Particle displacements in the elastic deformation of amorphous materials: local fluctuations vs. non-affine field

We study the local disorder in the deformation of amorphous materials by decomposing the particle displacements into a continuous, inhomogeneous field and the corresponding fluctuations. We compare these fields to the commonly used non-affine displacements in an elastically deformed 2D Lennard-Jones glass. Unlike the non-affine field, the fluctuations are very localized, and exhibit a much smaller (and system size independent) correlation length, on the order of a particle diameter, supporting the applicability of the notion of local "defects" to such materials. We propose a scalar "noise" field to characterize the fluctuations, as an additional field for extended continuum models, e.g., to describe the localized irreversible events observed during plastic deformation.Comment: Minor corrections to match the published versio

A survey of statistical network models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference

Computational Thinking in Mathematics and Computer Science: What Programming Does to Your Head

How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and mathematics come together to inform and shape our interpretation of a classical result in mathematics: Euclid\u27s algorithm that finds the greatest common divisor of two integers

A Pre-Proposal - Summer Faculty Careers Institute for Ph.D. students, Postdoctoral Fellows, and Junior Faculty

http://deepblue.lib.umich.edu/bitstream/2027.42/88564/1/2003_FIPSE_PFF_7.2.pd

Stress response inside perturbed particle assemblies

The effect of structural disorder on the stress response inside three dimensional particle assemblies is studied using computer simulations of frictionless sphere packings. Upon applying a localised, perturbative force within the packings, the resulting {\it Green's} function response is mapped inside the different assemblies, thus providing an explicit view as to how the imposed perturbation is transmitted through the packing. In weakly disordered arrays, the resulting transmission of forces is of the double-peak variety, but with peak widths scaling linearly with distance from the source of the perturbation. This behaviour is consistent with an anisotropic elasticity response profile. Increasing the disorder distorts the response function until a single-peak response is obtained for fully disordered packings consistent with an isotropic description.Comment: 8 pages, 7 figure captions To appear in Granular Matte

Optical characteristics of nanocrystalline AlxGa1-xN thin films deposited by hollow cathode plasma-assisted atomic layer deposition

Cataloged from PDF version of article.Gallium nitride (GaN), aluminum nitride (AlN), and AlxGa(1-x)N films have been deposited by hollow cathode plasma-assisted atomic layer deposition at 200 degrees C on c-plane sapphire and Si substrates. The dependence of film structure, absorption edge, and refractive index on postdeposition annealing were examined by x-ray diffraction, spectrophotometry, and spectroscopic ellipsometry measurements, respectively. Well-adhered, uniform, and polycrystalline wurtzite (hexagonal) GaN, AlN, and AlxGa1-xN films were prepared at low deposition temperature. As revealed by the x-ray diffraction analyses, crystallite sizes of the films were between 11.7 and 25.2 nm. The crystallite size of as-deposited GaN film increased from 11.7 to 12.1 and 14.4 nm when the annealing duration increased from 30 min to 2 h (800 degrees C). For all films, the average optical transmission was similar to 85% in the visible (VIS) and near infrared spectrum. The refractive indices of AlN and AlxGa1-xN were lower compared to GaN thin films. The refractive index of as-deposited films decreased from 2.33 to 2.02 (lambda = 550 nm) with the increased Al content x (0 400 nm). Postdeposition annealing at 900 degrees C for 2 h considerably lowered the refractive index value of GaN films (2.33-1.92), indicating a significant phase change. The optical bandgap of as-deposited GaN film was found to be 3.95 eV, and it decreased to 3.90 eV for films annealed at 800 degrees C for 30 min and 2 h. On the other hand, this value increased to 4.1 eV for GaN films annealed at 900 degrees C for 2 h. This might be caused by Ga2O3 formation and following phase change. The optical bandgap value of as-deposited AlxGa1-xN films decreased from 5.75 to 5.25 eV when the x values decreased from 1 to 0.68. Furthermore, postdeposition annealing did not affect the bandgap of Al-rich films. (C) 2014 American Vacuum Society

Hollow cathode plasma-assisted atomic layer deposition of crystalline AIN, GaN and AI Ga1- N thin films at low temperatures

Cataloged from PDF version of article.The authors report on the use of hollow cathode plasma for low-temperature plasma-assisted atomic layer deposition (PA-ALD) of crystalline AlN, GaN and AlxGa1 xN thin films with low impurity concentrations. Depositions were carried out at 200 C using trimethylmetal precursors and NH3 or N2/H2 plasma. X-ray photoelectron spectroscopy showed the presence of 2.5–3 at.% O in AlN and 1.5–1.7 at.% O in GaN films deposited using NH3 and N2/H2 plasma, respectively. No C impurities were detected within the films. Secondary ion mass spectroscopy analyses performed on the films deposited using NH3 plasma revealed the presence of O, C (both <1 at.%), and H impurities. GIXRD patterns indicated polycrystalline thin films with wurtzite crystal structure. Hollow cathode PA-ALD parameters were optimized for AlN and GaN thin films using N2/H2 plasma. Trimethylmetal and N2/H2 saturation curves evidenced the selflimiting growth of AlN and GaN at 200 C. AlN exhibited linear growth with a growth per cycle (GPC) of 1.0 A. For GaN, the GPC decreased with the increasing number of deposition cycles, indicating ˚ substrate-enhanced growth. The GPC calculated from a 900-cycle GaN deposition was 0.22 A. ˚ Ellipsometric spectra of the samples were modeled using the Cauchy dispersion function, from which the refractive indices of 59.2 nm thick AlN and 20.1 nm thick GaN thin films were determined to be 1.94 and 2.17 at 632 nm, respectively. Spectral transmission measurements of AlN, GaN and AlxGa1 xN thin films grown on double side polished sapphire substrates revealed near-ideal visible transparency with minimal absorption. Optical band edge values of the AlxGa1 xN films shifted to lower wavelengths with the increasing Al content, indicating the tunability of band edge values with the alloy composition

Pupil Control Ideology and Teacher Influence in the Classroom

Elementary Educatio