1,721,030 research outputs found
Fixed-Point Algorithms for Inverse Problems in Science and Engineering
No full text"Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational
X-ray diffraction microscopy
No full textX-ray diffraction phenomena have been used for decades to study matter at the nanometer and subnanometer scales. X-ray diffraction microscopy uses the far-field scattering of coherent X-rays to form the 2D or 3D image of a scattering object in a way that resembles crystallography. In this review, we describe the main principles, benefits, and limitations of diffraction microscopy. After sampling some of the milestones of this young technique and its close variants, we conclude with a short assessment of the current state of the field. Copyright © 2010 by Annual Reviews. All rights reserved
X-Ray Fluctuation Correlation Analysis: Single-Particle Structure And Short-Range Orientational Order
No full textSpatial correlations of X-ray scattering intensity have been applied in determining (1) the structure of single particles, and (2) local orientational order in disordered systems. While the mathematical treatment of diffraction data is almost identical in both cases, vastly different theories have been used to interpret the results in the two regimes. In (1), theories presented by Kam, Kirian, Saldin, and co-workers begin with the assumption that interference effects can be neglected in dilute systems. Interference effects at finite densities were not studied. On the other hand, in (2), the theory presented by Wochner, Altarelli, Kurta, and coworkers explicitly accounts for interference effects in dense systems. However, in this theory, physical interpretation of the data is difficult, and has progressed only slightly beyond phenomenological descriptions. We have developed an overarching 2D theory for intensity correlation analysis, merging ideas from theories in both (1) and (2), with mathematical simplicity close to Kirian's theory. A book-keeping device has also been developed, in which intensity correlations are represented by a graph expansion. Ensembleaveraging rules have been laid down to enable the calculation and interpretation of individual contributions to signal and noise. Key results on the effects of interference in single-particle structure determination have been verified in simulations. Through our new theory, we have also performed a preliminary assessment of the feasibility of studying orientational order in ambient water
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
UNDERSTANDING AND TUNING THE RHEOLOGY OF DENSE SUSPENSIONS VIA ITS MICROSTRUCTURE
No full text241 pagesColloidal suspensions consisting of solid particles in a fluid are ubiquitous in industry and everyday life. The flow properties of these materials are governed not just by the properties of the individual solvent and the particles, but also by the microstructure formed under flow. In this thesis, we show how we can understand and tune the flow properties of colloidal suspensions by studying and altering the microstructure, both at large flow rates and under confinement. At high flow rates, dense suspensions undergo shear thickening or an increase in viscosity with increasing stress. The microstructural change driving this increase is the formation of frictional force chains between the particles in these systems. Here we show that the viscosity of shear thickening suspensions can be decreased and tuned by applying orthogonal shear flows and acoustic perturbations that disrupt these force chains. By carefully tuning the duration of the perturbations and the applied flows we can generate viscosity metamaterials, which display different viscosities when probed at different time scales. As these protocols rely on altering the microstructure, it is important to understand the spatial distribution of the force network in shear thickening suspensions. We demonstrate a new technique, where we measure the instantaneous stress response after changing the direction of shear to determine the angular stress distribution. These multidirectional flows used to probe and manipulate the suspension leads us to develop a universal scaling framework that not only captures steady state shear thickening but also orthogonal superimposed perturbations and can easily be extended to other shear flows. Moreover, the scaling framework elucidates the close connection between shear thickening and critical phenomena, opening the door to importing the vast knowledge of equilibrium statistical mechanics into shear thickening. Finally, we focus on suspensions under confinement, where the presence of boundaries leads to numerous different microstructures. We study the role played by these structures in altering the forces between the particles and the resultant suspension viscosity both at low and high shear rates. Together, these studies elucidate the role of the microscale particle arrangements on the suspension viscosity and will be important for future work ranging from studying the statistical physics of shear thickening and yielding in amorphous materials to engineering fluids with specific flow properties
INVESTIGATION OF ADVANCED IMAGE RECONSTRUCTION ALGORITHMS FOR ELECTRON MICROSCOPY
No full textAberration-corrected optics have made transmission electron microscopy a widespread and essential tool for 2D/3D material characterization at the atomic scale. With the rapid development of hardware and novel experimental techniques, there is an increasing demand for advanced algorithms to work with new experimental data or improve existing techniques. In this dissertation, we investigate a variety of image reconstruction algorithms for tomography and ptychography - two fast growing areas in electron microscopy. Using experimental and simulated data, we examine the limitations of advanced reconstruction algorithms and propose new methods to improve existing methods. Chapter 1 provides an overview of transmission electron microscopy and introduces some basic concepts in imaging science. Chapter 2 takes a more in-depth discussion of elastic scattering in STEM and how beam propagation can be described analytically and computationally. The next two chapters focus on electron tomography, a technique that reconstructs the 3D structure of the object. Chapter 3 describes the experimental setup and demonstrates an efficient Fourier-based reconstruction framework that works well with novel experimental techniques, including dual-axis tomography and through-focal tomography. In Chapter 4, we investigate the popular sparsity-exploiting reconstruction algorithms - exploring their practical limitations in the context of electron tomography. Chapter 5 introduces electron ptychography, a diffractive imaging technique that is enabled by the recent development of a high dynamic range detector. Here we demonstrate a full-field ptychographic reconstruction that doubles the spatial resolution of the traditional lens limitations. Finally, in Chapter 6 we further study the practical limitations of ptychography and propose new strategies for reconstructions
Dealings with Data Physics, Machine Learning and Geometry
Full text linkCollecting and interpreting data is key to developing an understanding of the physical underpinnings of observable events. As such, questions of how to generate, curate and otherwise wrangle data become central as systems of interest become increasingly difficult to access experimentally and the sheer quantity of raw information explodes. The data explored in this dissertation covers a wide range of sources and methods. On the more traditional end, we explore simulation data of the two dimensional non-equilibrium random-field Ising model which we treat with a novel analytic normal form theory of the Renormalization Group. Branching out from condensed matter, we explore several machine learning and sampling methods in various contexts. The machine learning projects in particular include three lines of investigation: an unsupervised machine learning analysis of sectors of the economy extracted from stock return data, an analysis of the computational neural networks successfully applied to experimental ATLAS data in a recent Kaggle challenge, and an exploration of the geometrical underpinnings of canonical neural networks using a Jeffrey’s Prior sampling of trained networks
L2 Minimal Algorithms
No full text43 pagesWe consider putting certain tensors into forms with approximately minimum L2 norm. These tensors describe strategies for computing linear or bilinear maps. Such forms are of interest from a practical perspective because they are particularly numerically stable. They are of interest from a theoretical perspective because they may be unique up to certain orthogonal or unitary transformations. The main tensors of interest represent (commutative, real) "matrix multiplication algorithms" or "bilinear algorithms." We explain how an algorithm's L2 minimal form might be thought of as optimally stable and as close to attaining the nuclear norm as possible. We demonstrate an algorithm "Strop" that has minimum L2 norm among all rank 7 algorithms for 2x2 matrix multiplication. This leads to better error for typical large matrices than Strassen, at the cost of more operations. Putting Strassen's (or any such) algorithm into this form requires "only" a convex optimization problem on positive definite matrices. In some situations, this optimization enables us to check when algorithms are equivalent in a natural sense. As a stepping stone we consider L2 minimal forms for analogous "linear algorithms." Such forms have been the subject of extensive study by invariant theorists, but are less known in other circles. We give simple examples of when the existence of these forms, and their use in equivalence testing, is apparent from an optimization perspective
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