arXiv subjects

Ying Liang

Publications and source records attributed to Ying Liang.

At least 55 records · Page 3Linked to original sources

arXiv2023

Stability for inverse source problems of the stochastic Helmholtz equation with a white noise

This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and uniqueness of solutions. The stability estimates are deduced for the inverse source problems, which aim to determine the strength of the random source. To enhance the stability of the inverse source problems, we incorporate a priori information regarding the regularity and support of the strength. In the case of homogeneous media, a Hölder stability estimate is established, providing a quantitative measure of the stability for reconstructing the source strength. For the more challenging scenario of inhomogeneous media, a logarithmic stability estimate is presented, capturing the intricate interactions between the source and the varying medium properties.

math.AP↗

arXiv2023

Doping driven metal-insulator transition in disordered graphene

Controlling the metal-insulator transition in graphene-based material is a crucial topic as it directly impacts its potential applications. Inspired by recent experiments, we study the effects of doping and bond disorder on metal-insulator transition in graphene within the Hubbard model on a honeycomb lattice. By using the determinant quantum Monte Carlo method, we first conduct tests on the value of under various parameters, such as electron density, on-site interactions, temperature, and lattice size, so as to select the appropriate parameters to alleviate the impact of the sign problem. Given the knowledge that bond disorder can lead to a mental-insulator transition, our study has revealed, after ruling out the influence of size effects, that the critical strength of disorder increases as the electron density decreases while decreasing as the on-site interactions increase. Furthermore, we compared our results with experimental data and concluded that, in actual graphene materials, the localization effect induced by doping plays a dominant role, resulting in an insulating phase.

cond-mat.str-el↗

arXiv2023

A data-assisted two-stage method for the inverse random source problem

We propose a data-assisted two-stage method for solving an inverse random source problem of the Helmholtz equation. In the first stage, the regularized Kaczmarz method is employed to generate initial approximations of the mean and variance based on the mild solution of the stochastic Helmholtz equation. A dataset is then obtained by sampling the approximate and corresponding true profiles from a certain a-priori criterion. The second stage is formulated as an image-to-image translation problem, and several data-assisted approaches are utilized to handle the dataset and obtain enhanced reconstructions. Numerical experiments demonstrate that the data-assisted two-stage method provides satisfactory reconstruction for both homogeneous and inhomogeneous media with fewer realizations.

math.NA↗

arXiv2023

A direct probing method of an inverse problem for the Eikonal equation

In this paper, we propose a direct probing method for the inverse problem based on the Eikonal equation. For the Eikonal equation with a point source, the viscosity solution represents the least travel time of wave fields from the source to the point at the high-frequency limit. The corresponding inverse problem is to determine the inhomogeneous wave-speed distribution from the first-arrival time data at the measurement surfaces corresponding to distributed point sources, which is called transmission travel-time tomography. At the low-frequency regime, the reconstruction approximates the frequency-depend wave-speed distribution. We analyze the Eikonal inverse problem and show that it is highly ill-posed. Then we developed a direct probing method that incorporates the solution analysis of the Eikonal equation and several aspects of the velocity models. When the wave-speed distribution has a small variation from the homogeneous medium, we reconstruct the inhomogeneous media using the filtered back projection method. For the high-contrast media, we assume a background medium and develop the adjoint-based back projection method to identify the variations of the medium from the assumed background.

math.AP↗

arXiv2022

Antiferromagnetic fluctuations and a dominant $d_{xy}$-wave pairing symmetry in nickelate-based superconductors

Motivated by recent experimental studies on superconductivity found in nickelate-based materials, we study the temperature dependence of the spin correlation and the superconducting pairing interaction within an effective two-band Hubbard model by the quantum Monte Carlo method. Based on parameters extracted from first-principles calculations, our intensive numerical results reveal that the pairing with a $d_{xy}$-wave symmetry firmly dominates over other pairings at low temperature, which is mainly determined by the Ni 3$d$ orbital. It is also found that the effective pairing interaction is enhanced as the on-site interaction increases, demonstrating that the superconductivity is driven by strong electron-electron correlation. Even though the $(π,π)$ antiferromagnetic correlation could be enhanced by electronic interaction, there is no evidence for long-range antiferromagnetic order exhibited in nickelate-based superconductors. Moreover, our results offer possible evidence that the pure electron correlation may not account for the charge density wave state observed in nickelates.

cond-mat.supr-con↗

arXiv2022

Doping-dependent metal-insulator transition in a disordered Hubbard model

We study the effect of disorder and doping on the metal-insulator transition in a repulsive Hubbard model on a square lattice using the determinant quantum Monte Carlo method. First, with the aim of making our results reliable, we compute the sign problem with various parameters such as temperature, disorder, on-site interactions, and lattice size. We show that in the presence of randomness in the hopping elements, the metal-insulator transition occurs and the critical disorder strength differs at different fillings. We also demonstrate that doping is a driving force behind the metal-insulator transition.

cond-mat.str-el↗

arXiv2022

Least-Squares Method for Inverse Medium Problems

We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the first stage, while a total least-squares method with mixed regularization is used to recover the medium profile in the second stage. The total least-squares method is designed to minimize the residual of the model equation and the data fitting, along with an appropriate regularization, in an attempt to significantly improve the accuracy of the approximation obtained from the first stage. We shall also present an analysis on the well-posedness and convergence of this algorithm. Numerical experiments are carried out to verify the accuracies and robustness of this novel two-stage least-squares algorithm, with great tolerance of noise.

math.NA↗

arXiv2021

Mott insulating state and $d+id$ superconductivity in an ABC graphene trilayer

Motivated by the recently experimental reported signatures of the tunable Mott insulating state and superconductivity in an ABC graphene trilayer superlattice, we investigate the charge compressibility, the spin correlation, and the superconducting instability within the Hubbard model on a three-layer honeycomb lattice. It is found that an antiferromagnetically ordered Mott insulator emerges beyond a critical $U_c$ at half-filling, and the electronic correlation drives a $d+id$ superconducting pairing to be dominant over other pairing patterns in a wide doped region. The effective pairing interaction with $d+id$ pairing symmetry is strongly enhanced with the increasing of on-site interaction, and suppressed as the interlayer coupling strength increases. Our intensive numerical results demonstrate that the insulating state and superconductivity in an ABC graphene trilayer are driven by strong electric correlation, and it may offer an attractive systems to explore rich correlated behaviors.

cond-mat.str-el↗

arXiv2020

Synchronized Fractionation and Phase Separation in Binary Colloids

Fractionation is necessary for self-assembly in multicomponent mixtures. Here, reversible fractionation and crystallization are realized and studied in a two-dimensional binary colloids which is supersaturated by enhancing the attraction between colloidal particles. As a deep and fast supersaturation results in gels with a uniform distribution of binary particles, a gradual quasistatic supersaturating process leads to a two-step crystallization in which small particles and large particles are fractionated as coexisting crystal and liquid phases respectively. Fractionation occurs as well in the quasistatic melting of gel. We show that the synchronized fractionation and phase separation arises from the competition between the size-dependent repulsion and the tunable attraction. The results in this study demonstrate a robust mechanism of fractionation via phase separation, and have important implication in understanding the reversible formation of membraneless organelles in living cells.

cond-mat.soft↗

arXiv2020

Intermediate Phase in Interacting Dirac Fermions with Staggered Potential

By performing exact quantum Monte Carlo simulations of a model of interacting Dirac Fermions with staggered potential, we reveal a novel intermediate phase where the electronic correlations drive a band insulator metallic, and at a larger interaction, drive the metal to Mott insulator. We also show that the Mott insulating phase is antiferromagnetic. A complete phase diagram is achieved by studying the phase transitions at large staggered potential and interaction strengths, which shows that the intermediate state is robust and occupies a large part of the phase diagram and that it should be more feasible to be detected experimentally.

cond-mat.str-el↗

arXiv2019

Mathematical and numerical study of a three-dimensional inverse eddy current problem

We study an inverse problem associated with an eddy current model. We first address the ill-posedness of the inverse problem by proving the compactness of the forward map with respect to the conductivity and the non-uniqueness of the recovery process. Then by virtue of non-radiating source conceptions, we establish a regularity result for the tangential trace of the true solution on the boundary, which is necessary to justify our subsequent mathematical formulation. After that, we formulate the inverse problem as a constrained optimization problem with an appropriate regularization and prove the existence and stability of the regularized minimizers. To facilitate the numerical solution of the nonlinear non-convex constrained optimization, we introduce a feasible Lagrangian and its discrete variant. Then the gradient of the objective functional is derived using the adjoint technique. By means of the gradient, a nonlinear conjugate gradient method is formulated for solving the optimization system, and a Sobolev gradient is incorporated to accelerate the iterative process. Numerical examples are provided to demonstrate the feasibility of the proposed algorithm.

math.AP↗

arXiv2016

Tunable Weyl Semi-metal and its Possible Realization in Optical Lattice

Weyl semimetal (WSM) is an exotic topological state in condensed matter physics. In this paper, based on a two-band cubic lattice model, we studied WSMs with a pair of tunable Weyl nodes. It is pointed out that there exist three types of WSMs with different tilt strengths: type-I WSM, type-II WSM and type-1.5 WSM. In particular, type-1.5 WSM has one type-I node and one type-II node. We studied chiral modes, surface Fermi arcs and quantum anomalous Hall effect in different types of WSMs. In addition, we give an experimental setup to realize the different types of WSMs based on timely technique.

cond-mat.str-el↗

arXiv2016

Electronic transport of bilayer graphene with asymmetry line defects

In this paper, we study the quantum properties of a bilayer graphene with (asymmetry) line defects. The localized states are found around the line defects. Thus, the line defects on one certain layer of the bilayer graphene can lead to an electric transport channel. By adding a bias potential along the direction of the line defects, we calculate the electric conductivity of bilayer graphene with line defects using Landauer-Büttiker theory, and show that the channel affects the electric conductivity remarkably by comparing the results with those in a perfect bilayer graphene. This one-dimensional line electric channel has the potential to be applied in the nanotechnology engineering.

cond-mat.mes-hall↗

arXiv2016

The Simulation of Non-Abelian Statistics of Majorana Fermions in Ising Chain with Z2 Symmetry

In this paper, we numerically study the non-Abelian statistics of the zero-energy Majorana fermions on the end of Majorana chain and show its application to quantum computing by mapping it to a spin model with special symmetry. In particular, by using transverse-field Ising model with Z2 symmetry, we verify the nontrivial non-Abelian statistics of Majorana fermions. Numerical evidence and comparison in both Majorana-representation and spin-representation are presented. The degenerate ground states of a symmetry protected spin chain therefore previde a promising platform for topological quantum computation.

cond-mat.mes-hall↗

arXiv2016

Character of frustration on magnetic correlation in doped Hubbard model

The magnetic correlation in the Hubbard model on a two-dimensional anisotropic triangular lattice is studied by using the determinant quantum Monte Carlo method. Around half filling, it is found that the increasing frustration $t'/t$ could change the wave vector of maximum spin correlation along ($π,π$)$\rightarrow$($π,\frac{5π}{6}$)$\rightarrow$($\frac{5π}{6},\frac{5π}{6}$)$\rightarrow$ ($\frac{2π}{3},\frac{2π}{3}$), indicating the frustration's remarkable effect on the magnetism. In the studied filling region =1.0-1.3, the doping behaves like some kinds of {\it{frustration}}, which destroys the $(π,π)$ AFM correlation quickly and push the magnetic order to a wide range of the $(\frac{2π}{3},\frac{2π}{3})$ $120^{\circ}$ order when the $t'/t$ is large enough. Our non-perturbative calculations reveal a rich magnetic phase diagram over both the frustration and electron doping.

cond-mat.str-el↗

arXiv2015

Topological Hierarchy Insulators and Topological Fractal Insulators

Topological insulators are new states of quantum matter with metallic edge/surface states. In this paper, we pointed out that there exists a new type of particle-hole symmetry-protected topological insulator - topological hierarchy insulator (THI), a composite topological state of a (parent) topological insulator and its defect-induced topological mid-gap states. A particular type of THI is topological fractal insulator, that is a THI with self-similar topological structure. In the end, we discuss the possible experimental realizations of THIs.

cond-mat.str-el↗

arXiv2014

DualTable: A Hybrid Storage Model for Update Optimization in Hive

Hive is the most mature and prevalent data warehouse tool providing SQL-like interface in the Hadoop ecosystem. It is successfully used in many Internet companies and shows its value for big data processing in traditional industries. However, enterprise big data processing systems as in Smart Grid applications usually require complicated business logics and involve many data manipulation operations like updates and deletes. Hive cannot offer sufficient support for these while preserving high query performance. Hive using the Hadoop Distributed File System (HDFS) for storage cannot implement data manipulation efficiently and Hive on HBase suffers from poor query performance even though it can support faster data manipulation.There is a project based on Hive issue Hive-5317 to support update operations, but it has not been finished in Hive's latest version. Since this ACID compliant extension adopts same data storage format on HDFS, the update performance problem is not solved. In this paper, we propose a hybrid storage model called DualTable, which combines the efficient streaming reads of HDFS and the random write capability of HBase. Hive on DualTable provides better data manipulation support and preserves query performance at the same time. Experiments on a TPC-H data set and on a real smart grid data set show that Hive on DualTable is up to 10 times faster than Hive when executing update and delete operations.

cs.DB↗

arXiv2013

Magnetic Orders of Correlated Topological Insulators at Finite Temperature

In this paper, we study the magnetic orders of two dimensional correlated topological insulators including the correlated Chern insulator and the correlated Z2 topological insulator at finite temperature. For the 2D correlated Chern insulator, we found that thermal-fluctuation-induced magnetic order appears in the intermediate interaction region of the correlated Chern insulator. On the contrary, for the correlated Z2 topological insulator there doesn't exist the thermal-fluctuation-induced magnetic order. In the end, we give an explanation on the difference.

cond-mat.str-el↗