arXiv subjects

Xiaoyu Wei

Publications and source records attributed to Xiaoyu Wei.

8 recordsLinked to original sources

arXiv2026

Quadrature by Matched Asymptotic Expansion (QBMAX): Accelerating Evaluation of Layer Potentials with Boundary Layers

Evaluating layer potentials with rapidly decaying kernels becomes computationally challenging in the presence of boundary layers, as occurs for Helmholtz layer potentials with large imaginary wavenumbers. We introduce Quadrature by Matched Asymptotic Expansion (QBMAX), a high-order method that extends the Quadrature by Expansion (QBX) framework by incorporating the kernel's asymptotic decay behavior directly into the Taylor expansion of the potential. Numerical results in both 2D and 3D show improvements of up to four digits over QBX for the tested large-parameter cases, while the methods can perform similarly for smaller parameters or more strongly curved geometries. A symbolic weighted operation-count model indicates comparable costs for forming the two expansion kernels. The Taylor expansions have the same formal order, while QBMAX reduces the truncation-error constants in the flat-boundary model and generally exhibits less convergence degradation in the reported experiments.

math.NA↗

arXiv2026

Interface-Confined Superconductivity with Thickness-Independent Superfluid Stiffness in (Pb,Sn)Te/FeTe Bilayers

Interface-induced superconductivity in FeTe-based heterostructures provides a promising route toward topological superconductivity, yet the roles of the neighboring layers topology, symmetry, and electronic structure remain unresolved. In this work, we employ molecular beam epitaxy to grow Pb1-xSnxTe/FeTe bilayers and use angle-resolved photoemission spectroscopy to track the evolution of the Pb1-xSnxTe layer from a trivial insulator to a topological crystalline insulator hosting multiple Dirac surface states. Electrical transport measurements reveal robust superconductivity throughout the entire composition range, with a nearly constant superconducting transition temperature of ~12 K despite substantial changes in the electronic structure and topology of Pb1-xSnxTe. Double-coil mutual-inductance measurements further reveal comparable superfluid stiffness across the topological phase transition and nearly thickness-independent superfluid stiffness despite large variations in the constituent-layer thicknesses, demonstrating that superconductivity is confined near the interface. These results establish that superconductivity in FeTe-based heterostructures is largely insensitive to the topology, crystal symmetry, and detailed electronic structure of the neighboring layer, supporting a primary origin in modifications to the FeTe layer. The coexistence of interface-confined superconductivity and tunable multiple Dirac surface states in Pb1-xSnxTe/FeTe bilayers provides a versatile platform for exploring topological superconductivity and interactions among multiple Majorana zero modes.

cond-mat.supr-con↗

arXiv2025

Unveiling the landscape of Mottness and its proximity to superconductivity in 4Hb-TaS$_2$

Mott physics is at the root of a plethora of many-body quantum phenomena in quantum materials. Recently, the stacked or twisted structures of van der Waals (vdW) materials have emerged as a unique platform for realizing exotic correlated states in the vicinity of the Mott transition. However, the definitive feature of Mottness and how it rules the low-energy electronic state remain elusive and experimentally inaccessible in many interesting regimes. Here, we quantitatively describe a filling-controlled Mott state and its interplay with superconductivity by scanning tunnelling spectroscopy in a vdW bulk heterostructure, 4Hb-TaS$_2$, that interleaves strongly correlated 1T-TaS$_2$ layers with superconducting 1H-Ta$_2$ layers. The fine tunability of electron doping induced by interlayer charge transfer allows us to continuously track the spectral function with unsurpassed energy resolution from a depleted narrow band (0.2 electrons per site) toward a Mott transition at half filling. The gradually emerging Mott-Hubbard bands, followed by the sharpening and vanishing of the central quasiparticle peak as predicted in the Brinkman-Rice scenario, unambiguously demonstrate the Mott physics at play. Importantly, the renormalization of the low-energy electrons acts destructively on the superconducting pairing potential, leaving behind nonsuperconducting, paramagnetic puddles at the nanoscale. Our results reveal a seminal system near the border of the Mott criterion that enables us to illustrate the predictive power of the Hubbard model, and set such heterostructures as promising ground for realizing new correlated states in the heavily doped Mott regime.

cond-mat.supr-con↗

arXiv2023

Integral Equation Methods for the Morse-Ingard Equations

We present two (a decoupled and a coupled) integral-equation-based methods for the Morse-Ingard equations subject to Neumann boundary conditions on the exterior domain. Both methods are based on second-kind integral equation (SKIE) formulations. The coupled method is well-conditioned and can achieve high accuracy. The decoupled method has lower computational cost and more flexibility in dealing with the boundary layer; however, it is prone to the ill-conditioning of the decoupling transform and cannot achieve as high accuracy as the coupled method. We show numerical examples using a Nyström method based on quadrature-by-expansion (QBX) with fast-multipole acceleration. We demonstrate the accuracy and efficiency of the solvers in both two and three dimensions with complex geometry.

math.NA↗

arXiv2022

Exact domain truncation for the Morse-Ingard equations

Morse and Ingard give a coupled system of time-harmonic equations for the temperature and pressure of an excited gas. These equations form a critical aspect of modeling trace gas sensors. Like other wave propagation problems, the computational problem must be closed with suitable far-field boundary conditions. Working in a scattered-field formulation, we adapt a nonlocal boundary condition proposed earlier for the Helmholtz equation to this coupled system. This boundary condition uses a Green's formula for the true solution on the boundary, giving rise to a nonlocal perturbation of standard transmission boundary conditions. However, the boundary condition is exact and so Galerkin discretization of the resulting problem converges to the restriction of the exact solution to the computational domain. Numerical results demonstrate that accuracy can be obtained on relatively coarse meshes on small computational domains, and the resulting algebraic systems may be solved by GMRES using the local part of the operator as an effective preconditioner.

math.NA↗

arXiv2020

First-Principles Experimental Demonstration of Ferroelectricity in a Thermotropic Nematic Liquid Crystal: Spontaneous Polar Domains and Striking Electro-Optics

We report the experimental determination of the structure and response to applied electric field of the lower-temperature nematic phase of the previously reported calamitic compound 4-[(4-nitrophenoxy)carbonyl]phenyl2,4-dimethoxybenzoate (RM734). We exploit its electro-optics to visualize the appearance, in the absence of applied field, of a permanent electric polarization density, manifested as a spontaneously broken symmetry in distinct domains of opposite polar orientation. Polarization reversal is mediated by field-induced domain wall movement, making this phase ferroelectric, a 3D uniaxial nematic having a spontaneous, reorientable, polarization locally parallel to the director. This polarization density saturates at a low temperature value of ~ 6 microcoulombs/cm-sqd, the largest ever measured for an organic material or for any fluid. This polarization is comparable to that of solid state ferroelectrics, and is close to the average value obtained by assuming perfect, polar alignment of molecular long axes in the nematic. We find a host of spectacular optical and hydrodynamic effects driven by ultra-low applied field (E~1V/cm), produced by the coupling of the large polarization to nematic birefringence and flow. Electrostatic self-interaction of the polarization charge renders the transition from the nematic phase mean-field-like and weakly first-order, and controls the director field structure of the ferroelectric phase. Atomistic molecular dynamics simulation reveals short-range polar molecular interactions that favor ferroelectric ordering, including a tendency for head-to-tail association into polar, chain-like assemblies having polar lateral correlations. These results indicate a significant potential for transformative new nematic science and technology based on the enhanced understanding, development, and exploitation of molecular electrostatic interaction.

cond-mat.soft↗

arXiv2020

An Integral Equation Method for the Cahn-Hilliard Equation in the Wetting Problem

We present an integral equation approach to solving the Cahn-Hilliard equation equipped with boundary conditions that model solid surfaces with prescribed Young's angles. The discretization of the system in time using convex splitting leads to a modified biharmonic equation at each time step. To solve it, we split the solution into a volume potential computed with free space kernels, plus the solution to a second kind integral equation (SKIE). The volume potential is evaluated with the help of a box-based volume-FMM method. For non-box domains, source density is extended by solving a biharmonic Dirichlet problem. The near-singular boundary integrals are computed using quadrature by expansion (QBX) with FMM acceleration. Our method has linear complexity in the number of surface/volume degrees of freedom and can achieve high order convergence with adaptive refinement to manage error from function extension.

math.NA↗

arXiv2016

An efficient iterative thresholding method for image segmentation

We proposed an efficient iterative thresholding method for multi-phase image segmentation. The algorithm is based on minimizing piecewise constant Mumford-Shah functional in which the contour length (or perimeter) is approximated by a non-local multi-phase energy. The minimization problem is solved by an iterative method. Each iteration consists of computing simple convolutions followed by a thresholding step. The algorithm is easy to implement and has the optimal complexity $O(N \log N)$ per iteration. We also show that the iterative algorithm has the total energy decaying property. We present some numerical results to show the efficiency of our method.

cs.CV↗