Monte Carlo Simulation of Growth of Crystalline and Amorphous Silicon

1985 ◽  
Vol 63 ◽  
Author(s):  
Brian W. Dodson ◽  
Paul A. Taylor
Keyword(s):  
Monte Carlo ◽  
Interaction Model ◽  
Three Dimensions ◽  
Atomic Configuration ◽  
Potential Growth ◽  
Continuous Space ◽  
Monte Carlo Techniques ◽  
Stages Of Growth ◽  
Lennard Jones ◽  
Accurate Treatment

ABSTRACTThe authors have previously introduced a method, based on Monte Carlo techniques, for simulation of crystal growth processes in a continuous space. We have applied the method, initially used to simulate growth of two-dimensional Lennard-Jones systems, to treat growth of silicon in three dimensions. The interaction model for silicon is taken to be the recently introduced Stillinger-Weber (S-W) potential, which is a two- and threebody classical potential. Although the early stages of growth seem to be well modelled by the S-W potential, growth of even a single monolayer of epitaxial (111) silicon does not seem to be possible. Modifications to the S-W potential were considered, and found to be unacceptable physically. More accurate treatment of non-ideal atomic configuration energies is necessary to arrive at physically realistic growth simulations.

Stability and Growth of Lennard-Jones Strained Layer Superlattice Interfaces

1984 ◽  
Vol 37 ◽  
Author(s):  
Brian W. Dodson
Keyword(s):  
Monte Carlo ◽  
Model System ◽  
Interatomic Potentials ◽  
Growth Processes ◽  
Strained Layer ◽  
Monte Carlo Techniques ◽  
Lennard Jones ◽  
Strained Layer Superlattice ◽  
The Stability

AbstractIn the context of a model system whose atoms interact via Lennard-Jones (LJ) interatomic potentials, we have studied the stability of an initially perfect strained layer superlattice interface (SLS) and the process of growth of a mismatched layer on a substrate using Monte Carlo techniques. An initially perfect SLS interface is found to be metastable up to 12% mismatch, a much higher value than is found on real SLS systems. In contrast, we find that, within the limitations of the calculations, a perfect SLS interface cannot be grown in an LJ system. The implications of these results for understanding SLS growth processes is discussed.

COMPARISON BETWEEN MOLECULAR DYNAMICS AND MONTE CARLO DESCRIPTIONS OF SOLID–LIQUID PHASE-TRANSITION OF LENNARD–JONES FLUIDS

2010 ◽  
Vol 21 (03) ◽  
pp. 349-363 ◽  
Author(s):  
A. S. MARTINS ◽  
C. X. S. SEIXAS ◽  
L. B. dos SANTOS ◽  
P. R. RIOS
Keyword(s):  
Phase Transition ◽  
Molecular Dynamics ◽  
Monte Carlo ◽  
Liquid Phase ◽  
Structural Evolution ◽  
Liquid Phase Transition ◽  
Monte Carlo Techniques ◽  
Lennard Jones ◽  
Liquid Transition ◽  
Solid Liquid

Molecular dynamics and Monte Carlo techniques are employed for the study of Lennard–Jones fluids near the solid–liquid transition region. Systematic comparisons between the predictions of both techniques are discussed, with particular emphasis on the structural evolution and location of the transition (melting) temperature Tm.

Random Walk Monte Carlo Simulation of Diffusive Ferromagnetic Ising Spin under Lennard-Jones Interaction

2013 ◽  
Vol 431 ◽  
pp. 57-60
Author(s):  
Jutarop Reungyos ◽  
Yongyut Laosiritaworn
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Magnetic Particles ◽  
Ferromagnetic Interaction ◽  
Continuous Space ◽  
Lennard Jones ◽  
Ising Spin ◽  
Simulation Time ◽  
Ising Spins

This work investigated properties of diffusive magnetic particles. Random walk Monte Carlo method was used to simulate the Ising spin diffusing and flipping to examine the properties of the system. The Ising spins interact among themselves via Lennard-Jones interaction. Metropolis algorithm was employed to update spins configuration on the continuous space. The volume of Ising spins, magnetization and magnetic susceptibility, were investigated as functions of temperature, number of Ising spins in the system and simulation time. It was found that, at low temperatures, the Ising spins tend to stay close even at long simulation time, where finite magnetization was found suggesting the ferromagnetic preference. However, at high temperatures, paramagnetic behavior reveals as ferromagnetic interaction ceases with time passing. This is due to role of spin diffusing which causes the spins to disperse and hence ferromagnetic interaction among spins reduces.

scholarly journals Quantum dynamics in transverse-field Ising models from classical networks

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Markus Schmitt ◽  
Markus Heyl
Keyword(s):  
Monte Carlo ◽  
Quantum Dynamics ◽  
Transverse Field ◽  
Ising Models ◽  
Three Dimensions ◽  
Many Body ◽  
Monte Carlo Techniques ◽  
Many Body Theory ◽  
Monte Carlo Algorithms ◽  
Universal Structure

The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques. Our perturbative construction encodes time-evolved quantum states of spin-1/2 systems in a network of classical spins with local couplings and can be directly generalized to other spin systems and higher spins. Using this construction we compute the transient dynamics in one, two, and three dimensions including local observables, entanglement production, and Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy of this approach by comparisons to exact results. We include a mapping to equivalent artificial neural networks, which were recently introduced to provide a universal structure for classical network wave functions.

Bayesian Estimation of DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Likelihood Function ◽  
Academic Research ◽  
Dynamic Stochastic General Equilibrium ◽  
Computational Techniques ◽  
Dsge Models ◽  
Monte Carlo Techniques ◽  
Dynamic Stochastic ◽  
Theoretical Foundations

Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysis at central banks. This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations. The book is essential reading for graduate students, academic researchers, and practitioners at policy institutions.

Neutron dose evaluation of Elekta Linac at two energies (10 & 18 MV) by MCNP code and comparison with experimental measurements

2014 ◽  
Vol 6 (1) ◽  
pp. 1006-1015
Author(s):  
Negin Shagholi ◽  
Hassan Ali ◽  
Mahdi Sadeghi ◽  
Arjang Shahvar ◽  
Hoda Darestani ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Measurement Data ◽  
Calculated Data ◽  
High Energy ◽  
Neutron Dose ◽  
Dose Assessment ◽  
Photon Flux ◽  
Dose Equivalent ◽  
Monte Carlo Techniques ◽  
Neutron Dose Equivalent

Medical linear accelerators, besides the clinically high energy electron and photon beams, produce other secondary particles such as neutrons which escalate the delivered dose. In this study the neutron dose at 10 and 18MV Elekta linac was obtained by using TLD600 and TLD700 as well as Monte Carlo simulation. For neutron dose assessment in 2020 cm2 field, TLDs were calibrated at first. Gamma calibration was performed with 10 and 18 MV linac and neutron calibration was done with 241Am-Be neutron source. For simulation, MCNPX code was used then calculated neutron dose equivalent was compared with measurement data. Neutron dose equivalent at 18 MV was measured by using TLDs on the phantom surface and depths of 1, 2, 3.3, 4, 5 and 6 cm. Neutron dose at depths of less than 3.3cm was zero and maximized at the depth of 4 cm (44.39 mSvGy-1), whereas calculation resulted  in the maximum of 2.32 mSvGy-1 at the same depth. Neutron dose at 10 MV was measured by using TLDs on the phantom surface and depths of 1, 2, 2.5, 3.3, 4 and 5 cm. No photoneutron dose was observed at depths of less than 3.3cm and the maximum was at 4cm equal to 5.44mSvGy-1, however, the calculated data showed the maximum of 0.077mSvGy-1 at the same depth. The comparison between measured photo neutron dose and calculated data along the beam axis in different depths, shows that the measurement data were much more than the calculated data, so it seems that TLD600 and TLD700 pairs are not suitable dosimeters for neutron dosimetry in linac central axis due to high photon flux, whereas MCNPX Monte Carlo techniques still remain a valuable tool for photonuclear dose studies.

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

scholarly journals Random Sampling Many-Dimensional Sets Arising in Control

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 580
Author(s):  
Pavel Shcherbakov ◽  
Mingyue Ding ◽  
Ming Yuchi
Keyword(s):  
Monte Carlo ◽  
Random Sampling ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Computational Mathematics ◽  
Closed Form Solutions ◽  
Monte Carlo Techniques ◽  
Control Optimization ◽  
Point Representation ◽  
Hit And Run

Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas of computational mathematics, optimization, data processing, etc. Whereas for regularly shaped sets such sampling is immediate to arrange, for nontrivial, implicitly specified domains these techniques are not easy to implement. We consider the so-called Hit-and-Run algorithm, a representative of the class of Markov chain Monte Carlo methods, which became popular in recent years. To perform random sampling over a set, this method requires only the knowledge of the intersection of a line through a point inside the set with the boundary of this set. This component of the Hit-and-Run procedure, known as boundary oracle, has to be performed quickly when applied to economy point representation of many-dimensional sets within the randomized approach to data mining, image reconstruction, control, optimization, etc. In this paper, we consider several vector and matrix sets typically encountered in control and specified by linear matrix inequalities. Closed-form solutions are proposed for finding the respective points of intersection, leading to efficient boundary oracles; they are generalized to robust formulations where the system matrices contain norm-bounded uncertainty.

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