Quiet engine program flight engine design study

The results are presented of a preliminary flight engine design study based on the Quiet Engine Program high-bypass, low-noise turbofan engines. Engine configurations, weight, noise characteristics, and performance over a range of flight conditions typical of a subsonic transport aircraft were considered. High and low tip speed engines in various acoustically treated nacelle configurations were included

The Bravyi-Kitaev transformation for quantum computation of electronic structure

Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev [S. B. Bravyi, A.Yu. Kitaev, Annals of Physics 298, 210-226 (2002)], that reduces the simulation cost to O(log n) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time-step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure

Pole structure of the Hamiltonian ζ\zeta-function for a singular potential

We study the pole structure of the $\zeta$-function associated to the Hamiltonian $H$ of a quantum mechanical particle living in the half-line $\mathbf{R}^+$, subject to the singular potential $g x^{-2}+x^2$. We show that $H$ admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter $g$. The $\zeta$-functions of these operators present poles which depend on $g$ and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered.Comment: 12 pages, 1 figure, RevTeX. References added. Version to appear in Jour. Phys. A: Math. Ge

Lifshitz fermionic theories with z=2 anisotropic scaling

We construct fermionic Lagrangians with anisotropic scaling z=2, the natural counterpart of the usual z=2 Lifshitz field theories for scalar fields. We analyze the issue of chiral symmetry, construct the Noether axial currents and discuss the chiral anomaly giving explicit results for two-dimensional case. We also exploit the connection between detailed balance and the dynamics of Lifshitz theories to find different z=2 fermionic Lagrangians and construct their supersymmetric extensions.Comment: Typos corrected, comment adde

Honey bee foraging distance depends on month and forage type

To investigate the distances at which honey bee foragers collect nectar and pollen, we analysed 5,484 decoded waggle dances made to natural forage sites to determine monthly foraging distance for each forage type. Firstly, we found significantly fewer overall dances made for pollen (16.8 %) than for non-pollen, presumably nectar (83.2 %; P < 2.2 × 10−23). When we analysed distance against month and forage type, there was a significant interaction between the two factors, which demonstrates that in some months, one forage type is collected at farther distances, but this would reverse in other months. Overall, these data suggest that distance, as a proxy for forage availability, is not significantly and consistently driven by need for one type of forage over the other

Why do house-hunting ants recruit in both directions?

To perform tasks, organisms often use multiple procedures. Explaining the breadth of such behavioural repertoires is not always straightforward. During house hunting, colonies of Temnothorax albipennis ants use a range of behaviours to organise their emigrations. In particular, the ants use tandem running to recruit naïve ants to potential nest sites. Initially, they use forward tandem runs (FTRs) in which one leader takes a single follower along the route from the old nest to the new one. Later, they use reverse tandem runs (RTRs) in the opposite direction. Tandem runs are used to teach active ants the route between the nests, so that they can be involved quickly in nest evaluation and subsequent recruitment. When a quorum of decision-makers at the new nest is reached, they switch to carrying nestmates. This is three times faster than tandem running. As a rule, having more FTRs early should thus mean faster emigrations, thereby reducing the colony’s vulnerability. So why do ants use RTRs, which are both slow and late? It would seem quicker and simpler for the ants to use more FTRs (and higher quorums) to have enough knowledgeable ants to do all the carrying. In this study, we present the first testable theoretical explanation for the role of RTRs. We set out to find the theoretically fastest emigration strategy for a set of emigration conditions. We conclude that RTRs can have a positive effect on emigration speed if FTRs are limited. In these cases, low quorums together with lots of reverse tandem running give the fastest emigration

Model of the best-of-N nest-site selection process in honeybees

The ability of a honeybee swarm to select the best nest site plays a fundamental role in determining the future colony’s fitness. To date, the nest-site selection process has mostly been modelled and theoretically analysed for the case of binary decisions. However, when the number of alternative nests is larger than two, the decision process dynamics qualitatively change. In this work, we extend previous analyses of a valuesensitive decision-making mechanism to a decision process among N nests. First, we present the decisionmaking dynamics in the symmetric case of N equal-quality nests. Then, we generalise our findings to a best-of-N decision scenario with one superior nest and N – 1 inferior nests, previously studied empirically in bees and ants. Whereas previous binary models highlighted the crucial role of inhibitory stop-signalling, the key parameter in our new analysis is the relative time invested by swarm members in individual discovery and in signalling behaviours. Our new analysis reveals conflicting pressures on this ratio in symmetric and best-of-N decisions, which could be solved through a time-dependent signalling strategy. Additionally, our analysis suggests how ecological factors determining the density of suitable nest sites may have led to selective pressures for an optimal stable signalling ratio

Discrete Symmetries in the Weyl Expansion for Quantum Billiards

We consider two and three-dimensional quantum billiards with discrete symmetries. We derive the first terms of the Weyl expansion for the level density projected onto the irreducible representations of the symmetry group. As an illustration the method is applied to the icosahedral billiard. The paper was published in J. Phys. A /27/ (1994) 4317-4323Comment: 8 printed pages Latex fil

Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows

We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN], on the vanishing viscosity limit of circularly symmetric viscous flow in a disk with rotating boundary, shown there to converge to the inviscid limit in $L^2$-norm as long as the prescribed angular velocity $\alpha(t)$ of the boundary has bounded total variation. Here we establish convergence in stronger $L^2$ and $L^p$-Sobolev spaces, allow for more singular angular velocities $\alpha$, and address the issue of analyzing the behavior of the boundary layer. This includes an analysis of concentration of vorticity in the vanishing viscosity limit. We also consider such flows on an annulus, whose two boundary components rotate independently. [LMN] Lopes Filho, M. C., Mazzucato, A. L. and Nussenzveig Lopes, H. J., Vanishing viscosity limit for incompressible flow inside a rotating circle, preprint 2006

The trace of the heat kernel on a compact hyperbolic 3-orbifold

The heat coefficients related to the Laplace-Beltrami operator defined on the hyperbolic compact manifold H^3/\Ga are evaluated in the case in which the discrete group \Ga contains elliptic and hyperbolic elements. It is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace of the heat kernel, elliptic elements modify all coefficients of the asymptotic expansion, but the Weyl term, which remains unchanged. Some physical consequences are briefly discussed in the examples.Comment: 11 page