Acoustic controlled rotation and orientation

Acoustic energy is applied to a pair of locations spaced about a chamber, to control rotation of an object levitated in the chamber. Two acoustic transducers applying energy of a single acoustic mode, one at each location, can (one or both) serve to levitate the object in three dimensions as well as control its rotation. Slow rotation is achieved by initially establishing a large phase difference and/or pressure ratio of the acoustic waves, which is sufficient to turn the object by more than 45 deg, which is immediately followed by reducing the phase difference and/or pressure ratio to maintain slow rotation. A small phase difference and/or pressure ratio enables control of the angular orientation of the object without rotating it. The sphericity of an object can be measured by its response to the acoustic energy

Single mode levitation and translation

A single frequency resonance mode is applied by a transducer to acoustically levitate an object within a chamber. This process allows smooth movement of the object and suppression of unwanted levitation modes that would urge the object to a different levitation position. A plunger forms one end of the chamber, and the frequency changes as the plunger moves. Acoustic energy is applied to opposite sides of the chamber, with the acoustic energy on opposite sides being substantially 180 degrees out of phase

Gate Defined Quantum Confinement in Suspended Bilayer Graphene

Quantum confined devices that manipulate single electrons in graphene are emerging as attractive candidates for nanoelectronics applications. Previous experiments have employed etched graphene nanostructures, but edge and substrate disorder severely limit device functionality. Here we present a technique that builds quantum confined structures in suspended bilayer graphene with tunnel barriers defined by external electric fields that break layer inversion symmetry, thereby eliminating both edge and substrate disorder. We report clean quantum dot formation in two regimes: at zero magnetic field B using the single particle energy gap induced by a perpendicular electric field and at B > 0 using the quantum Hall ferromagnet {\nu} = 0 gap for confinement. Coulomb blockade oscillations exhibit periodicity consistent with electrostatic simulations based on local top gate geometry, a direct demonstration of local control over the band structure of graphene. This technology integrates single electron transport with high device quality and access to vibrational modes, enabling broad applications from electromechanical sensors to quantum bits.Comment: 22 pages, 9 figures, includes supplementary informatio

SEAHT: A computer program for the use of intersecting arcs of altimeter data for sea surface height refinement

The SEAHT program is designed to process multiple passes of altimeter data with intersecting ground tracks, with the estimation of corrections for orbital errors to each pass such that the data has the best overall agreement at the crossover points. Orbit error for each pass is modeled as a polynomial in time, with optional orders of 0, 1, or 2. One or more passes may be constrained in the adjustment process, thus allowing passes with the best orbits to provide the overall level and orientation of the estimated sea surface heights. Intersections which disagree by more than an input edit level are not used in the error parameter estimation. In the program implementation, passes are grouped into South-North passes and North-South passes, with the North-South passes partitioned out for the estimation of orbit error parameters. Computer core utilization is thus dependent on the number of parameters estimated for the set of South-North arcs, but is independent on the number of North-South passes. Estimated corrections for each pass are applied to the data at its input data rate and an output tape is written which contains the corrected data

Assembling homology classes in automorphism groups of free groups

The observation that a graph of rank $n$ can be assembled from graphs of smaller rank $k$ with $s$ leaves by pairing the leaves together leads to a process for assembling homology classes for $Out(F_n)$ and $Aut(F_n)$ from classes for groups $\Gamma_{k,s}$, where the $\Gamma_{k,s}$ generalize $Out(F_k)=\Gamma_{k,0}$ and $Aut(F_k)=\Gamma_{k,1}$. The symmetric group $\Sigma_s$ acts on $H_*(\Gamma_{k,s})$ by permuting leaves, and for trivial rational coefficients we compute the $\Sigma_s$-module structure on $H_*(\Gamma_{k,s})$ completely for $k \leq 2$. Assembling these classes then produces all the known nontrivial rational homology classes for $Aut(F_n)$ and $Out(F_n)$ with the possible exception of classes for $n=7$ recently discovered by L. Bartholdi. It also produces an enormous number of candidates for other nontrivial classes, some old and some new, but we limit the number of these which can be nontrivial using the representation theory of symmetric groups. We gain new insight into some of the most promising candidates by finding small subgroups of $Aut(F_n)$ and $Out(F_n)$ which support them and by finding geometric representations for the candidate classes as maps of closed manifolds into the moduli space of graphs. Finally, our results have implications for the homology of the Lie algebra of symplectic derivations.Comment: Final version for Commentarii Math. Hel