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Partition Density Functional Theory for Semi-Infinite and Periodic SystemsKelsie A. Niffenegger (5930087) 03 January 2019 (has links)
<div>Partition Density Functional Theory (P-DFT) is a formally exact method to find the ground-state energy and density of molecules via self-consistent calculations on isolated fragments. It is being used to improve the accuracy of Kohn-Sham DFT (KS-DFT) calculations and to lower their computational cost. Here, the method has been extended to be applicable to semi-infinite and periodic systems. This extension involves the development of new algorithms to calculate the exact partition potential, a central quantity of P-DFT. A novel feature of these algorithms is that they are applicable to systems of constant chemical potential, and not only to systems of constant electron number. We illustrate our method on one-dimensional model systems designed to mimic metal-atom interfaces and atomic chains. From extensive numerical tests on these model systems, we infer that: 1.) The usual derivative discontinuities of open-system KS-DFT are reduced (but do not disappear completely) when an atom is at a nite distance from a metallic reservoir; 2.) In situations where we do not have chemical potential equalization between fragments of a system, a new constraint for P-DFT emerges which relates the fragment chemical potentials and the combined system chemical potential; 3.) P-DFT is an ideal method for studying charge transfer and fragment interactions due to the correct ensemble treatment of fractional electron charges; 4.) Key features of the partition potential at the metalatom interface are correlated to well-known features of the underlying KS potential; and 5.) When there is chemical potential equalization between an atom and a metal surface it is interacting with, there is strong charge transfer between the metal and atom. In these cases of charge transfer the density response to an innitesimal change in the chemical potential is located almost exclusively around the atom. On the other hand, when the fragment chemical potentials do not equalize, the density response only aects the surface Friedel oscillations in the metal.</div>
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High density urban form : a case study of Quarry Bay, Hong Kong /Tsui, Hon-yung. January 1996 (has links)
Thesis (M.U.D.)--University of Hong Kong, 1997. / Includes bibliographical references (leaves 100-104).
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Nested low-density lattice codes based on non-binary LDPC codesGhiya, Ankit 20 December 2010 (has links)
A family of low-density lattice codes (LDLC) is studied based on Construction-A for lattices. The family of Construction-A codes is already known to contain a large capacity-achieving subset. Parallels are drawn between coset non-binary low-density parity-check (LDPC) codes and nested low-density Construction-A lattices codes. Most of the related research in LDPC domain assumes optimal power allocation to encoded codeword. The source coding problem of mapping message to power optimal codeword for any LDPC code is in general, NP-hard. In this thesis, we present a novel method for encoding and decoding lattice based on non-binary LDPC codes using message-passing algorithms. / text
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Measuring the performance of recent generalized gradient approximations to density functional theory in molecules and solidsRoss, Seth L. 29 June 2011 (has links)
Density functional theory is a successful theory used in physics, chemistry and
nanoscience to describe the ground state properties of solids and molecules. It calculates
ground state energies and related properties by using the density of the valence
electrons as a fundamental variable. In a system of interacting electrons, the electrons
will correlate due to the Pauli exclusion principle, as well as their coulomb
repulsion. This interaction energy is known as the exchange-correlation energy and
is approximated in density functional theory because it is the only unknown in the
energy as a functional of density. The simplest model to approximate this exchangecorrelation
energy is the local density approximation, which only relies on the local
density of the valence electrons at every point. Generalized gradient approximations
are approximations which build upon the local density approximation by also using
the gradient of the local density. Recently, many new versions of the generalized gradient
approximation have been developed to attempt to obtain better energetic and
structural properties either at the same time, or at the expense of the other. In this
study, we examine the performance of these models by calculating the atomization
energy of the AE6 test set. The cohesive energy, lattice constant and bulk modulus of
a four solid test set was also calculated. These calculations were done using ABINIT,
a density functional theory code that uses a pseudopotential model with plane waves
to examine molecules and solids. One of the more recently developed generalized
gradient approximation models, the SOGGA, is tested to compare with the standard
models. The accuracy of using a pseudopotential model is also tested. It was found
that by using a generalized gradient approximation that was better for energy calculations,
the structural property calculations would not be as accurate. The SOGGA
is a functional that approximates structural properties of solids accurately but does
not calculate energies as well. It was also found that using a pseudopotential model
resulted in a 1% difference from the all electron calculations. / Density functional theory -- Molecular data -- Solids -- Second order GGA -- Discussions and conclusions. / Department of Physics and Astronomy
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Bisphosphonate treatment of children and adolescents with osteogenesis imperfecta (OI) : effects on clinical symptoms and bone turnover /Åström, Eva, January 2007 (has links)
Diss. (sammanfattning) Stockholm : Karolinska institutet, 2007. / Härtill 5 uppsatser.
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Residential density and building planning /Tong, Tung. January 1994 (has links)
Thesis (M. Sc.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 76-77).
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Land-use structure and population and employment densities empirical analysis of the Columbus (Ohio) metropolitan area /Lu, Jia. January 2008 (has links)
Thesis (Ph. D.)--Ohio State University, 2008.
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High density urban form a case study of Quarry Bay, Hong Kong /Tsui, Hon-yung. January 1996 (has links)
Thesis (M.U.D.)--University of Hong Kong, 1997. / Includes bibliographical references (leaves 100-104) Also available in print.
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Development density in Hong Kong : living environments vs living quality : a case study of Ap Lei Chau /Cheng, Ka-man, Clement, January 2005 (has links)
Thesis (M. Sc.)--University of Hong Kong, 2005.
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Efficient Estimation of Dynamic Density Functions with Applications in Streaming DataQahtan, Abdulhakim Ali Ali 11 May 2016 (has links)
Recent advances in computing technology allow for collecting vast amount of data that arrive continuously in the form of streams. Mining data streams is challenged by the speed and volume of the arriving data. Furthermore, the underlying distribution of the data changes over the time in unpredicted scenarios. To reduce the computational cost, data streams are often studied in forms of condensed representation, e.g., Probability Density Function (PDF).
This thesis aims at developing an online density estimator that builds a model called KDE-Track for characterizing the dynamic density of the data streams. KDE-Track estimates the PDF of the stream at a set of resampling points and uses interpolation to estimate the density at any given point. To reduce the interpolation error and computational complexity, we introduce adaptive resampling where more/less resampling points are used in high/low curved regions of the PDF. The PDF values at the resampling points are updated online to provide up-to-date model of the data stream. Comparing with other existing online density estimators, KDE-Track is often more accurate (as reflected by smaller error values) and more computationally efficient (as reflected by shorter running time).
The anytime available PDF estimated by KDE-Track can be applied for visualizing the dynamic density of data streams, outlier detection and change detection in data streams. In this thesis work, the first application is to visualize the taxi traffic volume in New York city. Utilizing KDE-Track allows for visualizing and monitoring the traffic flow on real time without extra overhead and provides insight analysis of the pick up demand that can be utilized by service providers to improve service availability. The second application is to detect outliers in data streams from sensor networks based on the estimated PDF. The method detects outliers accurately and outperforms baseline methods designed for detecting and cleaning outliers in sensor data. The third application is to detect changes in data streams. We propose a framework based on Principal Component Analysis (PCA) that reduces the problem of detecting changes in multidimensional data into the problem of detecting changes in the projected data on the principal components. We provide a theoretical analysis, which is support by experimental results to show that utilizing PCA reflects different types of changes in data streams on the projected data over one or more principal components. Our framework is accurate in detecting changes with low computational costs and scales well for high dimensional data.
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