Computations of the breakup of a liquid bridge are used to establish the limits of applicability of similarity solutions derived for different breakup regimes. These regimes are based on particular viscous-inertial balances, that is, different limits of the Ohnesorge number Oh. To accurately establish the transitions between regimes, the minimum bridge radius is resolved through four orders of magnitude using a purpose-built multiscale finite element method. This allows us to construct a quantitative phase diagram for the breakup phenomenon which includes the appearance of a recently discovered low-Oh viscous regime. The method used to quantify the accuracy of the similarity solutions allows us to identify a number of previously unobserved features of the breakup, most notably an oscillatory convergence towards the viscous-inertial similarity solution. Finally, we discuss how the new findings open up a number of challenges for both theoretical and experimental analysis.

Enzo (Enzo Developers, 2019a) is a block-structured adaptive mesh refinement code that is widely used to simulate astrophysical fluid flows (primarily, but not exclusively, cosmological structure formation, star formation, and turbulence). The code is a community project with dozens of users, and has contributed to hundreds of peer-reviewed publications in astrophysics, physics, and computer science. The code utilizes a Cartesian mesh can be run in one, two, or

To ensure a long-term quantum computational advantage, the quantum hardware should be upgraded to withstand the competition of continuously improved classical algorithms and hardwares. Here, we demonstrate a superconducting quantum computing systems Zuchongzhi 2.1, which has 66 qubits in a two-dimensional array in a tunable coupler architecture. The readout fidelity of Zuchongzhi 2.1 is considerably improved to an average of 97.74%. The more powerful quantum processor enables us to achieve larger-scale random quantum circuit sampling, with a system scale of up to 60 qubits and 24 cycles. The achieved sampling task is about 6 orders of magnitude more difficult than that of Sycamore [Nature 574, 505 (2019)] in the classic simulation, and 3 orders of magnitude more difficult than the sampling task on Zuchongzhi 2.0 [arXiv: 2106.14734 (2021)]. The time consumption of classically simulating random circuit sampling experiment using state-of-the-art classical algorithm and supercomputer is extended to tens of thousands of years (about 4.8 × 10 4 years), while Zuchongzhi 2.1 only takes about 4.2 hours, thereby significantly enhancing the quantum computational advantage.

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Quantum Fourier transforms (QFT) have gained increased attention with the rise of quantum walks, boson sampling, and quantum metrology. Here we present and demonstrate a general technique that simplifies the construction of QFT interferometers using both path and polarization modes. On that basis, we first observed the generalized Hong-Ou-Mandel effect with up to four photons. Furthermore, we directly exploited number-path entanglement generated in these QFT interferometers and demonstrated optical phase supersensitivities deterministically.