8 problems

Configurational thermostatting conjecture. It is possible to use the relaxation time $\tau$ for thermostatting configurational degrees of freedom while the momentum variables remai…

Consider systems like the molecular-dynamics system described in Section, and compare integration schemes by the efficiency with which they compute statistically accurate trajector…

Consider the molecular-dynamics system described in Section, integrated with the Störmer–Verlet method using time step $\Delta t$. The simulation is compared with the corresponding…

Let $X$ be the exact molecular-dynamics trajectory and $X_{\Delta t}$ its numerical approximation, viewed as random elements of $(C[0,T])^m$, and let $\rho$ be the Prokhorov metric…

Let $X$ be the exact trajectory and $X_{\Delta t}$ its numerical approximation with time step $\Delta t$, and let $\Pi\colon\mathbb{R}^m\rightarrow\mathbb{R}^k$ be the observable m…

Prokhorov approximation conjecture. For some small $\epsilon$, one has

Let a numerical trajectory be generated by a molecular-dynamics discretization over a long time interval, and let an exact trajectory solve the original differential equations. Sha…

Let $X$ denote the exact molecular-dynamics trajectory and $X_{\Delta t}$ its numerical trajectory with time step $\Delta t$. Let $\Pi \colon \mathbb{R}^m \rightarrow \mathbb{R}^k$…