A lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles

<p style='text-indent:20px;'>In this paper, we proceed as suggested in the final section of [<xref ref-type="bibr" rid="b2">2</xref>] and prove a lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles. This bound turns out to be around <inline-formula><tex-math id="M1">\begin{document}$ 0.02 $\end{document}</tex-math></inline-formula>, which is already physically meaningful, and we perform Monte Carlo simulations to provide a better empirical estimate for this value via entropy production inequalities. This finishes a complete quantitative estimate of the spectral gap of the Kac process.</p>

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Coarse-grained Langevin approximations and spatiotemporal acceleration for kinetic Monte Carlo simulations of diffusion of interacting particles

Chinese Annals of Mathematics Series B ◽

10.1007/s11401-009-0219-x ◽

2009 ◽

Vol 30 (6) ◽

pp. 653-682 ◽

Cited By ~ 2

Author(s):

Sasanka Are ◽

Markos A. Katsoulakis ◽

Anders Szepessy

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Kinetic Monte Carlo ◽

Coarse Grained ◽

Interacting Particles ◽

Kinetic Monte Carlo Simulations

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Exact Cram’er–Rao Lower Bound for Interferometric Phase Estimator

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1004-1005.1419 ◽

2014 ◽

Vol 1004-1005 ◽

pp. 1419-1426

Author(s):

Zhi Jie Mao ◽

Zhi Jun Yan ◽

Hong Wei Li ◽

Jin Meng

Keyword(s):

Monte Carlo ◽

Performance Analysis ◽

Lower Bound ◽

Monte Carlo Simulations ◽

Phase Estimation ◽

Interferometric Phase ◽

Estimation Problems ◽

General Phase ◽

Cramer Rao Lower Bound ◽

Close Form

We are concerned with the problem of interferometric phase estimation using multiple baselines. Simple close-form efficient expressions for computing the Cramer-Rao lower bound (CRLB) for general phase estimation problems is derived. Performance analysis of the interferometric phase estimation is carried out based on Monte Carlo simulations and CRLB calculation. We show that by utilizing the Cramer-Rao lower bound we are able to determine the combination of baselines that will enable us to achieve the most accurate estimating performance.

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

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164854 ◽

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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