Small displacement methods have been successfully used to calculate the lattice dynamical properties of crystals. It involves displacing atoms by a small amount in order induced forces on all supercell for computation force constants. Even though these are widely use, our knowledge, there is no systematic discussion optimal directions from crystal's symmetry point view nor rigorous error analys...

Locating atoms with higher precision Two major problems that limit the resolution and interpretation of electron microscopy images are lens aberrations multiple scattering. Chen et al. overcame these issues ptychography, a technique uses coherent scattering overlapping illumination spots to reconstruct an image from far-field diffraction patterns. This method works at is limited, not by optics,...

We study matter-wave scattering from an ultracold, many-body atomic system trapped in an optical lattice. The angular cross section of the target lattice for a matter wave is determined and is demonstrated to have a strong dependence on the many-body phase, superfluid, or Mott insulator. Analytical approaches are employed deep in the superfluid and Mott-insulator regimes, while intermediate poi...

Abstract Diesel particulate matter (DPM) is an area of concern from environmental point view due to its functionality settle in the respiratory channels when inhaled, cause inflammation tract, accumulate carcinogenic compounds, and adversely reflected cardiovascular functions, thus causing excess mortality. DPM consists agglomeration a numerous unions preimages germ structures, spherical form t...