Coulomb dominance

Despite all the effort to reduce both the frequency of Coulomb solves (periodic or not) and the computational complexity of each call when required, the long-range force evaluation remains the dominant computational cost of MD simulations. 

The dominant force in ionic liquids is Coulombic attraction between ions. The Coulombic attraction term is given by Equation (3.1-2) ... 

In the DC-biased structures considered here, the dynamics are dominated by electronic states in the conduction band [1]. A simplified version of the theory assumes that the excitation occurs only at zone center. This reduces the problem to an n-level system (where n is approximately equal to the number of wells in the structure), which can be solved using conventional first-order perturbation theory and wave-packet methods. A more advanced version of the theory includes all of the hole states and electron states subsumed by the bandwidth of the excitation laser, as well as the perpendicular k states. In this case, a density-matrix picture must be used, which requires a solution of the time-dependent Liouville equation. Substituting the Hamiltonian into the Liouville equation leads to a modified version of the optical Bloch equations [13,15]. These equations can be solved readily, if the k states are not coupled (i.e., in the absence of Coulomb interactions). 

The electron transport properties described earlier markedly differ when the particles are organized on the substrate. When particles are isolated on the substrate, the well-known Coulomb blockade behavior is observed. When particles are arranged in a close-packed hexagonal network, the electron tunneling transport between two adjacent particles competes with that of particle-substrate. This is enhanced when the number of layers made of particles increases and they form a FCC structure. Then ohmic behavior dominates, with the number of neighbor particles increasing. In the FCC structure, a direct electron tunneling process from the tip to the substrate occurs via an electrical percolation process. Hence a micro-crystal made of nanoparticles acts as a metal. 

Orientational disorder and packing irregularities in terms of a modified Anderson-Hubbard Hamiltonian [63,64] will lead to a distribution of the on-site Coulomb interaction as well as of the interaction of electrons on different (at least neighboring) sites as it was explicitly pointed out by Cuevas et al. [65]. Compared to the Coulomb-gap model of Efros and Sklovskii [66], they took into account three different states of charge of the mesoscopic particles, i.e. neutral, positively and negatively charged. The VRH behavior, which dominates the electrical properties at low temperatures, can conclusively be explained with this model. 

The free-electron gas was first applied to a metal by A. Sommerfeld (1928) and this application is also known as the Sommerfeld model. Although the model does not give results that are in quantitative agreement with experiments, it does predict the qualitative behavior of the electronic contribution to the heat capacity, electrical and thermal conductivity, and thermionic emission. The reason for the success of this model is that the quantum effects due to the antisymmetric character of the electronic wave function are very large and dominate the effects of the Coulombic interactions. 

First of all we note that the Fermi hole - which is due to the antisymmetry of the wave function - dominates by far the Coulomb hole. Second, another, very important property of the Fermi hole is that it, just like the total hole, integrates to -1... 

The adsorption of GFP molecules on mesoporous silicas takes place in three fundamental steps. First, the protein molecules in the bulk phase are transported close to the silica, either by convection or diffusion. Second, the protein is adsorbed on the surface of the silicas by electrostatic and Coulomb interactions which are mostly the dominant forces to be at stake. Third, the adsorbed proteins diffuse into the inner of pores and channels. 

It may not be necessary, however, to assume that the early stages of depassivation by annealing are due to buildup of the concentration of H° as AH complexes dissociate. While the equations of Sah et al. have focused attention on the ultimate formation of H2 as the dominant process in the later stages of annealing, it is quite possible that the rate of H2 formation may be relatively higher at early times than would be predicted by the simple n2 dependence in the original Eq. (117). When both H+ and H° are present, formation by H+ + H+ will be slow, because of Coulomb repulsion, and we shall see evidence in Sections 4a and 4b that H+ + H° may... 

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