Monte Carlo Simulations of Silica Polymerization and Network Formation

2011 ◽  
Vol 115 (32) ◽  
pp. 15988-16000 ◽  
Author(s):  
Ateeque Malani ◽  
Scott M. Auerbach ◽  
Peter A. Monson
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Network Formation ◽  
Silica Polymerization

scholarly journals Approximate Variational Estimation for a Model of Network Formation

2021 ◽  
pp. 1-30
Author(s):  
Angelo Mele ◽  
Lingjiong Zhu
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Network Formation ◽  
Mean Field ◽  
Approximation Error ◽  
Mean Field Approximation ◽  
Estimation Methods ◽  
Exponential Random Graph Models ◽  
Deterministic Method ◽  
Normalizing Constant

Abstract We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations, however convergence may be exponentially slow. We propose a deterministic method, based on a variational mean-field approximation of the ERGM's normalizing constant. We compute lower and upper bounds for the approximation error for any network size, adapting nonlinear large deviations results. This translates into bounds on the distance between true likelihood and mean-field likelihood. Monte Carlo simulations suggest that in practice our deterministic method performs better than our conservative theoretical approximation bounds imply, for a large class of models.

Low-voltage EDS of magnesium ferrite Dendrites in a FEG-SEM

1996 ◽  
Vol 54 ◽  
pp. 478-479
Author(s):  
Matthew T. Johnson ◽  
Ian M. Anderson ◽  
Jim Bentley ◽  
C. Barry Carter
Keyword(s):  
Monte Carlo ◽  
Quantitative Analysis ◽  
Monte Carlo Simulations ◽  
Cross Section ◽  
Spatial Resolution ◽  
Low Voltage ◽  
Magnesium Ferrite ◽  
X Ray ◽  
Interaction Volume ◽  
Ferrite Spinel

Energy-dispersive X-ray spectrometry (EDS) performed at low (≤ 5 kV) accelerating voltages in the SEM has the potential for providing quantitative microanalytical information with a spatial resolution of ∼100 nm. In the present work, EDS analyses were performed on magnesium ferrite spinel [(MgxFe1−x)Fe2O4] dendrites embedded in a MgO matrix, as shown in Fig. 1. spatial resolution of X-ray microanalysis at conventional accelerating voltages is insufficient for the quantitative analysis of these dendrites, which have widths of the order of a few hundred nanometers, without deconvolution of contributions from the MgO matrix. However, Monte Carlo simulations indicate that the interaction volume for MgFe2O4 is ∼150 nm at 3 kV accelerating voltage and therefore sufficient to analyze the dendrites without matrix contributions.Single-crystal {001}-oriented MgO was reacted with hematite (Fe2O3) powder for 6 h at 1450°C in air and furnace cooled. The specimen was then cleaved to expose a clean cross-section suitable for microanalysis.

MONTE CARLO SIMULATIONS OF ELECTRON DRIFT VELOCITIES IN THE NOBLE GASES AND THEIR MIXTURES

1979 ◽  
Vol 40 (C7) ◽  
pp. C7-63-C7-64
Author(s):  
A. J. Davies ◽  
J. Dutton ◽  
C. J. Evans ◽  
A. Goodings ◽  
P.K. Stewart
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Noble Gases ◽  
Electron Drift
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