Monte Carlo Studies of a Coupled ‘Elementary’ Reaction-Diffusion System in One Dimension

1994 ◽  
Vol 366 ◽  
Author(s):  
Anna Lin ◽  
Raoul Kopelman
Keyword(s):  
Monte Carlo ◽  
Mean Field ◽  
Reaction System ◽  
Mean Field Approximation ◽  
Rate Equations ◽  
Low Dimensions ◽  
Rate Laws ◽  
Diffusion Limited ◽  
Monte Carlo Studies ◽  
The Mean

ABSTRACTThe anomalous rate laws of diffusion limited elementary reactions in low dimensions have garnered attention over the past decade as researchers have become aware that the mean field approximation utilized in traditional kinetic rate equations is not valid in low and fractal dimensions. We use Monte Carlo simulations to study a diffusion limited system simultaneously undergoing A+B-->0 and A+A--> 0 reactions, a common situation in photochemistry. We are studying how this coupled system affects the attenuation of local fluctuations and thus the rate laws of the system in low dimensions and how these results compare to the mean field rate laws. Our results give useful guidelines for studying this type of reaction system experimentally.

Modulated Phases on the FCC(110) Surfaces with Adsorbate-Induced Reconstructions

2003 ◽  
Vol 10 (02n03) ◽  
pp. 189-194
Author(s):  
Min Kang ◽  
Makoto Kaburagi
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Correlation Function ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Modulated Phases ◽  
The Mean ◽  
Beg Model

We theoretically investigate the fcc(110) surfaces with missing row reconstructions induced by adatoms using the Blume–Emmery–Griffith (BEG) model. In the model, Kij is introduced to denote interactions between surface atoms and Jij to describe interactions between dipoles. The investigation by the mean field approximation has predicted that there appear modulated phases on the surfaces as the next-nearest-neighbor (NNN) and the nearest-neighbor (NN) interactions along the [001] direction become competitive. In this study, Monte Carlo simulations are performed to confirm the prediction. A correlation function defined by concentration operators in wave vector q space is calculated. The results show that the concentration modulations appear. The temperature versus the ratio of the NNN interaction K2 to the NN interaction K1 phase diagram is obtained. The possible features of the modulated phases in experiments are discussed.

Phase diagrams and magnetic properties of double perovskite Ba2CrMoO6

2015 ◽  
Vol 29 (27) ◽  
pp. 1550174 ◽  
Author(s):  
M. Ait-Tamerd ◽  
B. Abraime ◽  
K. El Maalam ◽  
A. Benyoussef ◽  
A. El Kenz ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Magnetic Properties ◽  
Phase Diagrams ◽  
Mean Field ◽  
Magnetic Behavior ◽  
Double Perovskite ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
The Mean

In this paper, the Monte Carlo simulation (MCS) and the mean field approximation (MFA) methods have been used to study the magnetic properties of double perovskite Ba2CrMoO6 in the framework of the Ising model, which is important for a better understanding of the magnetic behavior of this material. This compound is constituted of two magnetic cubic sublattices: one occupied by Mo[Formula: see text] and other occupied Cr[Formula: see text], the critical exponents and phase diagrams for this compound are determined. The critical behavior, compensation temperature and susceptibility are also determined.

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