arXiv subjects

Guidong Liu

Publications and source records attributed to Guidong Liu.

5 recordsLinked to original sources

arXiv2026

Stability analysis of consistent splitting implicit-explicit multistep methods up to ninth-order accuracy for incompressible flows

This work presents a concise, unified stability theory of high-order decoupled \lan{implicit-explicit linear multistep (IELM)} methods based on the well-known consistent splitting technique for the incompressible Navier-Stokes equation. With the help of the recent semi-generating function approach and the global discrete energy analysis, one can establish the unconditional stability of a consistent splitting IELM method with respect to the $\ell^{\infty}(H^1)\cap \ell^{2}(H^2)$ norm if the associated implicit-explicit controllability intensity is larger than $\sqrt{2}/2$, a constant determined by the Stokes pressure estimate. It is shown that the $\beta$-parameterized GBDF-$\rmk$ ($2\le \rmk\le5$) schemes and $\gamma$-parameterized SIELM-$\rmk$ ($2\le \rmk\le9$) schemes can fulfill this requirement of implicit-explicit controllability intensity by choosing proper parameters so that they can theoretically maintain the unconditional stability of the associated consistent splitting IELM methods. Numerical experiments are also included to support our theory.

math.NA↗

arXiv2026

Optimal asymptotic analyses on Laguerre and Hermite orthogonal approximation for functions of algebraic and logarithmic regularitiesYali

Based on the Hilb-type formula and van der Corput-type lemmas, we present optimal asymptotic estimates for the decay of the Laguerre and Hermite coefficients for functions with algebraic and logarithmic singularities, which in turn yield the convergence rates of the corresponding spectral orthogonal projections. Numerous examples are provided to verify the optimality of these asymptotic results.

math.NA↗

arXiv2024

Dynamic control of polarization conversion based on borophene nanostructures in optical communication bands

Polarized light has various potential applications in the communication bands, including optical communication, polarization imaging, quantum emission, and quantum communication. However, optimizing polarization control requires continuous improvements in areas such as dynamic tunability, materials, and efficiency. In this work, we propose a borophene-based structure capable of converting linearly polarized light into arbitrarily polarized light through the coherent excitation of localized surface plasmons (LSPs) in optical communication band. Furthermore, a double-layer borophene structure can be achieved by placing a second borophene array at the top of the first one with a 90° relative rotation of their crystalline plane. The rotation direction of the polarization state of the reflected light can be switched by independently controlling the carrier concentration of the two-layer borophene. Finally, a dipole source is used to realize the emission of polarized light, which is two orders of magnitude higher than the emission rate in free space, and the polarization state can be dynamically controlled by manipulating the carrier concentration. Our study is simple and compact, with potential applications in the fields of polarizers, polarization detectors, and quantum emitters.

physics.optics↗

arXiv2023

Pointwise error estimates and local superconvergence of Jacobi expansions

As one myth of polynomial interpolation and quadrature, Trefethen [30] revealed that the Chebyshev interpolation of $|x-a|$ (with $|a|<1 $) at the Clenshaw-Curtis points exhibited a much smaller error than the best polynomial approximation (in the maximum norm) in about $95\%$ range of $[-1,1]$ except for a small neighbourhood near the singular point $x=a.$ In this paper, we rigorously show that the Jacobi expansion for a more general class of $Φ$-functions also enjoys such a local convergence behaviour. Our assertion draws on the pointwise error estimate using the reproducing kernel of Jacobi polynomials and the Hilb-type formula on the asymptotic of the Bessel transforms. We also study the local superconvergence and show the gain in order and the subregions it occurs. As a by-product of this new argument, the undesired $\log n$-factor in the pointwise error estimate for the Legendre expansion recently stated in Babuuska and Hakula [5] can be removed. Finally, all these estimates are extended to the functions with boundary singularities. We provide ample numerical evidences to demonstrate the optimality and sharpness of the estimates.

math.NA↗

arXiv2022

Polaritonic coherent perfect absorption based on strong critical coupling between quasi-bound state in the continuum and exciton

Enhancement of light-matter interactions is of great importance for many nanophotonic devices, and one way to achieve it is to feed energy perfectly to the strongly coupled system. Here, we propose gap-perturbed dimerized gratings based on bulk WS2 for flexible control of the strong coupling between quasi-bound state in the continuum (quasi-BIC) and exciton. The simulation results show that when a gap perturbation is introduced into the system resulting in the Brillouin zone folding, BIC transforms into quasi-BIC whose quality factor (Q-factor) is related to the value of gap perturbation. The strong coupling results in the anti-crossover behavior of the absorption spectra, and thus a Rabi splitting energy of 0.235 eV is obtained. Temporal coupled-mode theory is employed to analyze the strong coupling system, and the absorption of the system could be enhanced, by modulating the damping rate of quasi-BIC to make the system satisfy the strong critical coupling condition. Furthermore, polaritonic coherent perfect absorption is achieved by using the two-port source excitation. This work could provide ideas for enhancing light-matter interactions and a promising prospect for polariton-based light-emitting or lasing devices.

physics.optics↗