We have imaged boron nitride nanotubes with atomic scale resolution using scanning tunneling microscopy. While some nanotubes show the expected triangular lattice pattern, the majority of the nanotubes show unusual stripe patterns which break the underlying symmetry of the boron nitride lattice. We identify the origin of the symmetry breaking and demonstrate that conventional STM imaging analys...

We prove that a Banach lattice X which does not contain the ln ∞uniformly has an equivalent norm which is uniformly Kadec-Klee for a natural topology τ on X. In case the Banach lattice is purely atomic, the topology τ is the coordinatewise convergence topology. 1980 Mathematics Subject Classification: Primary 46B03, 46B42.

U ltracold atomic gases offer unique opportunities to study quantum matter in a pristine, wellcontrolled environment. One general method for controlling the atoms and their interactions is to trap them in a so-called optical lattice—a periodic optical potential created by interfering laser beams. Lasers can “sculpt” such potentials with a spatial resolution determined by the laser light’s wavel...

We report surface microscopy characterizations of large size graphene films (up to mm) grown on polycrystalline Ni foils and transferred to Si/SiO2. Wrinkles in such films are studied by both atomic force microscopy (AFM) and scanning tunneling microscopy (STM). Local graphitic lattice structures of the films are imaged with atomic-resolution STM and compared with those of the highly ordered py...

We study theoretically a Fermi-Dirac atomic gas in a one-dimensional optical lattice coupled to a coherent electromagnetic field with a topologically nontrivial soliton phase profile. We argue that the resulting fractional eigenvalues of the particle number operator can be detected via light scattering. This could be a truly quantum mechanical measurement of particle number fractionalization in...

This paper presents VaqUoT – a University of Toronto tool for vacuity detection, built on top of NuSMV. In one model-checking pass, VaqUoT establishes the truth value of a CTL formula as well as the largest set of nonoverlapping subformulas in which that formula is vacuous. We describe the tool and evaluate its performance. During model-checking, properties are sometimes satisfied by models for...

We characterize the macroscopic effective mechanical behavior of a graphene sheet modeled by a hexagonal lattice with twoand three-point atomic interactions, using Γ-convergence.

We consider a simple model of lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. Internal dynamics of the atom is governed by the laser field which is treated to be classical with a large number of photons. Center-of-mass classical atomic motion is governed by the optical potential and the internal at...

We give three examples of large intervals in the lattice of (local) clones on an infinite set X, by exhibiting clones C1, C2, C3 such that: (1) the interval [C1, O] in the lattice of local clones is (as a lattice) isomorphic to {0, 1, 2, . . .} under the divisibility relation, (2) the interval [C2, O] in the lattice of local clones is isomorphic to the congruence lattice of an arbitrary semilat...

The atomic structures of SrTiO 3 (STO)/LaNiO 3 (LNO)/STO heterostructure interfaces were investigated by spherical aberration-corrected (C S) (scanning) transmission electron microscopy. Atomic displacement and lattice distortion measurements and electron energy loss spectroscopy (EELS) were used to quantitatively analyze the distortion of the interfacial octahedra and the bond length at the in...