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A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions
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Stabilized linear semi-implicit schemes for the nonlocal Cahn–Hilliard equation
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Ab-Initio Investigation of Finite Size Effects in Rutile Titania Nanoparticles with Semilocal and Nonlocal Density Functionals
In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and electronic gap of rutile titania nanoparticles with particle size. The surface energies and electronic gaps are calculated for cuboidal particles with minimum dimension ranging from 3.7 Angstrom (24 atoms) to 10.3 Angstrom (384 atoms) using a highly-parallel real-space DFT code to enable hybrid level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy, and evaluate the influence of defects on electronic gap and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 Angstrom. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the electronic gap and DOS is highly dependent on the shape and size of these particles. Furthermore, the DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the electronic gap play a key role in determining the eigen value distribution of nanoparticles and the electronic gap does not converge to the bulk limit for the particle sizes investigated.
Nonlocality and the critical Reynolds numbers of the minimum state magnetohydrodynamic turbulence
Magnetohydrodynamic (MHD) systems can be strongly nonlinear (turbulent) when their kinetic and magnetic Reynolds numbers are high, as is the case in many astrophysical and space plasma flows. Unfortunately these high Reynolds numbers are typically much greater than those currently attainable in numerical simulations of MHD turbulence. A natural question to ask is how can researchers be sure that their simulations have reproduced all of the most influential physics of the flows and magnetic fields? In this paper, a metric is defined to indicate whether the necessary physics of interest has been captured. It is found that current computing resources will typically not be sufficient to achieve this minimum state metric.
Analysis of nonlocal phonon thermal conductivity simulations showing the ballistic to diffusive crossover
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Temperature in a Peierls-Boltzmann treatment of nonlocal phonon heat transport
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Ab initio translationally invariant nonlocal one-body densities from no-core shell-model theory
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Neutron Skin Thickness of Ca 48 from a Nonlocal Dispersive Optical-Model Analysis
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A Unified Theory of Fractional Nonlocal and Weighted Nonlocal Vector Calculus.
Abstract not provided.
Variable Nonlocal Length Scale in a Peridynamic Body with Applications to Local-Nonlocal Coupling.
Abstract not provided.
Multiscale Finite Elements for Nonlocal Mechanics Models and Local-Nonlocal Coupling.
Abstract not provided.
Multiscale Finite Elements for Nonlocal Materials Models and Local-Nonlocal Coupling.
Abstract not provided.
NONLOCAL MODELS with APPROXIMATE NONLOCAL NEIGHBORHOODS: towards fast FEM.
Abstract not provided.
A UNIFIED DATA-DRIVEN framework for NONLOCAL OPERATORS: from local to nonlocal to fractional.
Abstract not provided.