Computer simulation accessible parameters

In principle, the expressions for pair potentials, osmotic pressure and second virial coefficients could be used as input parameters in computer simulations. The objective of performing such simulations is to clarify physical mechanisms and to provide a deeper insight into phenomena of interest, especially under those conditions where structural or thermodynamic parameters of the studied system cannot be accessed easily by experiment. The nature of the intermolecular forces responsible for protein self-assembly and phase behaviour under variation of solution conditions, including temperature, pH and ionic strength, has been explored using this kind of modelling approach (Dickinson and Krishna, 2001 Rosch and Errington, 2007 Blanch et al., 2002). 

Finally, the role of computer simulation has served to deepen our understanding of ionic hydration in systems that can be characterized by pairwise additive potentials (29). Since pressure and temperature are parameters characteristic of simulations, ionic hydration changes at nonambient conditions in regions far from those presently accessible to experiment can be studied. 

In previous papers we have reported on some detailed studies on the behaviour of the order parameter C, (T) which was assimilated to the correlation length for critical fluctuations accessible by means of neutron small-angle scattering as well some measurements on the molecular dynamics across the two phase transitions as explored by neutron quasielastic scattering as well as computer simulations. 

Before computers and efficient simulation methods became available, the canonical approach was the only way for a theoretical discussion of thermodynamic phenomena. On the experimental side, it was appealing to use the heat bath temperature as an external control parameter. Because of this, in equilibrium, temperature seemed to be an easily accessible parameter to control the macrostate of the system, and transition points of thermally driven phase transitions are typically defined by transition temperatures. The canonical analysis of phase transitions has been extremely successful and it enabled the introduction of fundamental physical concepts such as universality. 

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

In order to validate the reduced model (uncoupled population of Izhikevich neurons) we chose to perform comparisons with a direct simulation model. In this last model the internal state of each neuron is computed at each time step (with a forth-order Runge-Kutta method) using the equations of the Izhikevich model so we have complete access to individual information as opposed to the population density formalism where only the states distribution can be computed. The simulation parameters were 50 000 Izhikevich neurons in tonic spiking mode (a = 0.02, b = 0.2, c = —65, d = 6 as provided in [29]), a gaussian form of p(v, u, t) at t =0 and a constant input current of / =60 qA was applied to all neurons. The firing rate and the mean membrane potential (M M P) were computed at each time for the two methods during 15 ms. 

If there are more than two components in a mixture (as in a blend of a homopolymer with a copolymer), binary interaction parameters can be combined into a composite % parameter to describe the overall behavior of the system. For example, Choi and Jo [11] showed how the effects of copolymer sequence distribution in blends of polyethylene oxide) with poly(styrene-co-acrylic acid) can be described by an atomistic simulation approach to estimate the binary intermolecular interaction energies which are combined into a total interaction parameter for the blend. Their paper [11] also provides a list of the many preceding publications attempting to address the effects of copolymer composition, tacticity, and copolymer sequence distribution on polymer blend miscibility. In addition to the advances in computational hardware and software which have made atomistic simulations much faster and hence more accessible, work in recent years has significantly improved the accuracy of the force fields [12] used in such simulations. 

GB/S A Generalized-Born/Surface-Area. A method for simulating solvation implicitly, developed by W.C. Still s group at Columbia University. The solute-solvent electrostatic polarization is computed using the Generalized-Born equation. Nonpolar solvation effects such as solvent-solvent cavity formation and solute-solvent van der Waals interactions are computed using atomic solvation parameters, which are based on the solvent accessible surface area. Both water and chloroform solvation can be emulated. 

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