148,136 research outputs found
-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 - 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 - 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
Primordial Non-Gaussianity from LAMOST Surveys
The primordial non-Gaussianity (PNG) in matter density perturbation is a very
powerful probe of the physics of the very early Universe. The local PNG can
induce a distinct scale-dependent bias on the large scale structure
distribution of galaxies and quasars, which could be used for constraining it.
We study the detection limits on PNG from the surveys of the LAMOST telescope.
The cases of the main galaxy survey, the luminous red galaxy (LRG) survey, and
the quasar survey of different magnitude limits are considered. We find that
the MAIN1 sample (i.e. the main galaxy survey with one magnitude deeper than
the SDSS main galaxy survey, or r<18.8) could only provide very weak constraint
on PNG. For the MAIN2 sample (r<19.8) and the LRG survey, the 2\sigma (95.5%)
limit on the PNG parameter f_{NL} are |f_{NL}|<145 and |f_{NL}|<114
respectively, comparable to the current limit from cosmic microwave background
(CMB) data. The quasar survey could provide much more stringent constraint, and
we find that the 2\sigma limit for |f_{NL}| is between 50 and 103, depending on
the magnitude limit of the survey. With Planck-like priors on cosmological
parameters, the quasar survey with g<21.65 would improve the constraints to
|f_{NL}|<43 (2\sigma). We also discuss the possibility of further tightening
the constraint by using the relative bias method proposed by Seljak(2008).Comment: 8 pages, 2 figures, RAA accepte
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