Search for: All records

Understanding the mechanism that controls cement hydration and its stages is a long-standing challenge. Over a decade ago, the mineral dissolution theory was adopted from geochemistry to explain the hydration rate evolution of alite. The theory is not fully accepted by the community and deserves further investigation. In this work, we apply Kinetic Monte Carlo (KMC) simulations with the mineral dissolution theory as a conceptual framework to investigate and discuss alite dissolution. We build a Kossel crystal model system and parameterize the dissolution activation energies and frequencies based on experimental data. The resulting KMC model is capable of reproducing the dissolution rate and activation energies as a function of the dissolution free energy. The simulations indicate that mineral dissolution theory easily explains the induction and acceleration stages due to a continuous increase of the reactive area as the etch pits open. However, the deceleration stage is hardly reconcilable with the mechanism suggested in the literature, i.e. dislocation coalescence. Still, within the mineral dissolution theory umbrella, we propose and discuss an alternative mechanism based on dislocation exhaustion. 

In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number π . This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of π in a base determined by the ratio of the masses of the two particles. This base can be any integer, but it can also be an irrational number, or even the base can be π itself. This article reviews previous results for Galperin billiards and then pushes these results farther. We provide a complete explicit solution for the balls’ positions and velocities as a function of the collision number and time. We demonstrate that Galperin billiard can be mapped onto a two-particle Calogero-type model. We identify a second dynamical invariant for any mass ratio that provides integrability for the system, and for a sequence of specific mass ratios we identify a third dynamical invariant that establishes superintegrability. Integrability allows us to derive some new exact results for trajectories, and we apply these solutions to analyze the systematic errors that occur in calculating the digits of π with Galperin billiards, including curious cases with irrational number bases.