [001] and 011¯ step directions, respectively, has been investigated using scanning tunnelling microscopy (STM) and low energy electron diffraction. Ni(911) undergoes substantial step bunching in the presence of both adsorbates, with the (911)/N surface showing (411) facets, whereas for Ni(810), multiple steps 2–4 layers high are more typical. STM atomic-scale images show the (2×2)pg ‘clock’ reconstruction on the (100) terraces of the (810) surfaces with both C and N, although a second c(2×2) structure, most readily reconciled with a ‘rumpling’ reconstruction, is also seen on Ni(810)/N. On Ni(911), the clock reconstruction is not seen on the (100) terraces with either adsorbate, and these images are typified by protrusions on a (1×1) mesh. This absence of clock reconstruction is attributed to the different constraints imposed on the lateral movements of the surface Ni atoms adjacent to the up-step edge of the terraces with a [011] step direction

Renormalisation-theoretic analysis of non-equilibrium phase transitions II: The effect of perturbations on rate coefficients in the Becker-Doring equations

We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. In particular, we investigate the Becker-Doring (BD) equations, originally formulated to describe and analyse non-equilibrium phase transitions, but more recently generalised to describe a wide range of physicochemical problems. We consider here rate coefficients which depend on the cluster size in a power-law fashion, but now perturbed by small amplitude random noise. Power-law rate coefficients arise naturally in the theory of surface-controlled nucleation and growth processes. The noisy perturbations on these rates reflect the effect of microscopic variations in such mean-field coefficients, thermal fluctuations and/or experimental uncertainties. In the present paper we generalise our earlier work that identified the nine classes into which all dynamical behaviour must fall by investigating how random perturbations of the rate coefficients influence the steady-state and kinetic behaviour of the coarse-grained, renormalised system. We are hence able to confirm the existence of a set of up to nine universality classes for such BD systems.Comment: 30 pages, to appear in J Phys A Math Ge

Identifying the Azobenzene/Aniline reaction intermediate on TiO2-(110) : a DFT Study

Density functional theory (DFT) calculations, both with and without dispersion corrections, have been performed to investigate the nature of the common surface reaction intermediate that has been shown to exist on TiO2(110) as a result of exposure to either azobenzene (C6H5N═NC6H5) or aniline (C6H5NH2). Our results confirm the results of a previous DFT study that dissociation of azobenzene into two adsorbed phenyl imide (C6H5N) fragments, as was originally proposed, is not energetically favorable. We also find that deprotonation of aniline to produce this surface species is even more strongly energetically disfavored. A range of alternative surface species has been considered, and while dissociation of azobenzene to form surface C6H4NH species is energetically favored, the same surface species cannot form from adsorbed aniline. On the contrary, adsorbed aniline is much the most stable surface species. Comparisons with experimental determinations of the local adsorption site, the Ti–N bond length, the molecular orientation, and the associated C 1s and N 1s photoelectron core level shifts are all consistent with the DFT results for adsorbed aniline and are inconsistent with other adsorbed species considered. Possible mechanisms for the hydrogenation of azobenzene required to produce this surface species are discussed

Renormalisation-theoretic analysis of non-equilibrium phase transitions I: The Becker-Doring equations with power law rate coefficients

We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. We investigate the Becker-Dorging equations, originally formulated to describe and analyse non-equilibrium phase transitions, and more recently generalised to describe a wide range of physicochemical problems. In the present paper we analyse how the systematic coarse-graining renormalisation of the \BD system of equations affects the aggregation and fragmentation rate coefficients. We consider the case of power-law size-dependent cluster rate coefficients which we show lead to only three classes of system that require analysis: coagulation-dominated systems, fragmentation-dominated systems and those where coagulation and fragmentation are exactly balanced. We analyse the late-time asymptotics associated with each class.Comment: 18 pages, to appear in J Phys A Math Ge

CLIWOC multilingual meteorological dictionary

This dictionary is the first attempt to express the wealth of archaic logbook wind force terms in a form that is comprehensible to the modern-day reader. Oliver and Kington (1970) and Lamb (1982) have drawn attention to the importance of logbooks in climatic studies, and Lamb (1991) offered a conversion scale for early eighteenth century English wind force terms, but no studies have thus far pursued the matter to any greater depth. This text attempts to make good this deficiency, and is derived from the research undertaken by the CLIWOC project1 in which British, Dutch, French and Spanish naval and merchant logbooks from the period 1750 to 1850 were used to derive a global database of climatic information. At an early stage in the project it was apparent that many of the logbook weather terms, whilst conforming to a conventional vocabulary, possessed meanings that were unclear to twenty-first century readers or had changed over time. This was particularly the case for the important element of wind force; but no special plea is entered for the evolution in nautical vocabulary, which often reflected more wide-ranging changes in the respective native languages.The key objective was to translate the archaic vocabulary of the late eighteenth and early nineteenth century mariner into expressions directly comparable with the Beaufort Scale (see Appendix I). Only then could the projects scientific programme be embarked upon. This dictionary is the result of the largest undertaking into logbook studies that has yet been carried out. Several thousand logbooks from British, Dutch, French and Spanish archives were examined, and the exercise offered a unique opportunity to explore the vocabulary of the one hundred year period beginning in 1750. The logbooks from which the raw data have been abstracted range widely across the North and South Atlantic and the Indian Oceans. Only the Pacific, largely in consequence of the paucity of regular naval activity in that area, is not well represented. The range of climates encountered in this otherwise wide geographic domain gives ample opportunity for the full range of the mariners nautical weather vocabulary to be assessed, from the calms of the Equatorial regions, through the gales of the mid-latitude systems to the fearsome storms of the tropical latitudes. The Trade Winds belts, the Doldrums, the unsettled mid-latitudes, even the icy wastes of the high latitudes, are all embraced in this study. It is not here intended to pass any judgements on the climatological record of the logbooks, and this text seeks only to provide a means of understanding archaic wind force terms and, other than to indicate those items that were not commonly used, no information is given on the frequency with which different terms appeared in the logbooks. Attention is, furthermore, confined to Dutch, English, French and Spanish because these once great imperial powers were the only nations able to support wide-ranging ocean-going fleets with their attendant collections of logbooks and documents over this long period of time. The work is offered to the wider academic community in the hope that they will prove to be of as much value as it has been to the CLIWOC team

A Multi-scale Approach for Simulations of Kelvin Probe Force Microscopy with Atomic Resolution

The distance dependence and atomic-scale contrast observed in nominal contact potential difference (CPD) signals recorded by KPFM on surfaces of insulating and semiconducting samples, have stimulated theoretical attempts to explain such effects. We attack this problem in two steps. First, the electrostatics of the macroscopic tip-cantilever-sample system is treated by a finite-difference method on an adjustable nonuniform mesh. Then the resulting electric field under the tip apex is inserted into a series of atomistic wavelet-based density functional theory (DFT) calculations. Results are shown for a realistic neutral but reactive silicon nano-scale tip interacting with a NaCl(001) sample. Bias-dependent forces and resulting atomic displacements are computed to within an unprecedented accuracy. Theoretical expressions for amplitude modulation (AM) and frequency modulation (FM) KPFM signals and for the corresponding local contact potential differences (LCPD) are obtained by combining the macroscopic and atomistic contributions to the electrostatic force component generated at the voltage modulation frequency, and evaluated for several tip oscillation amplitudes A up to 10 nm. Being essentially constant over a few Volts, the slope of atomistic force versus bias is the basic quantity which determines variations of the atomic-scale LCPD contrast. Already above A = 0.1 nm, the LCPD contrasts in both modes exhibit almost the same spatial dependence as the slope. In the AM mode, this contrast is approximately proportional to $A^{-1/2}$, but remains much weaker than the contrast in the FM mode, which drops somewhat faster as A is increased. These trends are a consequence of the macroscopic contributions to the KPFM signal, which are stronger in the AM-mode and especially important if the sample is an insulator even at sub-nanometer separations where atomic-scale contrast appears.Comment: 19 pages, 13 figure

Belmont Criminal Law Journal Symposium 2017: Judicial Panel

Transcript of the Judicial Panel given during the 2017 Symposium featuring Chief Justice Jeffrey S. Bivins, Judge Joseph A. Woodruff, Judge Timothy L. Easter, and Judge Angelita B. Dalton

Optimal Principal Component Analysis in Distributed and Streaming Models

We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we want to output an $m \times k$ orthonormal matrix $U$ for which $$|| A - U U^T A ||_F^2 \le \left(1 + \epsilon \right) \cdot || A - A_k||_F^2,$$ where $A_k \in R^{m \times n}$ is the best rank-$k$ approximation to $A$. This paper provides improved algorithms for distributed PCA and streaming PCA.Comment: STOC2016 full versio