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We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half-filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional Renormalization Group scheme which allows for highly resolved calculations of wavevector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure $n$-th nearest neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when non-local density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough non-local terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semi-metallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second nearest neighbor interactions is not realized in our results with high momentum resolution., Comment: 24 pages, 7 figures

We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional insertions of truncated partitions of unity. These insertions decouple the fermionic propagators from the exchange propagators and lead to a separation of the underlying equations. We demonstrate that this separation is numerically advantageous and may pave the way for refined, large-scale computational investigations even in the case of complex multiband systems. Furthermore, on the basis of speedup data gained from our implementation, it is shown that this new variant facilitates efficient calculations on a large number of multi-core CPUs. We apply the scheme to the $t$,$t'$ Hubbard model on a square lattice to analyze the convergence of the results with the bond length of the truncation of the partition of unity. In most parameter areas, a fast convergence can be observed. Finally, we compare to previous results in order to relate our approach to other fRG studies., Comment: 26 pages, 9 figures

We investigate the superconducting pairing instabilities of eight-band models for the iron arsenides. Using a functional renormalization group treatment, we determine how the critical energy scale for superconductivity depends on the electronic band structure. Most importantly, if we vary the parameters from values corresponding to LaFeAsO to SmFeAsO, the pairing scale is strongly enhanced, in accordance with the experimental observation. We analyze the reasons for this trend and compare the results of the eight-band approach to those found using five-band models., Comment: 11 pages, 10 figures

Power-spectral-density calculations were made of the lateral responses to atmospheric turbulence for several conventional and short take-off and landing (STOL) airplanes. The turbulence was modeled as three orthogonal velocity components, which were uncorrelated, and each was represented with a one-dimensional power spectrum. Power spectral densities were computed for displacements, rates, and accelerations in roll, yaw, and sideslip. In addition, the power spectral density of the transverse acceleration was computed. Evaluation of ride quality based on a specific ride quality criterion was also made. The results show that the STOL airplanes generally had larger values for the rate and acceleration power spectra (and, consequently, larger corresponding root-mean-square values) than the conventional airplanes. The ride quality criterion gave poorer ratings to the STOL airplanes than to the conventional airplanes.

A method of computing the power spectral densities of the lateral response of airplanes to random atmospheric turbulence was adapted to an electronic digital computer. By use of this program, the power spectral densities of the lateral roll, yaw, and sideslip angular displacement of several conventional and STOL airplanes were computed. The results show that for the conventional airplanes, the roll response is more prominent than that for yaw or sideslip response. For the STOL airplanes, on the other hand, the yaw and sideslip responses were larger than the roll response. The response frequency of the STOL airplanes generally is higher than that for the conventional airplanes. This combination of greater sensitivity of the STOL airplanes in yaw and sideslip and the frequency at which they occur could be a factor causing the poor riding qualities of this class of airplanes.

An analytical method of computing the averaging effect of wing-span size on the loading of a wing induced by random turbulence was adapted for use on a digital electronic computer. The turbulence input was assumed to have a Dryden power spectral density. The computations were made for lift, rolling moment, and bending moment for two span load distributions, rectangular and elliptic. Data are presented to show the wing-span averaging effect for wing-span ratios encompassing current airplane sizes. The rectangular wing-span loading showed a slightly greater averaging effect than did the elliptic loading. In the frequency range most bothersome to airplane passengers, the wing-span averaging effect can reduce the normal lift load, and thus the acceleration, by about 7 percent for a typical medium-sized transport. Some calculations were made to evaluate the effect of using a Von Karman turbulence representation. These results showed that using the Von Karman representation generally resulted in a span averaging effect about 3 percent larger.

Gust loads on aircraft flying through random atmospheric turbulence are attenuated at high frequencies by the effects of unsteady lift and spanwise averaging. Previously derived theoretical results for these two effects are placed in a form which makes direct comparison possible. The attenuation effects from each cause are found to be of approximately equal magnitude for unswept wings of moderate aspect ratio. For small values of the ratio of wingspan to scale of turbulence, the attenuation due to spanwise averaging is a function only of reduced frequency based on wingspan and is independent of the ratio of wingspan to scale of turbulence.

Statistical analysis of simulated pilot ability to control lunar module approach and descent to lunar surface

Binocular viewing device for altitude estimation above spherical surface

Aerodynamic parameters effect on dynamic behavior on reentry vehicle

Visual techniques for astronaut determination of spacecraft altitude

Atmospheric braking for transfer into Martian orbit

The increasing utilization of simulators in many fields, in addition to aeronautics and space, requires the efficient use of these devices. It seemed that personnel highly influenced by the visual scene would make desirable subjects, particularly for those simulators without sufficient motion cues. In order to evaluate this concept, some measure of the degree of influence of the visual field on the subject in necessary. As part of this undertaking, 37 male and female subjects, including eight test pilots, were tested for their visual field dependency or independency. A version of Witkin's rod and frame apparatus was used for the tests. The results showed that nearly all the test subjects exhibited some degree of field dependency, the degree varying from very high field dependency to nearly zero field dependency in a normal distribution. The results for the test pilots were scattered throughout a range similar to the results for the bulk of male subjects. The few female subjects exhibited a higher field dependency than the male subjects. The male subjects exhibited a greater field dependency in the supine position than in the erect position, whereas the field dependency of the female subjects changed only slightly.