Optimal control of multiscale systems using reduced-order models

We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal control computed from the reduced-order model to control the original, high-dimensional system? The strategy "first reduce, then optimize"--rather than "first optimize, then reduce"--is motivated by the fact that solving optimal control problems for high-dimensional multiscale systems is numerically challenging and often computationally prohibitive. We state sufficient and necessary conditions, under which the "first reduce, then control" strategy can be employed and discuss when it should be avoided. We further give numerical examples that illustrate the "first reduce, then optmize" approach and discuss possible pitfalls

3-[(Cyclo­hexyl­idene)amino]-1-(4-methyl­phen­yl)thio­urea

In the title compound, C14H19N3S, the cyclo­hexane ring has a chair conformation. The almost planar amino­thio­urea unit (r.m.s. deviation = 0.0062 Å) is aligned at a dihedral angle of 45.23 (8)° with respect to the benzene ring. Inter­molecular N—H⋯N and N—H⋯S hydrogen bonding stabilizes the crystal structure

Galactic Disk Bulk Motions as Revealed by the LSS-GAC DR2

We report a detailed investigation of the bulk motions of the nearby Galactic stellar disk, based on three samples selected from the LSS-GAC DR2: a global sample containing 0.57 million FGK dwarfs out to $\sim$ 2 kpc, a local subset of the global sample consisting $\sim$ 5,400 stars within 150 pc, and an anti-center sample containing $\sim$ 4,400 AFGK dwarfs and red clump stars within windows of a few degree wide centered on the Galactic anti-center. The global sample is used to construct a three-dimensional map of bulk motions of the Galactic disk from the solar vicinity out to $\sim$ 2 kpc with a spatial resolution of $\sim$ 250 pc. Typical values of the radial and vertical components of bulk motion range from $-$15 km s$^{-1}$ to 15 km s$^{-1}$, while the lag behind the circular speed dominates the azimuthal component by up to $\sim$ 15 km s$^{-1}$. The map reveals spatially coherent, kpc-scale stellar flows in the disk, with typical velocities of a few tens km s$^{-1}$. Bending- and breathing-mode perturbations are clearly visible, and vary smoothly across the disk plane. Our data also reveal higher-order perturbations, such as breaks and ripples, in the profiles of vertical motion versus height. From the local sample, we find that stars of different populations exhibit very different patterns of bulk motion. Finally, the anti-center sample reveals a number of peaks in stellar number density in the line-of-sight velocity versus distance distribution, with the nearer ones apparently related to the known moving groups. The "velocity bifurcation" reported by Liu et al. (2012) at Galactocentric radii 10--11 kpc is confirmed. However, just beyond this distance, our data also reveal a new triple-peaked structure.Comment: 27 pages, 17 figures, Accepted for publication in a special issue of Research in Astronomy and Astrophysics on LAMOST science