Principal Investigator Nicolas Hadjiconstantinou
Variance reduction via simulating only the deviation from equilibrium can also be used as a powerful multiscale tool; it separates, in a seamless fashion, the local description into a part that is treated molecularly and a part that can be treated in ways that avoid the large cost associated with the molecular description but retain the same level of fidelity. In other words, the number of particles in the system adjusts dynamically, with regions where little happens described using few particles.
One example shows the reponse of a material (gas/semiconducting solid), originally at equilibrium, to a laser pulse. At any instant in time, regions that have not been affected by the pulse remain in equilibrium; in other words, a particle simulation of that region would reproduce the known properties of the equilibrium distribution. Consequently, describing such regions deterministically (using an equilibrium distribution) has two benefits: (a) it removes the statistical uncertainty associated with the molecular description (variance reduction); (b) it removes the computational cost associated with explicitly simulating the equilibrium regions with particles. Another example shows where the presence of bounded layers means that the a large part of the simulation domain is in equilibrium and can thus be described deterministically without using particles.
Additionally, using a spatially variable (local) equilibrium as the control, leads to a particle method which can seamlessly approach the Navier-Stokes limit Kn<<<1 (i.e. simulate large scale problems). This is because as Kn decreases, a local equilibrium description becomes more fitting and, consequently, increasingly larger fraction of the molecular distribution function can be relegated to the deterministic component of the description (the local equilibrium distribution) which is not simulated using particles.