Finite circular plate on elastic foundation centrally loaded by rigid spherical indenter

The analytical solution of a finite circular plate on an elastic foundation centrally loaded by the rigid indenter is discussed. The procedure to use NASTRAN as a subroutine to iteratively converge to this solution numerically is described

States near Dirac points of rectangular graphene dot in a magnetic field

In neutral graphene dots the Fermi level coincides with the Dirac points. We have investigated in the presence of a magnetic field several unusual properties of single electron states near the Fermi level of such a rectangular-shaped graphene dot with two zigzag and two armchair edges. We find that a quasi-degenerate level forms near zero energy and the number of states in this level can be tuned by the magnetic field. The wavefunctions of states in this level are all peaked on the zigzag edges with or without some weight inside the dot. Some of these states are magnetic field-independent surface states while the others are field-dependent. We have found a scaling result from which the number of magnetic field-dependent states of large dots can be inferred from those of smaller dots.Comment: Physical review B in pres

Adaptive control of a manipulator with a flexible link

An adaptive controller for a manipulator with one rigid link and one flexible link is presented. The performance and robustness of the controller are demonstrated by numerical simulation results. In the simulations, the manipulator moves in a gravitational field and a finite element model represents the flexible link

Towards A Background Independent Quantum Gravity

We recapitulate the scheme of emergent gravity to highlight how a background independent quantum gravity can be defined by quantizing spacetime itself.Comment: 25 pages, 2 figures, Proceedings of 7th International Conference "Quantum Theory and Symmetries" (QTS-7) in Prague, Czech Republic, August, 201

Bounded Gaps Between Products of Distinct Primes

Let $r \ge 2$ be an integer. We adapt the Maynard-Tao sieve to produce the asymptotically best-known bounded gaps between products of $r$ distinct primes. Our result applies to positive-density subsets of the primes that satisfy certain equidistribution conditions. This improves on the work of Thorne and Sono