The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the α−x plane of sphere radius ratio α and relative concentration x are at the Kepler lim...
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The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the α−x plane of sphere radius ratio α and relative concentration x are at the Kepler limit α=1, where packings are monodisperse. Utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [S. Torquato and Y. Jiao, Phys. Rev. E 82, 061302 (2010)], we present the most comprehensive determination to date of the phase diagram in (α,x) for the densest binary sphere packings. Unexpectedly, we find many distinct new densest packings.
As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gauss...
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As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based on our previous methods for the linear SchrSdinger equation, for the Schrodinger-Poisson equations, and then check their validity for this weakly-nonlinear system.
We present an algorithm generating a collection of fat arcs which bound the zero set of a given bivariate polynomial in Bernstein-Bezier representation. We demonstrate the performance of the algorithm (in particular t...
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ISBN:
(纸本)9783642116193
We present an algorithm generating a collection of fat arcs which bound the zero set of a given bivariate polynomial in Bernstein-Bezier representation. We demonstrate the performance of the algorithm (in particular the convergence rate) and we apply the results to the computation of intersection curves between implicitly defined algebraic surfaces and rational parametric surfaces.
The key issues in CO2 sequestration monitoring involve accurate monitoring, from the injection stage to prediction & verification, of CO2 movement over time for environmental considerations. A natural non-intrusiv...
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Compressive sensing (CS) is a new approach to simultaneous sensing and compression for sparse and compressible signals. While the discrete Fourier transform has been widely used for CS of frequency-sparse signals, it ...
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A controlled quantum system possesses a search landscape defined by the observable value as a functional of the control field. Within the search landscape, there exist level sets of controls giving the same observable...
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Understanding the interaction between atomic hydrogen and solid tungsten is important for the development of fusion reactors in which proposed tungsten walls would be bombarded with high energy particles including hyd...
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The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model...
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The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model selection for the general case of arbitrary (random or deterministic) design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence- termed as the worst-case coherence and the average coherence-among the columns of a design matrix. It utilizes these two measures of coherence to provide an in-depth analysis of a simple, model-order agnostic one-step thresholding (OST) algorithm for model selection and proves that OST is feasible for exact as well as partial model selection as long as the design matrix obeys an easily verifiable property, which is termed as the coherence property. One of the key insights offered by the ensuing analysis in this regard is that OST can successfully carry out model selection even when methods based on convex optimization such as the lasso fail due to the rank deficiency of the submatrices of the design matrix. In addition, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimally when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio in the measurement system is not too high. Finally, two other key contributions of the paper are that (i) it provides bounds on the average coherence of Gaussian matrices and Gabor frames, and (ii) it extends the results on model selection using OST to low-complexity, model-order agnostic recovery of sparse signals with arbitrary nonzero entries. In particular, this part of the analysis in the paper implies that an Alltop Gabor frame together with OST can successfully carr
We propose a nonlocal kinetic energy density functional (KEDF) for semiconductors based on the expected asymptotic behavior of its susceptibility function. The KEDF’s kernel depends on both the electron density and t...
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We propose a nonlocal kinetic energy density functional (KEDF) for semiconductors based on the expected asymptotic behavior of its susceptibility function. The KEDF’s kernel depends on both the electron density and the reduced density gradient, with an internal parameter formally related to the material’s static dielectric constant. We determine the accuracy of the KEDF within orbital-free density functional theory (DFT) by applying it to a variety of common semiconductors. With only two adjustable parameters, the KEDF reproduces quite well the exact noninteracting KEDF (i.e., Kohn-Sham DFT) predictions of bulk moduli, equilibrium volumes, and equilibrium energies. The two parameters in our KEDF are sensitive primarily to changes in the local crystal structure (such as atomic coordination number) and exhibit good transferability between different tetrahedrally-bonded phases. This local crystal structure dependence is rationalized by considering Thomas-Fermi dielectric screening theory.
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