Trajectory generation for road vehicle obstacle avoidance using convex optimization

This paper presents a method for trajectory generation using convex optimization to find a feasible, obstacle-free path for a road vehicle. Consideration of vehicle rotation is shown to be necessary if the trajectory is to avoid obstacles specified in a fixed Earth axis system. The paper establishes that, despite the presence of significant non-linearities, it is possible to articulate the obstacle avoidance problem in a tractable convex form using multiple optimization passes. Finally, it is shown by simulation that an optimal trajectory that accounts for the vehicle’s changing velocity throughout the manoeuvre is superior to a previous analytical method that assumes constant speed

An earth pole-sitter using hybrid propulsion

In this paper we investigate optimal pole-sitter orbits using hybrid solar sail and solar electric propulsion (SEP). A pole-sitter is a spacecraft that is constantly above one of the Earth's poles, by means of a continuous thrust. Optimal orbits, that minimize propellant mass consumption, are found both through a shape-based approach, and solving an optimal control problem, using a direct method based on pseudo-spectral techniques. Both the pure SEP case and the hybrid case are investigated and compared. It is found that the hybrid spacecraft allows consistent savings on propellant mass fraction. Finally, is it shown that for sufficiently long missions (more than 8 years), a hybrid spacecraft, based on mid-term technology, enables a consistent reduction in the launch mass for a given payload, with respect to a pure SEP spacecraft

Quantum Phase Transition in the Normal State of High-Tc Cuprates at Optimum Doping

By using a 60 T magnetic field to suppress superconductivity in La2-pSrpCuO4, (LSCO) we reveal an anomalous peak in the Hall number, located at optimum doping and developing at temperatures below the zero-field superconducting transition temperature, Tc. The anomaly bears a striking resemblance to observations in Bi2Sr2-xLaxCuO6+delta (BSLCO) [F. F. Balakirev et al., Nature (London) 424, 912 (2003)], suggesting a normal state phenomenology common to the cuprates that underlies the high-temperature superconducting phase. The peak is ascribed to the transformation of the "Fermi arcs" into a conventional FS, the signature of a Fermi surface reconstruction associated with a quantum phase transition (QPT) near optimum doping and co-incident with the collapse of the pseudogap state.Comment: 16 pages, 4 figure

Vanishing spin alignment : experimental indication of triaxial 28Si+28Si\bf ^{28}Si + {^{28}Si} nuclear molecule

Fragment-fragment-$\gamma$ coincidences have been measured for $\rm ^{28}Si + {^{28}Si}$ at an energy corresponding to the population of a conjectured resonance in $^{56}$Ni. Fragment angular distributions as well as $\gamma$-ray angular correlations indicate that the spin orientations of the outgoing fragments are perpendicular to the orbital angular momentum. This differs from the $\rm ^{24}Mg+{^{24}Mg}$ and the $\rm ^{12}C+{^{12}C}$ resonances, and suggests two oblate $\rm ^{28}Si$ nuclei interacting in an equator-to-equator molecular configuration.Comment: 14 pages standard REVTeX file, 3 ps Figures -- Accepted for publication in Physical Review C (Rapid Communication

The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized $J$-$J'$ model interpolating between both systems by varying $J'/J$ from $J'/J=0$ (bounce limit) to $J'/J=1$ (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce ($J'/J=0$) and maple-leaf ($J'/J=1$) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range $0 \le J'/J \lesssim J'_c/J$ and that the magnetic order parameter varies only weakly with $J'/J$. At $J'_c \approx 1.45 J$ a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-$J'$ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for $J'/J \gtrsim 1.07$ and another one at 2/3 of saturation emerging only at large $J'/J \gtrsim 3$.Comment: 9 pages, 10 figure