No abstract

SUMMARYThe bounce-back boundary condition for lattice Boltzmann simulations is evaluated for¯ow about an in®nite periodic array of cylinders. The solution is compared with results from a more accurate boundary condition formulation for the lattice Boltemann method and with ®nite difference solutions. The bounce-back boundary condition is used to simulate boundaries of cylinders with both circular and octagonal cross-sections. The convergences of the velocity and total drag associated with this method are slightly sublinear with grid spacing. Error is also a function of relaxation time, increasing exponentially for large relaxation times. However, the accuracy does not exhibit a trend with Reynolds number between 0Á1 and 100. The square lattice Boltzmann grid conforms to the octagonal cylinder but only approximates the circular cylinder, and the resulting error associated with the octagonal cylinder is half the error of the circular cylinder. The bounce-back boundary condition is shown to yield accurate lattice Boltzmann simulations with reduced computational requirements for computational grids of 1706170 or ®ner, a relaxation time less than 1Á5 and any Reynolds number from 0Á1 to 100. For this range of parameters the root mean square error in velocity and the relative error in drag coef®cient are less than 1 per cent for the octagonal cylinder and 2 per cent for the circular cylinder.

SUMMARYDynamic models of nanometer-scale phenomena often require an explicit consideration of interactions among a large number of atoms or molecules. The corresponding mathematical representation may thus be high dimensional, nonlinear, and stochastic, incompatible with tools in nonlinear control theory that are designed for low-dimensional deterministic equations. We consider here a general class of probabilistic systems that are linear in the state, but whose input enters as a function multiplying the state vector. Model reduction is accomplished by grouping probabilities that evolve together, and truncating states that are unlikely to be accessed. An error bound for this reduction is also derived. A system identification approach that exploits the inherent linearity is then developed, which generates all coefficients in either a full or reduced model. These concepts are then extended to extremely high-dimensional systems, in which kinetic Monte Carlo (KMC) simulations provide the input-output data. This work was motivated by our interest in thin film deposition. We demonstrate the approaches developed in the paper on a KMC simulation of surface evolution during film growth, and use the reduced model to compute optimal temperature profiles that minimize surface roughness.

This article applies kinetic Monte Carlo simulations to interpret experimental measurements in the polymerization of hyperbranched poly(ether esters)s in a melt condensation of A2 oligomers and B3 monomers. Building on the analytical modeling of Flory and Stockmayer, additional effects of cycle formation, unequal reactivities, and end-capping reagents are added into the simulations to describe A2 + B3 polymerization in the absence of a solvent. The experimental data have been published separately, and here it is compared to the model predictions in order to quantitatively assess whether the data are consistent with these models. On the basis of the modeling, we conclude that cycle formation is negligible, suppression of the third B group is insignificant, and the mobility of the free B3 monomer leads to enhancement of its reaction rate. The addition of the monofunctional end-capping reagents does not necessarily lead to suppression of branching in the A2 + B3 system and depends sensitively on the stoichiometry of the reactants.