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Polarization-entangled photons are indispensable to numerous quantum technologies and fundamental studies. In this paper, we propose and demonstrate a novel source that generates collinear polarization-entangled photons by simultaneously achieving two distinct types of phase-matching conditions (noncritically birefringent and quasi phase matching) in a periodically poled nonlinear crystal with a large poling period of 2 mm. The photon pairs are generated in a polarization-entangled state with a fidelity and concurrence of 0.998 and 0.935, respectively, and violate the Clauser-Horne-Shimony-Holt inequality by 84 standard deviations. The compact source does not require interferometer, delicate domain structures, or post selection, and is advantageous for scalable quantum computing and communication, where many replicas or chip-scale devices are needed.

MIDI-sheet music alignment is the task of finding correspondences between a MIDI representation of a piece and its corresponding sheet music images. Rather than using optical music recognition to bridge the gap between sheet music and MIDI, we explore an alternative approach: projecting the MIDI data into pixel space and performing alignment in the image domain. Our method converts the MIDI data into a crude representation of the score that only contains rectangular floating notehead blobs, a process we call bootleg score synthesis. Furthermore, we project sheet music images into the same bootleg space by applying a deep watershed notehead detector and filling in the bounding boxes around each detected notehead. Finally, we align the bootleg representations using a simple variant of dynamic time warping. On a dataset of 68 real scanned piano scores from IMSLP and corresponding MIDI performances, our method achieves a 97.3% accuracy at an error tolerance of one second, outperforming several baseline systems that employ optical music recognition., Comment: 8 pages, 6 figures, 1 table. Accepted paper at the International Society for Music Information Retrieval Conference (ISMIR) 2019

We consider the Landau-Lifshitz equations of ferromagnetism (including the harmonic map heat-flow and Schroedinger flow as special cases) for degree m equivariant maps from R^2 to S^2. If m \geq 3, we prove that near-minimal energy solutions converge to a harmonic map as t goes to infinity (asymptotic stability), extending previous work down to degree m = 3. Due to slow spatial decay of the harmonic map components, a new approach is needed for m=3, involving (among other tools) a "normal form" for the parameter dynamics, and the 2D radial double-endpoint Strichartz estimate for Schroedinger operators with sufficiently repulsive potentials (which may be of some independent interest). When m=2 this asymptotic stability may fail: in the case of heat-flow with a further symmetry restriction, we show that more exotic asymptotics are possible, including infinite-time concentration (blow-up), and even "eternal oscillation"., Comment: 34 pages

This paper is to describe a design and fabrication method for a valve-less peristaltic micro-pump. The valve-less peristaltic micro-pump with three membrane chambers in a serial is actuated by three piezoelectric (PZT) actuators. With the fluidic flow design, liquid in the flow channel is pumped to a constant flow speed ranged from 0.4 to 0.48 mm/s. In term of the maximum flow rate of the micro-pump is about 365 mircoliters/min, when the applied voltage is 24V and frequency 50 Hz. Photolithography process was used to fabricate the micro-pump mold. PDMS molding and PDMS bonding method were used to fabricate the micro-channel and actuator chambers. A portable drive controller was designed to control three PZT actuators in a proper sequence to drive the chamber membrane. Then, all parts were integrated into the portable valve-less peristaltic micro-pump system., Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838)

We study global behavior of small solutions of the Gross-Pitaevskii equation in three dimensions. We prove that disturbances from the constant equilibrium with small, localized energy, disperse for large time, according to the linearized equation. Translated to the defocusing nonlinear Schr\"odinger equation, this implies asymptotic stability of all plane wave solutions for such disturbances. We also prove that every linearized solution with finite energy has a nonlinear solution which is asymptotic to it. The key ingredients are: (1) some quadratic transforms of the solutions, which effectively linearize the nonlinear energy space, (2) a bilinear Fourier multiplier estimate, which allows irregular denominators due to a degenerate non-resonance property of the quadratic interactions, and (3) geometric investigation of the degeneracy in the Fourier space to minimize its influence., Comment: 44 pages. Preprint of an article submitted for consideration in Communications in Contemporary Mathematics

We study asymptotic behaviour at time infinity of solutions close to the non-zero constant equilibrium for the Gross-Pitaevskii equation in two and three spatial dimensions. We construct a class of global solutions with prescribed dispersive asymptotic behavior, which is given in terms of the linearized evolution.

We investigate the asymptotic behavior at time infinity of solutions close to a non-zero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau Schroedinger) equation. We prove that, in dimensions larger than 3, small perturbations can be approximated at time infinity by the linearized evolution, and the wave operators are homeomorphic around 0 in certain Sobolev spaces., Comment: 13 pages

For the Schr\"odinger flow from $R^2 \times R^+$ to the 2-sphere $S^2$, it is not known if finite energy solutions can blow up in finite time. We study equivariant solutions whose energy is near the energy of the family of equivariant harmonic maps. We prove that such solutions remain close to the harmonic maps until the blow up time (if any), and that they blow up if and only if the length scale of the nearest harmonic map goes to zero., Comment: 35 pages