Tunable far-infrared laser spectroscopy of hydrogen bonds: The K_a = O(u)→1(g) rotation-tunneling spectrum of the HCI dimer

The ground state K_a =0(u)→1(g) b‐type subband of the rotation–tunneling spectrum of the symmetric ^(35)Cl–^(35)Cl,^(37)Cl–^(37)Cl, and the mixed ^(35)Cl–^(37)Cl hydrogen chloride dimers have been recorded near 26.3 cm^(−1) with sub‐Doppler resolution in a continuous two‐dimensional supersonic jet with a tunable far‐infrared laser spectrometer. Quadrupole hyperfine structure from the chlorine nuclei has been resolved. From the fitted rotational constants a (H^(35)Cl)_2 center‐of‐mass separation of 3.81 Å is derived for the K_a =1(g) levels, while the nuclear quadrupole coupling constants yield a vibrationally averaged angular structure for both tunneling states of approximately 20–25 deg for the hydrogen bonded proton and at least 70–75 deg for the external proton. This nearly orthogonal structure agrees well with that predicted by ab initio theoretical calculations, but the observed splittings and intensity alterations of the lines indicate that the chlorine nuclei are made equivalent by a large amplitude tunneling motion of the HCl monomers. A similar geared internal rotation tunneling motion has been found for the HF dimer, but here the effect is much greater. The ground state tunneling splittings are estimated to lie between 15–18 cm^(−1), and the selection rules observed indicate that the trans tunneling path dominates the large amplitude motion, as expected, provided the dimer remains planar. From the observed hyperfine constants, we judge the dimer and its associated tunneling motion to be planar to within 10°

Position-squared coupling in a tunable photonic crystal optomechanical cavity

We present the design, fabrication, and characterization of a planar silicon photonic crystal cavity in which large position-squared optomechanical coupling is realized. The device consists of a double-slotted photonic crystal structure in which motion of a central beam mode couples to two high-Q optical modes localized around each slot. Electrostatic tuning of the structure is used to controllably hybridize the optical modes into supermodes which couple in a quadratic fashion to the motion of the beam. From independent measurements of the anti-crossing of the optical modes and of the optical spring effect, the position-squared vacuum coupling rate is measured to be as large as 245 Hz to the fundamental in-plane mechanical resonance of the structure at 8.7MHz, which in displacement units corresponds to a coupling coefficient of 1 THz/nm$^2$. This level of position-squared coupling is approximately five orders of magnitude larger than in conventional Fabry-Perot cavity systems.Comment: 11 pages, 6 figure

Zero-Temperature Structures of Atomic Metallic Hydrogen

Ab initio random structure searching with density functional theory was used to determine the zero-temperature structures of atomic metallic hydrogen from 500 GPa to 5 TPa. Including zero point motion in the harmonic approximation, we estimate that molecular hydrogen dissociates into a monatomic body-centered tetragonal structure near 500 GPa (r_s = 1.225), which then remains stable to 2.5 TPa (r_s = 0.969). At higher pressures, hydrogen stabilizes in an ...ABCABC... planar structure that is remarkably similar to the ground state of lithium, which compresses to the face-centered cubic lattice beyond 5 TPa (r_s < 0.86). At this level of theory, our results provide a complete ab initio description of the atomic metallic structures of hydrogen, resolving one of the most fundamental and long outstanding issues concerning the structures of the elements.Comment: 9 pages; 4 figure

On Time-optimal Trajectories for a Car-like Robot with One Trailer

In addition to the theoretical value of challenging optimal control problmes, recent progress in autonomous vehicles mandates further research in optimal motion planning for wheeled vehicles. Since current numerical optimal control techniques suffer from either the curse of dimens ionality, e.g. the Hamilton-Jacobi-Bellman equation, or the curse of complexity, e.g. pseudospectral optimal control and max-plus methods, analytical characterization of geodesics for wheeled vehicles becomes important not only from a theoretical point of view but also from a prac tical one. Such an analytical characterization provides a fast motion planning algorithm that can be used in robust feedback loops. In this work, we use the Pontryagin Maximum Principle to characterize extremal trajectories, i.e. candidate geodesics, for a car-like robot with one trailer. We use time as the distance function. In spite of partial progress, this problem has remained open in the past two decades. Besides straight motion and turn with maximum allowed curvature, we identify planar elastica as the third piece of motion that occurs along our extr emals. We give a detailed characterization of such curves, a special case of which, called \emph{merging curve}, connects maximum curvature turns to straight line segments. The structure of extremals in our case is revealed through analytical integration of the system and adjoint equations

Real-Time Quasi Dense Two-Frames Depth Map for Autonomous Guided Vehicles

International audienceThis paper presents a real-time and dense structure from motion approach, based on an efficient planar parallax motion decomposition, and also proposes several optimizations to improve the optical flow firstly computed. Later, it is estimated using our own GPU implementation of the well-known pyramidal algorithm of Lucas and Kanade. Then, each pair of points previously matched is evaluated according to the spatial continuity constraint provided by the Tensor Voting framework applied in the 4-D joint space of image coordinates and motions. Thus, assuming the ground locally planar, the homography corresponding to its image motion is robustly and quickly estimated using RANSAC on designated well-matched pairwise by the prior Tensor Voting process. Depth map is finally computed from the parallax motion decomposition. The initialization of successive runs is also addressed, providing noticeable enhancement, as well as the hardware integration using the CUDA technology