L1L^1-optimality conditions for circular restricted three-body problems

In this paper, the L1-minimization for the translational motion of a spacecraft in a circular restricted three-body problem (CRTBP) is considered. Necessary con- ditions are derived by using the Pontryagin Maximum Principle, revealing the existence of bang-bang and singular controls. Singular extremals are detailed, re- calling the existence of the Fuller phenomena according to the theories developed by Marchal in Ref. [14] and Zelikin et al. in Refs. [12, 13]. The sufficient opti- mality conditions for the L1-minimization problem with fixed endpoints have been solved in Ref. [22]. In this paper, through constructing a parameterised family of extremals, some second-order sufficient conditions are established not only for the case that the final point is fixed but also for the case that the final point lies on a smooth submanifold. In addition, the numerical implementation for the optimality conditions is presented. Finally, approximating the Earth-Moon-Spacecraft system as a CRTBP, an L1-minimization trajectory for the translational motion of a spacecraft is computed by employing a combination of a shooting method with a continuation method of Caillau et al. in Refs. [4, 5], and the local optimality of the computed trajectory is tested thanks to the second-order optimality conditions established in this paper

Optimality conditions applied to free-time multi-burn optimal orbital transfers

While the Pontryagin Maximum Principle can be used to calculate candidate extremals for optimal orbital transfer problems, these candidates cannot be guaranteed to be at least locally optimal unless sufficient optimality conditions are satisfied. In this paper, through constructing a parameterized family of extremals around a reference extremal, some second-order necessary and sufficient conditions for the strong-local optimality of the free-time multi-burn fuel-optimal transfer are established under certain regularity assumptions. Moreover, the numerical procedure for computing these optimality conditions is presented. Finally, two medium-thrust fuel-optimal trajectories with different number of burn arcs for a typical orbital transfer problem are computed and the local optimality of the two computed trajectories are tested thanks to the second-order optimality conditions established in this paper

Two-hole ground state wavefunction: Non-BCS pairing in a tt-JJ two-leg ladder system

Superconductivity is usually described in the framework of the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which even includes the resonating-valence-bond (RVB) wavefunction proposed for the high-temperature superconductivity in the cuprate. A natural question is \emph{if} any fundamental physics could be possibly missed by applying such a scheme to strongly correlated systems. Here we study the pairing wavefunction of two holes injected into a Mott insulator/antiferromagnet in a two-leg ladder using variational Monte Carlo (VMC) approach. By comparing with density matrix renormalization group (DMRG) calculation, we show that a conventional BCS or RVB pairing of the doped holes makes qualitatively wrong predictions and is incompatible with the fundamental pairing force in the $t$-$J$ model, which is kinetic-energy-driven by nature. By contrast, a non-BCS-like wavefunction incorporating such novel effect will result in a substantially enhanced pairing strength and improved ground state energy as compared to the DMRG results. We argue that the non-BCS form of such a new ground state wavefunction is essential to describe a doped Mott antiferromagnet at finite doping.Comment: 11 pages, 5 figure

Recording accurate process documentation in the presence of failures

Scientific and business communities present unprecedented requirements on provenance, where the provenance of some data item is the process that led to that data item. Previous work has conceived a computer-based representation of past executions for determining provenance, termed process documentation, and has developed a protocol, PReP, to record process documentation in service oriented architectures. However, PReP assumes a failure free environment. The presence of failures may lead to inaccurate process documentation, which does not reflect reality and hence cannot be trustful and utilized. This paper outlines our solution, F-PReP, a protocol for recording accurate process documentation in the presence of failures