An algorithm for the systematic disturbance of optimal rotational solutions

An algorithm for introducing a systematic rotational disturbance into an optimal (i.e., single axis) rotational trajectory is described. This disturbance introduces a motion vector orthogonal to the quaternion-defined optimal rotation axis. By altering the magnitude of this vector, the degree of non-optimality can be controlled. The metric properties of the distortion parameter are described, with analogies to two-dimensional translational motion. This algorithm was implemented in a motion-control program on a three-dimensional graphic workstation. It supports a series of human performance studies on the detectability of rotational trajectory optimality by naive observers

High effectiveness contour matching contact heat exchanger

There is a need in the art for a heat exchanger design having a flexible core providing contour matching capabilities, which compensates for manufacturing tolerance and distortion buildups, and which accordingly furnishes a relatively uniform thermal contact conductance between the core and external heat sources under essentially all operating conditions. The core of the heat exchanger comprises a top plate and a bottom plate, each having alternate rows of pins attached. Each of the pins fits into corresponding tight-fitting recesses in the opposite plate

Final Report: Wall Effects in Cavity Flows

The wall effects in cavity flows past an arbitrary two-dimensional body is investigated for both pure-drag and lifting cases based on an inviscid nonlinear flow theory. The over-all features of various theoretical flow models for inviscid cavity flows under the wall effects are discussed from the general momentum consideration in comparison with typical viscous, incompressible wake flows in a channel. In the case of pure drag cavity flows, three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant jet models, are applied to evaluate the solution. Methods of numerical computation are discussed for bodies of arbitrary shape, and are carried out in detail for wedges of all angles. The final numerical results are compared between the different flow models, and the differences pointed out. Further analysis of the results has led to development of several useful formulas for correcting the wall effect. In the lifting flow case, the wall effect on the pressure and hydrodynamic forces acting on arbitrary body is formulated for the choked cavity flow in a closed water tunnel of arbitrary shape, and computed for the flat plate with a finite cavity in a straight tunnel

First-principles investigation of magnetism and electronic structures of substitutional 3d3d transition-metal impurities in bcc Fe

The magnetic and electronic structures of $3d$ impurity atoms from Sc to Zn in ferromagnetic body-centered cubic iron are investigated using the all-electron full-potential linearized augmented plane-wave method based on the generalized gradient approximation (GGA). We found that in general, the GGA results are closer to the experimental values than those of the local spin density approximation. The calculated formation enthalpy data indicate the importance of a systematic study on the ternary Fe-C-$X$ systems rather than the binary Fe-$X$ systems, in steel design. The lattice parameters are optimized and the conditions for spin polarization at the impurity sites are discussed in terms of the local Stoner model. Our calculations, which are consistent with previous work, imply that the local spin-polarizations at Sc, Ti, V, Cu, and Zn are induced by the host Fe atoms. The early transition-metal atoms couple antiferromagnetically, while the late transition-metal atoms couple ferromagnetically, to the host Fe atoms. The calculated total magnetization ($M$) of bcc Fe is reduced by impurity elements from Sc to Cr as a result of the antiferromagnetic interaction, with the opposite effect for solutes which couple ferromagnetically. The changes in $M$ are attributed to nearest neighbor interactions, mostly between the impurity and host atoms. The atom averaged magnetic moment is shown to follow generally the well-known Slater-Pauling curve, but our results do not follow the linearity of the Slater-Pauling curve. We attribute this discrepancy to the weak ferromagnetic nature of bcc Fe. The calculated Fermi contact hyperfine fields follow the trend of the local magnetic moments. The effect of spin-orbit coupling is found not to be significant although it comes into prominence at locations far from the impurity sites.Comment: 26 pages, 11 figure

Maxwell--Chern-Simons gauged non-relativistic O(3) model with self-dual vortices

A non-relativistic version of the 2+1 dimensional gauged Chern-Simons O(3) sigma model, augmented by a Maxwell term, is presented and shown to support topologically stable static self-dual vortices. Exactly like their counterparts of the ungauged model, these vortices are shown to exhibit Hall behaviour in their dynamics.Comment: 12 pages, LateX, to appear in Mod. Phys. Lett. 199

New Candidates for Topological Insulators : Pb-based chalcogenide series

Here, we theoretically predict that the series of Pb-based layered chalcogenides, Pb$_n$Bi$_2$Se$_{n+3}$ and Pb$_n$Sb$_2$Te$_{n+3}$, are possible new candidates for topological insulators. As $n$ increases, the phase transition from a topological insulator to a band insulator is found to occur between $n=2$ and 3 for both series. Significantly, among the new topological insulators, we found a bulk band gap of 0.40eV in PbBi$_2$Se$_4$ which is one of the largest gap topological insulators, and that Pb$_2$Sb$_2$Te$_5$ is located in the immediate vicinity of the topological phase boundary, making its topological phase easily tunable by changing external parameters such as lattice constants. Due to the three-dimensional Dirac cone at the phase boundary, massless Dirac fermions also may be easily accessible in Pb$_2$Sb$_2$Te$_5$

Vortex Loops and Majoranas

We investigate the role that vortex loops play in characterizing eigenstates of interacting Majoranas. We first give some general results, and then we focus on ladder Hamiltonian examples to test further ideas. Two methods yield exact results: i.) We utilize the mapping of spin Hamiltonians to quartic interactions of Majoranas and show under certain conditions the spectra of these two examples coincide. ii) In cases with reflection-symmetric Hamiltonians, we use reflection positivity for Majoranas to characterize vortices. Aside from these exact results, two additional methods suggest wider applicability of these results: iii.) Numerical evidence suggests similar behavior for certain systems without reflection symmetry. iv.) A perturbative analysis also suggests similar behavior without the assumption of reflection symmetry.Comment: 28 page

Localisation of Fermions to brane: Codimension d≥2d \geq 2

We investigate $4+d$ dimensional fermionic models in which the system in codimension-$d$ supports a topologically stable solution, and in which the fermion may be localised to the brane, with power law in 'instanton' backgrounds and exponentially in 'soliton' backgrounds. When the fermions are isoscalars, the mechanism fails, while for isospinor fermions it is successful. As backgrounds we consider instantons of Yang--Mills and sigma models in even codimensions, solitons of sigma models in odd codimensions, as well as solitons of Higgs and Goldstone models in all codimensions.Comment: 20 pages latex; expande

Dark Energy Constraints from Galaxy Cluster Peculiar Velocities

Future multifrequency microwave background experiments with arcminute resolution and micro-Kelvin temperature sensitivity will be able to detect the kinetic Sunyaev-Zeldovich (kSZ) effect, providing a way to measure radial peculiar velocities of massive galaxy clusters. We show that cluster peculiar velocities have the potential to constrain several dark energy parameters. We compare three velocity statistics (the distribution of radial velocities, the mean pairwise streaming velocity, and the velocity correlation function) and analyze the relative merits of these statistics in constraining dark energy parameters. Of the three statistics, mean pairwise streaming velocity provides constraints that are least sensitive to velocity errors: the constraints on parameters degrades only by a factor of two when the random error is increased from 100 to 500 km/s. We also compare cluster velocities with other dark energy probes proposed in the Dark Energy Task Force report. For cluster velocity measurements with realistic priors, the eventual constraints on the dark energy density, the dark energy equation of state and its evolution are comparable to constraints from supernovae measurements, and better than cluster counts and baryon acoustic oscillations; adding velocity to other dark energy probes improves constraints on the figure of merit by more than a factor of two. For upcoming Sunyaev-Zeldovich galaxy cluster surveys, even velocity measurements with errors as large as 1000 km/s will substantially improve the cosmological constraints compared to using the cluster number density alone.Comment: 25 pages, 10 figures. Results and conclusions unchanged. Minor changes to match the accepted version in Physical Review