Temperature-scaling Monte Carlo

Valleau, J. P. Temperature-and-density-scaling Monte-Carlo methodology and the canonical thermodynamics of Lennard-Jonesium. Mol. Sim. 2005, 31, 223-253... 

In this section we review several studies of phase transitions in adsorbed layers. Phase transitions in adsorbed (2D) fluids and in adsorbed layers of molecules are studied with a combination of path integral Monte Carlo, Gibbs ensemble Monte Carlo (GEMC), and finite size scaling techniques. Phase diagrams of fluids with internal quantum states are analyzed. Adsorbed layers of H2 molecules at a full monolayer coverage in the /3 X /3 structure have a higher transition temperature to the disordered phase compared to the system with the heavier D2 molecules this effect is... 

FIG. 14 Phase diagram of the quantum APR model in the Q -T plane. The solid curve shows the line of continuous phase transitions from an ordered phase at low temperatures and small rotational constants to a disordered phase according to the mean-field approximation. The symbols show the transitions found by the finite-size scaling analysis of the path integral Monte Carlo data. The dashed line connecting these data is for visual help only. (Reprinted with permission from Ref. 328, Fig. 2. 1997, American Physical Society.)... 

FIG. 19 Scaling plot for the relaxation of the mean chain length L t) after a T-jump from Tq = 0.35 to a series of final temperatures, given as a parameter along with the respective L o s. The same Monte Carlo results [64] as in Fig. 5 are used. Full line denotes the scaling function f x = = (0.215 + 8x) . In the inset the... 

Monte Carlo simulations have been done on the TV x x cubic lattice (TV = 27) with the lattice spacing h = 0.8 [47,49] for a bulk system. The usual temperature factor k T is set to 1, since it only sets the energy scale. The following periodic boundary conditions are used = [Pg.714]

Fig. 18. Phase diagram of the centered rectangular lattice gas model with ==0, 3/4 2 = V3> vJ

Fig. 24. Contour plot of the structure factor (the kinematic LEED intensity) of a x y/i monolayer in a triangular lattice gas with nearest-neighbor repulsion, at a temperature k TIi = 0.355 (about 5% above T ) and a chemical potential // = 1.5 (0c = 0.336 at the transition temperature.) Contour increments are in a (common) logarithmic scale separated by 0.1, starting with 3.2 at the outermost contour. Center of the surface Brillouin zon is to the left k, and k the radial and azimuthal components of kH, are in units of nlXla, a being the lattice spacing. Data are based on averages over 2x10 Monte Carlo steps per site. (From Bartelt et...

Fig. 30. Phase diagram of a model for Si/W(110) in the temperature versus 9 plane. Experimentally determined interactions J Jj,are used. Full dots are from Monte Carlo calculations, while triangles are based on transfer matrix finite size scaling using strip widths of 8 and 12. The point labelled L indicates approximate location of Lifshitz point. The dotted line indicates the transition region between the (5 x l)and(6 x 1) phases. (From...

Combustion of aluminum particle as fuel, and oxygen, air, or steam as oxidant provides an attractive propulsion strategy. In addition to hydrocarbon fuel combustion, research is focussed on determining the particle size and distribution and other relevant parameters for effectively combusting aluminum/oxygen and aluminum/steam in a laboratory-scale atmospheric dump combustor by John Foote at Engineering Research and Consulting, Inc. (Chapter 8). A Monte-Carlo numerical scheme was utilized to estimate the radiant heat loss rates from the combustion products, based on the measured radiation intensities and combustion temperatures. These results provide some of the basic information needed for realistic aluminum combustor development for underwater propulsion. 

Results of an experimental program in which aluminum particles were burned with steam and mixtures of oxygen and argon in small-scale atmospheric dump combustor are presented. Measurements of combustion temperature, radiation intensity in the wavelength interval from 400 to 800 nm, and combustion products particle size distribution and composition were made. A combustion temperature of about 2900 K was measured for combustion of aluminum particles with a mixture of 20%(wt.) O2 and 80%(wt.) Ar, while a combustion temperature of about 2500 K was measured for combustion of aluminum particles with steam. Combustion efficiency for aluminum particles with a mean size of 17 yum burned in steam with O/F) / 0/F)st 1-10 and with residence time after ignition estimated at 22 ms was about 95%. A Monte Carlo numerical method was used to estimate the radiant heat loss rates from the combustion products, based on the measured radiation intensities and combustion temperatures. A peak heat loss rate of 9.5 W/cm was calculated for the 02/Ar oxidizer case, while a peak heat loss rate of 4.8 W/cm was calculated for the H2O oxidizer case. 

Figure 7.9. Variation of (a) the Gibbs energy, (b) ttie enthalpy and (c) the entropy with temperature (scaled to the nearest-nei bour interaction energy J ) for the complex structure A15. Comparison between BWG CVM in the tetrahedron approximation ( ) and the Monte Carlo method (—) (Turchi and Finel 1992).

The search for local minima in the neighborhood of a given local minimum is usually performed by the excitation of the system from this state followed by the relaxation of the system. If the relaxation of the excited system results in a state different from the initial state (and explored earlier), then a new local minimum is found, otherwise the evolution of the excited system is continued. The ways of moving out of the initial state can be different in temperature accelerated dynamics (TAD) by Sorensen and Voter [78], MD is used at high temperatures in the activation-relaxation technique (ART) by Mousseau and Barkema [79] and the local activated Monte Carlo method (LAMC) [80], the system evolves along the direction opposite to the direction of the force in the long-scale kinetic Monte Carlo... 

Many computational studies of the permeation of small gas molecules through polymers have appeared, which were designed to analyze, on an atomic scale, diffusion mechanisms or to calculate the diffusion coefficient and the solubility parameters. Most of these studies have dealt with flexible polymer chains of relatively simple structure such as polyethylene, polypropylene, and poly-(isobutylene) [49,50,51,52,53], There are, however, a few reports on polymers consisting of stiff chains. For example, Mooney and MacElroy [54] studied the diffusion of small molecules in semicrystalline aromatic polymers and Cuthbert et al. [55] have calculated the Henry s law constant for a number of small molecules in polystyrene and studied the effect of box size on the calculated Henry s law constants. Most of these reports are limited to the calculation of solubility coefficients at a single temperature and in the zero-pressure limit. However, there are few reports on the calculation of solubilities at higher pressures, for example the reports by de Pablo et al. [56] on the calculation of solubilities of alkanes in polyethylene, by Abu-Shargh [53] on the calculation of solubility of propene in polypropylene, and by Lim et al. [47] on the sorption of methane and carbon dioxide in amorphous polyetherimide. In the former two cases, the authors have used Gibbs ensemble Monte Carlo method [41,57] to do the calculations, and in the latter case, the authors have used an equation-of-state method to describe the gas phase. 

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