Towards Long-endurance Flight: Design and Implementation of a Variable-pitch Gasoline-engine Quadrotor

Majority of today's fixed-pitch, electric-power quadrotors have short flight endurance ($<$ 1 hour) which greatly limits their applications. This paper presents a design methodology for the construction of a long-endurance quadrotor using variable-pitch rotors and a gasoline-engine. The methodology consists of three aspects. Firstly, the rotor blades and gasoline engine are selected as a pair, so that sufficient lift can be comfortably provided by the engine. Secondly, drivetrain and airframe are designed. Major challenges include airframe vibration minimization and power transmission from one engine to four rotors while keeping alternate rotors contra-rotating. Lastly, a PD controller is tuned to facilitate preliminary flight tests. The methodology has been verified by the construction and successful flight of our gasoline quadrotor prototype, which is designed to have a flight time of 2 to 3 hours and a maximum take-off weight of 10 kg.Comment: 6 page

Constraint Satisfaction with Counting Quantifiers

We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly between exists^1:=exists and exists^n:=forall (the domain being of size n) already affords the maximal possible complexity of QCSPs (which have both exists and forall), being Pspace-complete for a suitably chosen template. Next, we focus on the complexity of subsets of counting quantifiers on clique and cycle templates. For cycles we give a full trichotomy -- all such problems are in L, NP-complete or Pspace-complete. For cliques we come close to a similar trichotomy, but one case remains outstanding. Afterwards, we consider the generalisation of CSPs in which we augment the extant quantifier exists^1:=exists with the quantifier exists^j (j not 1). Such a CSP is already NP-hard on non-bipartite graph templates. We explore the situation of this generalised CSP on bipartite templates, giving various conditions for both tractability and hardness -- culminating in a classification theorem for general graphs. Finally, we use counting quantifiers to solve the complexity of a concrete QCSP whose complexity was previously open

Light-Enhanced Spin Fluctuations and d-Wave Superconductivity at a Phase Boundary

Time-domain techniques have shown the potential of photo-manipulating existing orders and inducing new states of matter in strongly correlated materials. Using time-resolved exact diagonalization, we perform numerical studies of pump dynamics in a Mott-Peierls system with competing charge and spin density waves. A light-enhanced $d$-wave superconductivity is observed when the system resides near a quantum phase boundary. By examining the evolution of spin, charge and superconducting susceptibilities, we show that a sub-dominant state in equilibrium can be stabilized by photomanipulating charge order to allow superconductivity to appear and dominate. This work provides an interpretation of light-induced superconductivity from the perspective of order competition, and offers a promising approach for designing novel emergent states out of equilibrium.Comment: 5 pages, 4 figure

A Fidelity Study of the Superconducting Phase Diagram in the 2D Single-band Hubbard Model

Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range d-wave pair field term, which precipitates a superconducting state in the d-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the d-wave pair/spin/charge-density matrices. The calculations show a d-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion U and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping t'. We also demonstrate that negative t' plays an important role in facilitating d-wave superconductivity.Comment: 10 pages, 13 figure

Three-level mixing model for nuclear chiral rotation: Role of planar component

Three- and two-level mixing models are proposed to understand the doubling of states at the same spin and parity in triaxially-deformed atomic nuclei with odd numbers of protons and neutrons. The Particle-Rotor Model for such nuclei is solved using the newly proposed basis which couples angular momenta of two valence nucleons and the rotating triaxial mean-field into left-handed $|\mathcal{L}\rangle$, right-handed $|\mathcal{R}\rangle$, and planar $|\mathcal{P}\rangle$ configurations. The presence and the impact of the planar component is investigated as a function of the total spin for mass A$\approx$130 nuclei with the valence h$_{11/2}$ proton particle, valence h$_{11/2}$ neutron hole and the maximum difference between principle axes allowed by the quadrupole deformation of the mean field. It is concluded that at each spin value the higher-energy member of a doublet of states is built on the anti-symmetric combination of $|\mathcal{L}\rangle$ and $|\mathcal{R}\rangle$ and is free of the $|\mathcal{P}\rangle$ component, indicating that it is of pure chiral geometry. For the lower-energy member of the doublet, the contribution of the $|\mathcal{P}\rangle$ component to the eigenfunction first decreases and then increases as a function of the total spin. This trend as well as the energy splitting between the doublet states are both determined by the Hamiltonian matrix elements between the planar ($|\mathcal{P}\rangle$) and non-planar ($|\mathcal{L}\rangle$ and $|\mathcal{R}\rangle$) subspaces of the full Hilbert space.Comment: 12 pages, 5 figures, accepted as a Rapid Communication in Physical Review

Comparison of differential gain in single quantum well and bulk double heterostructure lasers

The differential gain in single quantum well and bulk double heterostructure lasers is compared. In variance with previous predictions, no differential gain enhancement is found in single quantum well structure lasers at room temperature. Only at low temperatures do the quantum well lasers possess higher differential gain than bulk double heterostructure lasers. The results have important implications in the area of high speed phenomena for these devices