Partition function estimation of Gibbs random field images using Monte Carlo simulations

1993 ◽  
Vol 39 (4) ◽  
pp. 1322-1332 ◽  
Author(s):  
G.G. Potamianos ◽  
J.K. Goutsias
Keyword(s):  
Monte Carlo ◽  
Partition Function ◽  
Monte Carlo Simulations ◽  
Random Field ◽  
Function Estimation ◽  
Gibbs Random Field

THE BOSONIC STRING REPRESENTED AS Φ3 GRAPHS: NEW MONTE-CARLO SIMULATIONS

1990 ◽  
Vol 05 (10) ◽  
pp. 771-785 ◽  
Author(s):  
J. AMBJØRN ◽  
D. BOULATOV ◽  
V. A. KAZAKOV
Keyword(s):  
Monte Carlo ◽  
Partition Function ◽  
Monte Carlo Simulations ◽  
Critical Exponent ◽  
Space Dimension ◽  
Asymptotic Form ◽  
Bosonic String ◽  
Target Space ◽  
Logarithmic Corrections

We discuss a new method for measuring the critical exponent γ for the partition function of the bosonic string. The statistics seems very good and the fit to γconsistent with the assumed asymptotic form for the partition function for dimensions d=1–6. The results are in agreement with analytical results when the target space dimension is d=0, but disagree when d=1. We conjecture that this is due to the appearance of logarithmic corrections to the asymptotic form of the partition function. These corrections might persist for d>1 and might render the determination of γquite difficult.

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.

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