Theory Monte Carlo simulation

FIG. 1 Total local density p(z) for bulk density p = 0.821 and e /k T = 4.25. The solid line is for PYl theory, the dashed line is for HNCl approximation and the points denote the Monte Carlo simulation results. (Reprinted from S. Sokolowski, D. Henderson, A. Trokhymchuk, O. Pizio. Density profiles of associating fluid near a hard wall PY/EMSA and HNC/EMSA singlet theory, Physica A, 220, 22-32. (1995), with permission from Elsevier Science.)... 

FIG. 9 Changes of the monolayer film critical temperature with the concentration of impurities obtained from the Monte Carlo simulations (open circles) and resulting from the mean field theory (solid line). (Reprinted from A. Patrykiejew. Monte Carlo studies of adsorption. II Localized monolayers on randomly heterogeneous surfaces. Thin Solid Films, 205 189-196, with permision from Elsevier Science.)... 

A. Milchev, W. Paul, K. Binder. Polymer chains confined into tubes with attractive walls A Monte Carlo simulation. Macromol Theory Simul 5 305-323, 1994. 

K. Kremer, K. Binder. Dynamics of polymer chains confined into tubes Scaling theory and Monte Carlo simulations. J Chem Phys 7 6381-6394, 1984. 

A. Milchev, K. Binder. Osmotic pressure, atomic pressure and the virial equation of state of polymer solutions Monte Carlo simulations of a bead-spring model. Macromol Theory Simul 5 915-929, 1994. 

The first step in studying phenomenological theories (Ginzburg-Landau theories and membrane theories) has usually been to minimize the free energy functional of the model. Fluctuations are then included at a later stage, e.g., using Monte Carlo simulations. The latter will be discussed in Sec. V and Chapter 14. 

G. Gompper, M. Kraus. Ginzburg-Landau theory of ternary amphiphilic systems. II. Monte Carlo simulations. Phys Rev E 47 4301- 312, 1993. 

S. Murad, J. G. Powles, B. Holtz. Osmosis and reverse osmosis in solutions Monte-Carlo simulations and van der Waals one-fluid theory. Mol Phys 55 1473, 1995. 

FIG. 22 Monte Carlo simulations (solid lines) in isotropic systems and comparison to results of volume averaging theory (horizontal bars). (Reproduced with kind permission of Kluwer Academic Publishers from Ref 398, Fig. 6 and 8, Copyright Kluwer Academic Publishers.)... 

Ab initio methods allow the nature of active sites to be elucidated and the influence of supports or solvents on the catalytic kinetics to be predicted. Neurock and coworkers have successfully coupled theory with atomic-scale simulations and have tracked the molecular transformations that occur over different surfaces to assess their catalytic activity and selectivity [95-98]. Relevant examples are the Pt-catalyzed NO decomposition and methanol oxidation. In case of NO decomposition, density functional theory calculations and kinetic Monte Carlo simulations substantially helped to optimize the composition of the nanocatalyst by alloying Pt with Au and creating a specific structure of the PtgAu7 particles. In catalytic methanol decomposition the elementary pathways were identified... 

Thus we have found that the screening should be more efficient than in the Debye-Hiickel theory. The Debye length l//c is shorter by the factor 1 — jl due to the hard sphere holes cut in the Coulomb integrals which reduce the repulsion associated with counterion accumulation. A comparison with Monte Carlo simulation results [20] bears out this view of the ion size effect [19]. 

Dodd, L. R. and Theodorou, D. N. Atomistic Monte Carlo Simulation and Continuum Mean Field Theory of the Structure and Equation of State Properties of Alkane and Polymer Melts. Vol 116,pp, 249-282,... 

Figure 9. The measured momentum density of an aluminium film. In the left panel we show the measured momentum density near the Fermi level (error bars), the result of the LMTO calculations (dashed line) and the result of these calculations in combination with Monte Carlo simulations taking into account the effects of multiple scattering (full line). In the central panel we show in a similar way the energy spectrum near zero momentum. In the right panel we again show the energy spectrum, but now the theory is that of an electron gas, taking approximately into account the effects of electron-electron correlation (dashed) and this electron gas theory plus Monte Carlo simulations (solid line).

The same normalisation of theory to the experiment is used as in the momentum density plot. Clearly the Monte Carlo simulation compares better with the experiment than the LMTO calculation by itself, but at high binding energies there is still a significant amount of intensity missing in the theory. 

Van Bavel, A. P., Hermse, C. G. M., Hopstaken, M. J. P. et al. (2004) Quantifying lateral adsorbate interactions by kinetic Monte-Carlo simulations and density-functional theory NO dissociation on Rh(100) , Phys. Chem. Chem. Phys., 6, 1830. 

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