Macromolecular dimensions obtained by an efficient Monte Carlo method: The mean square end‐to‐end separation

1979 ◽  
Vol 70 (8) ◽  
pp. 3984-3988 ◽  
Author(s):  
Frederic Mandel
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Mean Square ◽  
The Mean ◽  
End To End

scholarly journals On the Acceleration of the Multi-Level Monte Carlo Method

2015 ◽  
Vol 52 (2) ◽  
pp. 307-322 ◽  
Author(s):  
Kristian Debrabant ◽  
Andreas Röβler
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Order Of Convergence ◽  
Optimal Order ◽  
Weak Approximation ◽  
Mean Square ◽  
Optimal Order Of Convergence ◽  
Computational Costs ◽  
The Mean ◽  
Multi Level

The multi-level Monte Carlo method proposed by Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper a modified multi-level Monte Carlo estimator is proposed with significantly reduced computational costs. As the main result, it is proved that the modified estimator reduces the computational costs asymptotically by a factor (p / α)2 if weak approximation methods of orders α and p are applied in the case of computational costs growing with the same order as the variances decay.

scholarly journals On the Acceleration of the Multi-Level Monte Carlo Method

2015 ◽  
Vol 52 (02) ◽  
pp. 307-322 ◽  
Author(s):  
Kristian Debrabant ◽  
Andreas Röβler
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Order Of Convergence ◽  
Optimal Order ◽  
Weak Approximation ◽  
Mean Square ◽  
Optimal Order Of Convergence ◽  
Computational Costs ◽  
The Mean ◽  
Multi Level

The multi-level Monte Carlo method proposed by Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper a modified multi-level Monte Carlo estimator is proposed with significantly reduced computational costs. As the main result, it is proved that the modified estimator reduces the computational costs asymptotically by a factor (p / α)2 if weak approximation methods of orders α and p are applied in the case of computational costs growing with the same order as the variances decay.

Self‐avoiding walks with span limitations. I. The mean square end‐to‐end distance

1980 ◽  
Vol 72 (4) ◽  
pp. 2702-2707 ◽  
Author(s):  
Ronnie Barr ◽  
Chava Brender ◽  
Melvin Lax
Keyword(s):  
Mean Square ◽  
End Distance ◽  
The Mean ◽  
End To End ◽  
Self Avoiding Walks

scholarly journals The Reliability Model of Artificial Monitoring on the Anomalous Event in Expressway Tunnels and Monte Carlo Simulation

2019 ◽  
Vol 4 (3) ◽  
pp. p172
Author(s):  
Ling WU ◽  
Yueqi HU ◽  
Weihua ZHAO ◽  
Tong ZHU
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Video Surveillance ◽  
Warning System ◽  
Reliability Models ◽  
The Monte Carlo Method ◽  
Anomalous Event ◽  
Actual Operation ◽  
The Mean ◽  
Mean Time

Artificial monitoring remains to be a major way to detect anomalous events in expressway tunnels. To estimate the reliability of artificial monitoring on anomalous events in expressway tunnels, the video surveillance and mobile inspection based reliability models of artificial monitoring on the anomalous event in the expressway tunnel were built, and Monte Carlo method was applied to calculate the probability and mean time to detect the anomalous event at the specific time. The results showed that the Monte Carlo method could simulate video surveillance and mobile inspection, and obtain the probability distribution and mean time of detecting anomalous events. The mean time to spot the anomalous event was in reverse relation with the number of inspectors, the time of mobile inspection, and the reliability probability of the monitoring pre-warning system in tunnels and was in positive relationships with the departure interval. Combined with the actual operation cost, the model serves as a basis for the artificial monitoring package.

The study of time dependence of particle flux with multiplication in a random medium

2020 ◽  
Vol 35 (1) ◽  
pp. 11-20
Author(s):  
Galiya Z. Lotova ◽  
Guennady A. Mikhailov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Time Dependence ◽  
Particle Flux ◽  
Random Medium ◽  
The Mean ◽  
Exponential Asymptotics ◽  
Number Of Particles

AbstractAlgorithms of Monte Carlo method for estimating probabilistic moments of the parameter of time exponential asymptotics of particle flux with multiplication in a random medium are constructed. It was analytically and numerically shown that the asymptotics of the mean number of particles is close to an exponential one with the factor containing a summand proportional to square of time.

Simulation of Electron Transport in Silicon using Monte Carlo Method

2011 ◽  
Vol 284-286 ◽  
pp. 871-874
Author(s):  
Zan Wang ◽  
Lei Quan ◽  
Yi Wu Ruan
Keyword(s):  
Monte Carlo ◽  
Electron Transport ◽  
Monte Carlo Method ◽  
Electric Fields ◽  
Phonon Scattering ◽  
Mean Free Path ◽  
Intervalley Scattering ◽  
The Mean ◽  
Simulation Time ◽  
Electron Phonon Scattering

A Monte Carlo method is employed to investigate the properties of electron transport with considerations of electron-phonon scattering including intervalley scattering and intravalley scattering. Under different electric fields, the coupling relations between electrons and phonons are studied, and the behaviors of absorbing and releasing phonons from electrons are also analyzed. The results show the scattering events of absorbing phonons from electrons decrease with the increasing simulation time. At the same temperature, the mean free path of electron increases initially and then decreases with the increasing electric field intensity, and finally approaches an asymptotic value.

STUDY OF PHASE SEPARATION IN THE HUBBARD MODEL1

1991 ◽  
Vol 05 (01n02) ◽  
pp. 113-118
Author(s):  
A. Moreo
Keyword(s):  
Monte Carlo ◽  
Phase Separation ◽  
Monte Carlo Method ◽  
Quantum Monte Carlo ◽  
Chemical Potential ◽  
Repulsive Interaction ◽  
Two Dimensional ◽  
Quantum Monte Carlo Method ◽  
The Mean ◽  
Number Of Particles

We study the behavior of the mean number of particles <n> as a function of the chemical potential μ in the two dimensional Hubbard model with both attractive and repulsive interaction, using a quantum Monte Carlo method. Working at U/t=10, 4 and −4 on lattices with 4×4, 6×6 and 8×8 sites, we do not find evidence of phase separation.

scholarly journals Semiflexible Polymer Enclosed in a 3D Compact Domain

2021 ◽  
Vol 9 ◽  
Author(s):  
Pavel Castro-Villarreal ◽  
J. E. Ramírez
Keyword(s):  
Persistence Length ◽  
Compact Domain ◽  
Mean Square ◽  
Shape Transition ◽  
Conformational States ◽  
Semiflexible Polymer ◽  
End Distance ◽  
The Mean ◽  
End To End ◽  
Polymer Shape

The conformational states of a semiflexible polymer enclosed in a volume V:=ℓ3 are studied as stochastic realizations of paths using the stochastic curvature approach developed in [Rev. E 100, 012503 (2019)], in the regime whenever 3ℓ/ℓp>1, where ℓp is the persistence length. The cases of a semiflexible polymer enclosed in a cube and sphere are considered. In these cases, we explore the Spakowitz–Wang–type polymer shape transition, where the critical persistence length distinguishes between an oscillating and a monotonic phase at the level of the mean-square end-to-end distance. This shape transition provides evidence of a universal signature of the behavior of a semiflexible polymer confined in a compact domain.

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