TEMPERATURE OF NONEQUILIBRIUM LATTICE SYSTEMS

2006 ◽  
Vol 17 (12) ◽  
pp. 1703-1715 ◽  
Author(s):  
ALBERTO PETRI ◽  
M. J. DE OLIVEIRA
Keyword(s):  
Monte Carlo ◽  
Heat Bath ◽  
Bath Temperature ◽  
Total System ◽  
Local Distribution ◽  
Lattice Systems ◽  
Potts Models ◽  
Monte Carlo Dynamics ◽  
Instantaneous Temperature ◽  
System Energy

We investigate the thermal quench of Ising and Potts models via Monte Carlo dynamics. We find that the local distribution of the site-site interaction energy has the same form as in the equilibrium case, a result that allows us to define an instantaneous temperature θ during the systems relaxation. We also find that, after an undercritical quench, θ equals the heat bath temperature in a finite time, while the total system energy is still decreasing due to the coarsening process.

scholarly journals Coupled Nosé-Hoover equations of motions without time scaling

2016 ◽  
Author(s):  
Ikuo Fukuda ◽  
Kei Moritsugu
Keyword(s):  
Physical System ◽  
Heat Bath ◽  
Bath Temperature ◽  
Model Systems ◽  
Total System ◽  
Canonical Distribution ◽  
Time Scaling ◽  
Original Scheme ◽  
Dynamics Simulations ◽  
Sampling Property

AbstractThe Nosé-Hoover (NH) equation of motion is widely used in molecular dynamics simulations. It enables us to set a constant temperature and produce the canonical distribution for a target physical system. For the purpose of investigating the physical system under fluctuating temperature, we have introduced a coupled Nosé-Hoover equation in our previous work [J. Phys. A 48 455001 (2015)]. The coupled NH equation implements a fluctuating heat-bath temperature in the NH equation of the physical system, and also keeps a statistically complete description via an invariant measure of the total system composed of the physical system and a “temperature system”. However, a difficulty lies in that the time development of the physical system may not correspond to the realistic physical process, because of the need of a scaled time average to compute thermodynamical quantities. The current work gives a solution by presenting a new scheme, which is free from the scaled time but retains the statistical description. By use of simple model systems, we validate the current scheme and compare with the original scheme. The sampling property of the current scheme is also clarified to investigate the effect of function setting used for the distribution of the total system.

scholarly journals Unfolding of Globular Proteins: Monte Carlo Dynamics of a Realistic Reduced Model

2003 ◽  
Vol 85 (5) ◽  
pp. 3271-3278 ◽  
Author(s):  
Andrzej Kolinski ◽  
Piotr Klein ◽  
Piotr Romiszowski ◽  
Jeffrey Skolnick
Keyword(s):  
Monte Carlo ◽  
Globular Proteins ◽  
Reduced Model ◽  
Monte Carlo Dynamics

scholarly journals Applicability of Quasi-Monte Carlo for lattice systems

2014 ◽  
Author(s):  
Andreas Ammon ◽  
Tobias Hartung ◽  
Karl Jansen ◽  
Hernan Leövey ◽  
Andreas Griewank ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Lattice Systems ◽  
Quasi Monte Carlo

scholarly journals THE SELF-ORGANIZED MULTI-LATTICE MONTE CARLO SIMULATION

2004 ◽  
Vol 15 (09) ◽  
pp. 1249-1268 ◽  
Author(s):  
DENIS HORVÁTH ◽  
MARTIN GMITRA
Keyword(s):  
Monte Carlo ◽  
Finite Size ◽  
Simulation Method ◽  
Monte Carlo Step ◽  
The Self ◽  
Square Lattice ◽  
Critical Systems ◽  
Lattice Systems ◽  
Steady Regime ◽  
Self Organized

Self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of the suggested simulation method is an artificial dynamics consisting of the well-known single-spin-flip Metropolis algorithm supplemented by a random walk on the temperature axis. The walk is biased towards the critical region through a feedback based on instantaneous energy and magnetization cumulants, which are updated at every Monte Carlo step and filtered through a special recursion algorithm. The simulations revealed the invariance of the temperature probability distribution function, once some self-organized critical steady regime is reached, which is called here noncanonical equilibrium. The mean value of this distribution approximates the pseudocritical temperature of canonical equilibrium. In order to suppress finite-size effects, the self-organized approach is extended to multi-lattice systems, where the feedback basis on pairs of instantaneous estimates of the fourth-order magnetization cumulant on two systems of different size. These replica-based simulations resemble, in Monte Carlo lattice systems, some of the invariant statistical distributions of standard self-organized critical systems.

scholarly journals Single cluster Monte Carlo dynamics for the Ising model

1990 ◽  
Vol 60 (5-6) ◽  
pp. 889-889 ◽  
Author(s):  
P. Tamayo ◽  
R. C. Brower ◽  
W. Klein
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Dynamics ◽  
Cluster Monte Carlo ◽  
Single Cluster

scholarly journals Coupled Simulations of Mechanical Deformation and Microstructural Evolution Using Polycrystal Plasticity and Monte Carlo Potts Models

1998 ◽  
Vol 538 ◽  
Author(s):  
C.C. Battaile ◽  
T.E. Buchheit ◽  
E.A. Holm ◽  
G.W. Wellman ◽  
M.K. Neilsen
Keyword(s):  
Monte Carlo ◽  
Constitutive Model ◽  
Grain Growth ◽  
Microstructural Evolution ◽  
Boundary Migration ◽  
Mechanical Deformation ◽  
Potts Models ◽  
Polycrystal Plasticity ◽  
Grain Fragmentation ◽  
Grain Growth Kinetics

AbstractThe microstructural evolution of heavily deformed polycrystalline Cu is simulated by coupling a constitutive model for polycrystal plasticity with the Monte Carlo Potts model for grain growth. The effects of deformation on boundary topology and grain growth kinetics are presented. Heavy deformation leads to dramatic strain-induced boundary migration and subsequent grain fragmentation. Grain growth is accelerated in heavily deformed microstructures. The implications of these results for the thermomechanical fatigue failure of eutectic solder joints are discussed.

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