arXiv subjects

Haiyun Dong

Publications and source records attributed to Haiyun Dong.

5 recordsLinked to original sources

arXiv2026

A well-balanced positivity-preserving discontinuous Galerkin method for shallow water models with variable density

In this paper, we present a numerical scheme designed for coupled systems of variable-topography shallow water flow and solute transport. By integrating a variable-density system with an expression for relative density of mixtures, a novel formulation of the coupled system is derived. To ensure the well-balanced property, auxiliary variables are introduced to reformulate the variable-density shallow water equations into a new form, which is then discretized using the discontinuous Galerkin (DG) method with the Lax-Friedrichs (LF) flux as the numerical flux. By selecting appropriate values for the auxiliary variables, we demonstrate that the proposed method accurately preserves steady-state solutions under still water conditions, thereby verifying its well-balanced nature. Furthermore, sufficient conditions for preserving the positivity of both water depth and concentration are proposed and rigorously proven. A positivity-preserving limiter is introduced to enforce these conditions. Finally, a series of numerical examples are conducted to validate the computational accuracy and effectiveness of the proposed method.

math.NA↗

arXiv2026

Wide-angle emission in cylindrical moiré lattices enabled by rolling origami

Twisted photonic lattices that form moiré superlattices have attracted significant attention owing to their unique properties, such as strong field confinement and high-quality factors, in which the localized optical modes can serve as efficient light sources. However, in conventional moiré lattices, the emission direction of confined modes is typically fixed, and achieving a broad range of emission angles through simple modulation remains a significant challenge. Here, we design and fabricate single-layer moiré photonic lattices into cylindrical geometries using a nanomembrane origami technique. This approach enables wide-angle localized-mode emission while maintaining stable single-mode operation and excellent spectral uniformity. The moiré supercells support localized flat-band modes under various effective twist angles, resulting in the observation of periodic localized-mode emission over a wide range of azimuthal angles. Our research provides an approach for developing moiré light sources on curved surfaces, offering significant potential in applications that demand spatial light control, including three dimensional imaging, light detection and ranging, and topological states manipulation.

physics.optics↗

arXiv2026

Mass conservation, positivity and energy identical-relation preserving scheme for the Navier-Stokes equations with variable density

In this paper, we consider a mass conservation, positivity and energy identical-relation preserving scheme for the Navier-Stokes equations with variable density. Utilizing the square transformation, we first ensure the positivity of the numerical fluid density, which is form-invariant and regardless of the discrete scheme. Then, by proposing a new recovery technique to eliminate the numerical dissipation of the energy and to balance the loss of the mass when approximating the reformation form, we preserve the original energy identical-relation and mass conservation of the proposed scheme. To the best of our knowledge, this is the first work that can preserve the original energy identical-relation for the Navier-Stokes equations with variable density. Moreover, the error estimates of the considered scheme are derived. Finally, we show some numerical examples to verify the correctness and efficiency.

math.NA↗

arXiv2024

Dynamic Phase Enabled Topological Mode Steering in Composite Su-Schrieffer-Heeger Waveguide Arrays

Topological boundary states localize at interfaces whenever the interface implies a change of the associated topological invariant encoded in the geometric phase. The generically present dynamic phase, however, which is energy and time dependent, has been known to be non-universal, and hence not to intertwine with any topological geometric phase. Using the example of topological zero modes in composite Su-Schrieffer-Heeger (c-SSH) waveguide arrays with a central defect, we report on the selective excitation and transition of topological boundary mode based on dynamic phase-steered interferences. Our work thus provides a new knob for the control and manipulation of topological states in composite photonic devices, indicating promising applications where topological modes and their bandwidth can be jointly controlled by the dynamic phase, geometric phase, and wavelength in on-chip topological devices.

physics.optics↗

arXiv2023

Symmetry induced selective excitation of topological states in SSH waveguide arrays

The investigation of topological state transition in carefully designed photonic lattices is of high interest for fundamental research, as well as for applied studies such as manipulating light flow in on-chip photonic systems. Here, we report on topological phase transition between symmetric topological zero modes (TZM) and antisymmetric TZMs in Su-Schrieffer-Heeger (SSH) mirror symmetric waveguides. The transition of TZMs is realized by adjusting the coupling ratio between neighboring waveguide pairs, which is enabled by selective modulation of the refractive index in the waveguide gaps. Bi-directional topological transitions between symmetric and antisymmetric TZMs can be achieved with our proposed switching strategy. Selective excitation of topological edge mode is demonstrated owing to the symmetry characteristics of the TZMs. The flexible manipulation of topological states is promising for on-chip light flow control and may spark further investigations on symmetric/antisymmetric TZM transitions in other photonic topological frameworks.

physics.optics↗