Simulation techniques direct methods

Molecular dynamics (MD) and Monte Carlo (MC) simulations are popular molecular simulation techniques. These methods are well suited for modeling supercapacitor because EDLs in supercapacitors are essentially molecular phenomena, e.g., the thickness of EDLs in supercapacitors is typically less than a few nanometers. The uni(]ue advantage of these methods is that they provide direct information on both the microstructure (e.g., ion density distribution across EDL, which is difficult to measure experimentally) and the macroscopic properties (e.g., its capacitance) of EDLs. This allows one to establish the microscopic origins of the capacitance of supercapacitors and thus helps guide the design and selection of electrode/electrolyte materials for supercapacitors. MD simulation, as... 

Alternative methods of analysis have been examined and evaluated. Shokoohi and Elrod[533] solved the Navier-Stokes equations numerically in the axisymmetric form. Bogy15271 used the Cosserat theory developed by Green.[534] Ibrahim and Linl535 conducted a weakly nonlinear instability analysis. The method of strained coordinates was also examined. In spite of the mathematical or computational elegance, all of these methods suffer from inherent complexity. Lee15361 developed a 1 -D, nonlinear direct-simulation technique that proved to be a simple and practical method for investigating the nonlinear instability of a liquid j et. Lee s direct-simulation approach formed the... 

The main goal of simulation methods is to obtain information on the spatial and temporal behavior of a complex system (a material), that is, on its structure and evolution. Simulation methods are subdivided into atomistic and phenomenological methods. Atomistic methods directly consider the evolution of the system of interest at the atomic level with regard to the microscopic structure of the substance. These methods include classical and quantum MD and various modifications of the MC technique. Phenomenological methods are based on macroscopic equations in which the atomistic nature of the material is not directly taken into account. Within the multiscale approach, both groups of methods mutually complement each other, which permits the physicochemical system under study to be described most comprehensively. 

It is not straightforward to calculate phase equilibria or chemical potentials in a simulation, and special techniques must be used. This has been an active research area over the past few years [15]. Several methods have been proposed, and these can be divided into direct methods, in which the coexistence properties of the phases are calculated directly, and indirect methods, where the chemical potential is first calculated and then used to determine the phase equilibrium conditions (Table 4). 

The Monte Carlo method has been applied more extensively to the study of solvation phenomena. Clementi has looked at solvent distribution around a large variety of amino acids and nucleotides. This work is summarized by Clementi in detail in this volume[l7e]. It should be noted that all this work on solvent using these powerful simulation techniques has appeared within the last five years and most of it even more recently. This is a direct result of the advances in computer technology as well as the adaptation of the... 

The combined limitations of direct and Green-Kubo simulations mean that neither may be satisfactory if one is interested in the small, but nonzero, field limit. To accomplish this, two simulation techniques have been developed. The first is commonly known as the subtraction method because it is based on... 

The calculations reported in this paper and a related series of publications indicate that it is now quite feasible to obtain reasonably accurate results for phase equilibria in simple fluid mixtures directly from molecular simulation. What is the possible value of such results Clearly, because of the lack of accurate intermolecular potentials optimized for phase equilibrium calculations for most systems of practical interest, the immediate application of molecular simulation techniques as a replacement of the established modelling methods is not possible (or even desirable). For obtaining accurate results, the intermolecular potential parameters must be fitted to experimental results, in much the same way as parameters for equation-of-state or activity coefficient models. This conclusion is supported by other molecular-simulation based predictions of phase equilibria in similar systems (6). However, there is an important difference between the potential parameters in molecular simulation methods and fitted parameters of thermodynamic models. Molecular simulation calculations, such as the ones reported here, involve no approximations beyond those inherent in the potential models. The calculated behavior of a system with assumed intermolecular potentials is exact for any conditions of pressure, temperature or composition. Thus, if a good potential model for a component can be developed, it can be reliably used for predictions in the absence of experimental information. 

Computer simulations of complex polyatomic systems became an important tool supplementing experimental studies and chemistry and materials science1,2. They can be used i) to get access to data not available directly in experimental measurements, ii) to verify hypotheses concerning the mechanism of the investigated process, Hi) and to make predictions. At different scales, methods based on different physical laws are used. At macroscopic scale, computer simulation techniques are... 

Direct Methods Direct-Space Techniques Patterson Methods Monte Carlo Simulated Annealing Genetic Algorithm Degree of Freedom Cost Function... 

Once the correlation functions have been solved, adsorption isotherms can be obtained from the Fourier transform of the direct correlation function Cc(r) [55]. The ROZ integral equation approach is noteworthy in that it yields model adsorption isotherms for disordered porous materials that have irregular pore geometries without resort to molecular simulation. In contrast, most other disordered structural models of porous solids implement GCMC or other simulation techniques to compute the adsorption isothem. However, no method has yet been demonstrated for determining the pore structure of model disordered or templated structures from experimental isotherm measurements using integral equation theory. 

The plume development in MD simulations can only be followed up to a few nanoseconds after the pulse, which is not enough to compare the data with various experimental techniques (such as MALDI, TOF-MS, shadowgra-phy, interferometry, or for PLD). The long-term plume expansion is then modeled by the direct simulation Monte Carlo method, which was recently applied to systems relevant to MALDI [112]. 

Experimental techniques for studying solvation include direct methods such as spectroscopic methods, diffraction techniques and light scattering. Use can also be made of indirect methods such as thermodynamic properties, conductance and activity coefficient studies, and diffusion. Computer simulation experiments have increasingly been playing a major role. 

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