Markov Chains of theM/G/1‐Type

Abstract

This article reports the main properties of M/G/1‐type Markov chains together with the classical and the most advanced algorithms for their analysis.

Deconstructing Electrostatics of Functionalized Metal Nanoparticles from Molecular Dynamics Simulations

“…In route (i), the charge volume map is evaluated on a 1 Å resolution grid using the tool of VMD1.9.3, using the effective atomic charges (with a Gaussian smearing using the vdW radius) and averaging over the trajectory frames. Three charge maps ρ NP ( r ), ρ ion ( r ), and ρ wat ( r ) for NPs, ions, and water are calculated and subsequently spherically averaged using in-house-coded Python scripts to obtain the corresponding radial functions ρ NP ( r ), ρ ion ( r ), and ρ wat ( r ). In the alternative route (ii), the ρ( r )’s are evaluated from the charge weighted radial distribution functions, namely, with ρ ( r ) = ∑ i N i V q i g i ( r ) = ∑ i n i ( r ) q i , where g i ( r ) is the pair distribution function between the NP center and the atoms of type i , and N i , q i , and n i ( r ) are their number, charge, and radial density, respectively.…”