Coarse graining a non-Markovian collisional model

Coarse graining

Multiscale simulations For nearly all systems of interest to us, the most transferrable and fundamental description of matter is one that invokes quantum mechanics. At the highest level of accuracy, this amounts to solving Schrodinger’s equation for all of the subatomic particles in a system. Computationally, many approximations need to be made in order to use ab initio methods, and even these ...

Coarse graining and control theory model reduction

We explain a method, inspired by control theory model reduction and interpolation theory, that rigorously establishes the types of coarse graining that are appropriate for systems with quadratic, generalized Hamiltonians. For such systems, general conditions are given that establish when local coarse grainings should be valid. Interestingly, our analysis provides a reduction method that is vali...

Predictive coarse-graining

Brute-force molecular dynamics simulations are limited by the exuberant number of degrees of freedom and the relatively small time-steps. As a result, only relatively small assemblies of molecules over small time spans are accessible with current and foreseeable computational capabilities. In order to overcome this limitation, coarse-grained models have been proposed which employ a much smaller...

Shape-Based Coarse Graining

Coarse-graining quivers

We describe a block-spin-like transformation on a simplified subset of the space of supersymmetric quiver gauge theories that arise on the worldvolumes of D-brane probes of orbifold geometries, by sequentially Higgsing the gauge symmetry in these theories. This process flows to lower worldvolume energies in the regions of the orbifold moduli space where the closed string blowup modes, and there...