Title: Distinguishing noisy crystal symmetries in coarse-grained computer simulations: New procedures for noise reduction and lattice reconstruction

Abstract: We suggest new modification (we call it a noise reduction procedure) for Steinhardt parameters which are often used for detecting crystalline structures in computer simulation of solids and soft matter systems. We have also developed a new methodology how to reconstruct "ideal" lattice structure in the whole simulation box that would be most close to a real noisy crystalline symmetry, when it is defined locally and then averaged over the whole box. For this second procedure, which we call lattice reconstruction procedure, we have developed an algorithm for finding the lattice vectors from the values of Steinhardt parameters obtained after the noise reduction procedure. We apply noise to the classical crystalline structures (sc, bcc, fcc, hcp), and use both procedures to detect the crystalline structures in these classical but noisy systems. We demonstrate advantages of our procedures in comparison with existing methods and discuss their applicability limits.