There has been a recent resurgence of experimental efforts to quantitatively determine the phase diagram of the Bose-Hubbard model by carefully analyzing experiments with ultracold bosonic atoms on an optical lattice. In many realizations of these experiments, the hopping amplitudes are not homogeneous throughout the lattice, but instead, the lattice has an anisotropy where hopping along one di...

Emily Stone Department of Mathematical Sciences, The University of Montana, Missoula, MT 59812 U.S.A. Abstract In this paper we present stability analysis of a nonlinear model for chatter vibration in a drilling operation. The results build our previous work [1, 2], where the model was developed and the nonlinear stability of the vibration modes as cutting width is varied was presented. Here we...

The paper reviews the controversy on the shape of the fcc-based phase diagram near the triple point among the disordered (A1), L1z and L1o phases. The discrepancy was originally between the cluster variation method (CVM) results and Monte Carlo (MC) simulation results, but the controversy developed into how to interpret MC results. The paper examines historically how the controversy started, ho...

This paper considers the eeect of site perturbations on Voronoi diagrams, where the sites are points in the plane. Given a bound on the distance that any site may move, we ask which pairs of Voronoi neighbors may become non-neighbors and which are guaranteed to remain neighbors. A pair of the second kind is called stable. The paper shows necessary and suucient conditions for stability. Algorith...

Abstract. We study the cancellations among Feynman diagrams that implement the Ward and SlavnovTaylor identities corresponding to the conserved supersymmetry current in supersymmetric quantum field theories. In particular, we show that the Faddeev-Popov ghosts of gaugeand supersymmetries never decouple from the physical fields, even for abelian gauge groups. The supersymmetric Slavnov-Taylor id...

In this paper, we study the problem of multi-robot coverage when the evolution of the robots’ positions is uncertain. More precisely, we use the popular Voronoi coverage control approach [1], which is based on the iterative construction of a centroidal Voronoi tessellation, and ask what happens to the control law and the Voronoi tessellation under actuation and measurement noise. We present a f...