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   Kang, Hao ; Ruan, Shigui ; Huang, Qimin ( January 2020 , Communications on Pure & Applied Analysis)

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2. A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks

   https://doi.org/10.1016/j.jcp.2021.110242  

   Dong, Suchuan ; Ni, Naxian ( June 2021 , Journal of Computational Physics)

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3. Tidal capture of stars by supermassive black holes: implications for periodic nuclear transients and quasi-periodic eruptions

   https://doi.org/10.1093/mnrasl/slad001  

   Cufari, M. ; Nixon, C. J. ; Coughlin, Eric R. ( January 2023 , Monthly Notices of the Royal Astronomical Society: Letters)

   Stars that plunge into the centre of a galaxy are tidally perturbed by a supermassive black hole (SMBH), with closer encounters resulting in larger perturbations. Exciting these tides comes at the expense of the star’s orbital energy, which leads to the naive conclusion that a smaller pericentre (i.e. a closer encounter between the star and SMBH) always yields a more tightly bound star to the SMBH. However, once the pericentre distance is small enough that the star is partially disrupted, morphological asymmetries in the mass lost by the star can yield an increase in the orbital energy of the surviving core, resulting in its ejection – not capture – by the SMBH. Using smoothed particle hydrodynamics simulations, we show that the combination of these two effects – tidal excitation and asymmetric mass-loss – results in a maximum amount of energy lost through tides of $\sim 2.5{{\ \rm per\ cent}}$ of the binding energy of the star, which is significantly smaller than the theoretical maximum of the total stellar binding energy. This result implies that stars that are repeatedly partially disrupted by SMBHs many (≳10) times on short-period orbits (≲few years), as has been invoked to explain the periodic nuclear transient ASASSN-14ko and quasi-periodic eruptions, must be bound to the SMBH through a mechanism other than tidal capture, such as a dynamical exchange (i.e. Hills capture).

    

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4. Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values

   https://doi.org/10.1016/j.jcp.2023.111954  

   Wilkening, Jon ; Zhao, Xinyu ( April 2023 , Journal of Computational Physics)

   We present a method of detecting bifurcations by locating zeros of a signed version of the smallest singular value of the Jacobian. This enables the use of quadratically convergent root-bracketing techniques or Chebyshev interpolation to locate bifurcation points. Only positive singular values have to be computed, though the method relies on the existence of an analytic or smooth singular value decomposition (SVD). The sign of the determinant of the Jacobian, computed as part of the bidiagonal reduction in the SVD algorithm, eliminates slope discontinuities at the zeros of the smallest singular value. We use the method to search for spatially quasi-periodic traveling water waves that bifurcate from large-amplitude periodic waves. The water wave equations are formulated in a conformal mapping framework to facilitate the computation of the quasi-periodic Dirichlet-Neumann operator. We find examples of pure gravity waves with zero surface tension and overhanging gravity-capillary waves. In both cases, the waves have two spatial quasi-periods whose ratio is irrational. We follow the secondary branches via numerical continuation beyond the realm of linearization about solutions on the primary branch to obtain traveling water waves that extend over the real line with no two crests or troughs of exactly the same shape. The pure gravity wave problem is of relevance to ocean waves, where capillary effects can be neglected. Such waves can only exist through secondary bifurcation as they do not persist to zero amplitude. The gravity-capillary wave problem demonstrates the effectiveness of using the signed smallest singular value as a test function for multi-parameter bifurcation problems. This test function becomes mesh independent once the mesh is fine enough. 

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5. Thermal studies of nanoporous thin films with added periodic nanopores—a new approach to evaluate the importance of phononic effects

   https://doi.org/10.1016/j.mtphys.2020.100179  

   Xiao, Y. ; Xu, D. ; Medina, F.J. ; Wang, S. ; Hao, Q. ( March 2020 , Materials Today Physics)

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