Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory

We study the pion leading-twist distribution amplitude (DA) within the framework of SVZ sum rules under the background field theory. To improve the accuracy of the sum rules, we expand both the quark propagator and the vertex (z\cdot \tensor{D})^n of the correlator up to dimension-six operators in the background field theory. The sum rules for the pion DA moments are obtained, in which all condensates up to dimension-six have been taken into consideration. Using the sum rules, we obtain \left|_{\rm 1\;GeV} = 0.338 \pm 0.032, \left|_{\rm 1\;GeV} = 0.211 \pm 0.030 and \left|_{\rm 1\;GeV} = 0.163 \pm 0.030. It is shown that the dimension-six condensates shall provide sizable contributions to the pion DA moments. We show that the first Gegenbauer moment of the pion leading-twist DA is $a^\pi_2|_{\rm 1\;GeV} = 0.403 \pm 0.093$, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.Comment: 13 pages, 7 figure

Efficient Trajectory Planning and Control for USV with Vessel Dynamics and Differential Flatness

Unmanned surface vessels (USVs) are widely used in ocean exploration and environmental protection fields. To ensure that USV can successfully perform its mission, trajectory planning and motion tracking are the two most critical technologies. In this paper, we propose a novel trajectory generation and tracking method for USV based on optimization theory. Specifically, the USV dynamic model is described with differential flatness, so that the trajectory can be generated by dynamic RRT* in a linear invariant system expression form under the objective of optimal boundary value. To reduce the sample number and improve efficiency, we adjust the trajectory through local optimization. The dynamic constraints are considered in the optimization process so that the generated trajectory conforms to the kinematic characteristics of the under-actuated hull, and makes it easier to be tracked. Finally, motion tracking is added with model predictive control under a sequential quadratic programming problem. Experimental results show the planned trajectory is more in line with the kinematic characteristics of USV, and the tracking accuracy remains a higher level

Geography and similarity of regional cuisines in China

Food occupies a central position in every culture and it is therefore of great interest to understand the evolution of food culture. The advent of the World Wide Web and online recipe repositories has begun to provide unprecedented opportunities for data-driven, quantitative study of food culture. Here we harness an online database documenting recipes from various Chinese regional cuisines and investigate the similarity of regional cuisines in terms of geography and climate. We found that the geographical proximity, rather than climate proximity is a crucial factor that determines the similarity of regional cuisines. We develop a model of regional cuisine evolution that provides helpful clues to understand the evolution of cuisines and cultures.Comment: 13 pages, 11 figures and 2 table

(7-Isopropyl-1,4a-dimethyl-1,2,3,4,4a,-9,10,10a-octa­hydro­phenanthren-1-yl)­methanaminium 4-toluene­sulfonate

In the title compound, C20H32N+·C7H7O3S−, the configurations of the two chiral centers observed in the protonated cation are consistent with previous reports. In the crystal structure, weak inter­molecular N—H⋯O hydrogen bonds link ions into chains which develop along the a axis. The isopropyl group and four CH groups of the attached benzene ring are disordered approximately equally over two positions

Analysis of strength and ductility of partially recrystallized Cu-4.5 wt.% Al

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Cooperative trajectory planning algorithm of USV-UAV with hull dynamic constraints

Efficient trajectory generation in complex dynamic environment stills remains an open problem in the unmanned surface vehicle (USV) domain. In this paper, a cooperative trajectory planning algorithm for the coupled USV-UAV system is proposed, to ensure that USV can execute safe and smooth path in the process of autonomous advance in multi obstacle maps. Specifically, the unmanned aerial vehicle (UAV) plays the role as a flight sensor, and it provides real-time global map and obstacle information with lightweight semantic segmentation network and 3D projection transformation. And then an initial obstacle avoidance trajectory is generated by a graph-based search method. Concerning the unique under-actuated kinematic characteristics of the USV, a numerical optimization method based on hull dynamic constraints is introduced to make the trajectory easier to be tracked for motion control. Finally, a motion control method based on NMPC with the lowest energy consumption constraint during execution is proposed. Experimental results verify the effectiveness of whole system, and the generated trajectory is locally optimal for USV with considerable tracking accuracy.Comment: 10 pages, 9 figure