Solid-on-Solid Monte Carlo Investigation of Islanding Kinetics During Heteroepitaxy

1995 ◽  
Vol 399 ◽  
Author(s):  
Ken Payne ◽  
Jeff Drucker
Keyword(s):  
Monte Carlo ◽  
Interaction Strength ◽  
Nucleation Theory ◽  
Island Size ◽  
Nucleation Barrier ◽  
Simple Cubic ◽  
Monte Carlo Investigation ◽  
Mc Simulation ◽  
Film Nucleation ◽  
Kinetics Of

ABSTRACTWe have investigated the kinetics of islanding during heteroepitaxy using a solid-on-solid Monte Carlo (SOS-MC) simulation. We simulate deposition by randomly depositing atoms onto a square grid with periodic boundary conditions. Arrhenius surface diffusion kinetics are dependent on the sum of a surface energy barrier (Ed) and the number of nearest neighbors multiplied by an adatom interaction strength (Eb). We confine growth to the first layer above the simple cubic substrate and investigate coverages < 1/2 monolayer. We monitor the evolution of film microstructure by producing island size distributions and plots which compare a cluster's area to perimeter ratio with that of a circle. We find that our simulation qualitatively correlates with results of classical film nucleation theory. A simple model is used to demonstrate the existence of a 'probabilistic nucleation barrier'.

Monte Carlo Investigation of Rare Magnetization Fluctuations in Ising Models

1998 ◽  
Vol 09 (04) ◽  
pp. 625-631 ◽  
Author(s):  
D. Stauffer
Keyword(s):  
Monte Carlo ◽  
Power Law ◽  
Ising Models ◽  
Magnetization Distribution ◽  
Stretched Exponential ◽  
Simple Cubic ◽  
Monte Carlo Investigation

For square and simple cubic Ising models at T=Tc, we look at the tails of the magnetization distribution for untypically large magnetizations. No indications for a stretched exponential or power law behavior are found.

Monte Carlo Simulation of Porous Layers Sintering

2007 ◽  
Vol 352 ◽  
pp. 5-8 ◽  
Author(s):  
I.G. Neizvestny ◽  
Natasha L. Shwartz ◽  
Z.Sh. Yanovitskaya ◽  
A.V. Zverev
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Annealing Temperature ◽  
Annealing Process ◽  
High Temperature Annealing ◽  
Sintering Process ◽  
Porous Layers ◽  
Simple Cubic ◽  
Film Porosity ◽  
Kinetics Of

Kinetics of porous layer evolution during high-temperature annealing was investigated by Monte Carlo simulation. Sintering process of spongy one-component films with randomly distributed pores was studied. Layers with porosity from 20% to 50% with simple cubic and diamond-like lattices were under examination. Sintering rate was demonstrated to be non-monotone in time for any film porosity and different lattice coordination number. Metastable states of the system, dependent on time and temperature of annealing process, were revealed. Estimation of annealing time necessary to reach the definite sintering level under changes of annealing temperature was suggested.

Faking and the Validity of Personality: A Monte Carlo Investigation

2005 ◽  
Author(s):  
Shawn Komar ◽  
Jennifer Theakston ◽  
Douglas J. Brown ◽  
Chet Robie
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Investigation

scholarly journals Polyelectrolyte Gels: A Unique Class of Soft Materials

Gels ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 102
Author(s):  
Ferenc Horkay
Keyword(s):  
Exchange Process ◽  
Interaction Strength ◽  
Soft Materials ◽  
Industrial Applications ◽  
Future Research ◽  
Swelling Kinetics ◽  
Polyelectrolyte Gels ◽  
Ion Exchange Process ◽  
Counter Ions ◽  
Kinetics Of

The objective of this article is to introduce the readers to the field of polyelectrolyte gels. These materials are common in living systems and have great importance in many biomedical and industrial applications. In the first part of this paper, we briefly review some characteristic properties of polymer gels with an emphasis on the unique features of this type of soft material. Unsolved problems and possible future research directions are highlighted. In the second part, we focus on the typical behavior of polyelectrolyte gels. Many biological materials (e.g., tissues) are charged (mainly anionic) polyelectrolyte gels. Examples are shown to illustrate the effect of counter-ions on the osmotic swelling behavior and the kinetics of the swelling of model polyelectrolyte gels. These systems exhibit a volume transition as the concentration of higher valence counter-ions is gradually increased in the equilibrium bath. A hierarchy is established in the interaction strength between the cations and charged polymer molecules according to the chemical group to which the ions belong. The swelling kinetics of sodium polyacrylate hydrogels is investigated in NaCl solutions and in solutions containing both NaCl and CaCl2. In the presence of higher valence counter-ions, the swelling/shrinking behavior of these gels is governed by the diffusion of free ions in the swollen network, the ion exchange process and the coexistence of swollen and collapsed states.

Multilevel Monte Carlo by using the Halton sequence

2020 ◽  
Vol 26 (3) ◽  
pp. 193-203
Author(s):  
Shady Ahmed Nagy ◽  
Mohamed A. El-Beltagy ◽  
Mohamed Wafa
Keyword(s):  
Monte Carlo ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Computational Cost ◽  
Random Numbers ◽  
Multilevel Monte Carlo ◽  
Halton Sequence ◽  
Random Generator ◽  
Mc Simulation ◽  
Multilevel Monte Carlo Method

AbstractMonte Carlo (MC) simulation depends on pseudo-random numbers. The generation of these numbers is examined in connection with the Brownian motion. We present the low discrepancy sequence known as Halton sequence that generates different stochastic samples in an equally distributed form. This will increase the convergence and accuracy using the generated different samples in the Multilevel Monte Carlo method (MLMC). We compare algorithms by using a pseudo-random generator and a random generator depending on a Halton sequence. The computational cost for different stochastic differential equations increases in a standard MC technique. It will be highly reduced using a Halton sequence, especially in multiplicative stochastic differential equations.

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