scholarly journals Counting figures in planar random configurations

1985 ◽  
Vol 22 (1) ◽  
pp. 68-81 ◽  
Author(s):  
A. M. Kellerer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Poisson Process ◽  
Recent Result ◽  
Field Of View ◽  
Fixed Field ◽  
Area And Perimeter ◽  
Standard Deviations

Random configurations are considered that are generated by a Poisson process of figures in the plane, and a recent result is used to derive formulae for the estimation of the number of figures, and their mean area and perimeter. The formulae require merely the determination of the area, the perimeter, and the Euler–Poincaré characteristic of the random configurations in a fixed field of view. There are no similar formulae for the standard deviations of the estimates; their magnitudes in typical cases are therefore assessed by Monte Carlo simulations.

scholarly journals Counting figures in planar random configurations

1985 ◽  
Vol 22 (01) ◽  
pp. 68-81 ◽  
Author(s):  
A. M. Kellerer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Poisson Process ◽  
Recent Result ◽  
Field Of View ◽  
Fixed Field ◽  
Area And Perimeter ◽  
Standard Deviations

Random configurations are considered that are generated by a Poisson process of figures in the plane, and a recent result is used to derive formulae for the estimation of the number of figures, and their mean area and perimeter. The formulae require merely the determination of the area, the perimeter, and the Euler–Poincaré characteristic of the random configurations in a fixed field of view. There are no similar formulae for the standard deviations of the estimates; their magnitudes in typical cases are therefore assessed by Monte Carlo simulations.

The electron transport that occurs within wurtzite zinc oxide and the application of stress

MRS Advances ◽  
2017 ◽  
Vol 2 (48) ◽  
pp. 2627-2632 ◽  
Author(s):  
Poppy Siddiqua ◽  
Michael S. Shur ◽  
Stephen K. O’Leary
Keyword(s):  
Monte Carlo ◽  
Zinc Oxide ◽  
Electron Transport ◽  
Velocity Field ◽  
Monte Carlo Simulations ◽  
Significant Role ◽  
Energy Gap ◽  
Device Application ◽  
The Impact

ABSTRACTWe examine how stress has the potential to shape the character of the electron transport that occurs within ZnO. In order to narrow the scope of this analysis, we focus on a determination of the velocity-field characteristics associated with bulk wurtzite ZnO. Monte Carlo simulations of the electron transport are pursued for the purposes of this analysis. Rather than focusing on the impact of stress in of itself, instead we focus on the changes that occur to the energy gap through the application of stress, i.e., energy gap variations provide a proxy for the amount of stress. Our results demonstrate that stress plays a significant role in shaping the form of the velocity-field characteristics associated with ZnO. This dependence could potentially be exploited for device application purposes.

scholarly journals The equation of state with non-equilibrium methods

2018 ◽  
Vol 175 ◽  
pp. 07028 ◽  
Author(s):  
Alessandro Nada ◽  
Michele Caselle ◽  
Marco Panero
Keyword(s):  
Monte Carlo ◽  
Equation Of State ◽  
Monte Carlo Simulations ◽  
Large Set ◽  
Yang Mills ◽  
Novel Technique ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
Jarzynski’S Equality

Jarzynski’s equality provides an elegant and powerful tool to directly compute differences in free energy in Monte Carlo simulations and it can be readily extended to lattice gauge theories to compute a large set of physically interesting observables. In this talk we present a novel technique to determine the thermodynamics of stronglyinteracting matter based on this relation, which allows for a direct and efficient determination of the pressure using out-of-equilibrium Monte Carlo simulations on the lattice. We present results for the equation of state of the SU(3) Yang-Mills theory in the confined and deconfined phases. Finally, we briefly discuss the generalization of this method for theories with fermions, with particular focus on the equation of state of QCD.

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