arXiv subjects

Zhilin Li

Publications and source records attributed to Zhilin Li.

At least 37 records · Page 2Linked to original sources

arXiv2024

Fourth-order compact finite difference schemes for solving biharmonic equations with Dirichlet boundary conditions

In this study, we propose a genuine fourth-order compact finite difference scheme for solving biharmonic equations with Dirichlet boundary conditions in both two and three dimensions. In the 2D case, we build upon the high-order compact (HOC) schemes for flux-type boundary conditions originally developed by Zhilin Li and Kejia Pan [SIAM J. Sci. Comput., 45 (2023), pp. A646-A674] to construct a high order compact discretization for coupled boundary conditions. When considering the 3D case, we modify carefully designed undetermined coefficient methods of Li and Pan to derive the finite difference approximations of coupled boundary conditions. The resultant FD discretization maintains the global fourth order convergence and compactness. Unlike the very popular Stephenson method, the number of unknows do not increase with dimensions. Besides, it is noteworthy that the condition number of the coefficient matrix increases at a rate of $O(h^{-2})$ in both 2D and 3D. We also validate the performance of the proposed genuine HOC methods through nontrivial examples.

math.NA↗

arXiv2024

Transcranial low-level laser stimulation in near infrared-II region for brain safety and protection

Background: The use of near-infrared lasers for transcranial photobiomodulation (tPBM) offers a non-invasive method for influencing brain activity and is beneficial for various neurological conditions. Objective: To investigate the safety and neuroprotective properties of tPBM using near-infrared (NIR)-II laser stimulation. Methods: We conducted thirteen experiments involving multidimensional and quantitative methods and measured serum neurobiomarkers, performed electroencephalogram (EEG) and magnetic resonance imaging (MRI) scans, assessed executive functions, and collected a subjective questionnaire. Results: Significant reductions (n=15) in neuron specific enolase (NSE) levels were observed after treatment, indicating neuroprotective effects. No structural or functional brain abnormalities were observed, confirming the safety of tPBM. Additionally, cognitive and executive functions were not impaired, with participants' feedback indicating minimal discomfort. Conclusions: Our data indicate that NIR-II tPBM is safe with specific parameters, highlighting its potential for brain protection.

q-bio.NC↗

arXiv2024

Inverse-current quantum electro-oscillations in a charge-density wave insulator

Quantum magneto-oscillations have long been a vital subject in condensed matter physics, with ubiquitous quantum phenomena and diverse underlying physical mechanisms. Here, we demonstrate the intrinsic and reproducible DC-current-driven quantum electro-oscillations with a periodicity in the inverse of the current (1/I), in quasi-one-dimensional charge-density-wave (CDW) insulators (TaSe$_4$)$_2$I and TaS$_3$ nanowires. Such oscillations manifest in the nearly infinite Fröhlich conductivity region where the undamped CDW flow forms in a finite electric current, and finally disappear after the oscillation index n reaches 1. A systematic investigation on the effect of temperature and magnetic field establishes that the observed electro-oscillations are a coherent quantum phenomenon. We discuss the possibilities of the physical mechanisms, including the formation of sliding-driven inherent Floquet sidebands. Our results introduce a new member in the family of quantum oscillations, and shed light on plausible avenues to explore novel physics and potential applications of coherent density-wave condensates.

cond-mat.mes-hall↗

arXiv2024

Topological Weyl Altermagnetism in CrSb

Altermagnets constitute a novel, third fundamental class of collinear magnetic ordered materials, alongside with ferro- and antiferromagnets. They share with conventional antiferromagnets the feature of a vanishing net magnetization. At the same time they show a spin-splitting of electronic bands, just as in ferromagnets, caused by the atomic exchange interaction. On the other hand, topology has recently revolutionized our understanding of condensed matter physics, introducing new phases of matter classified by intrinsic topological order. Here we connect the worlds of altermagnetism and topology, showing that the electronic structure of the altermagnet CrSb is topological and hosts a novel Weyl semimetallic state. Using high-resolution and spin angleresolved photoemission spectroscopy, we observe a large momentum-dependent spin-splitting in CrSb, reaching up to 1 eV, that induces altermagnetic Weyl nodes with an associated magnetic quantum number. At the surface we observe their spin-polarized topological Fermi-arcs. This establishes that in altermagnets the large energy scale intrinsic to the spin-splitting - orders of magnitude larger than the relativistic spin-orbit coupling - creates its own realm of robust electronic topology.

cond-mat.mtrl-sci↗

arXiv2024

Convex Combination Consistency between Neighbors for Weakly-supervised Action Localization

Weakly-supervised temporal action localization (WTAL) intends to detect action instances with only weak supervision, e.g., video-level labels. The current~\textit{de facto} pipeline locates action instances by thresholding and grouping continuous high-score regions on temporal class activation sequences. In this route, the capacity of the model to recognize the relationships between adjacent snippets is of vital importance which determines the quality of the action boundaries. However, it is error-prone since the variations between adjacent snippets are typically subtle, and unfortunately this is overlooked in the literature. To tackle the issue, we propose a novel WTAL approach named Convex Combination Consistency between Neighbors (C$^3$BN). C$^3$BN consists of two key ingredients: a micro data augmentation strategy that increases the diversity in-between adjacent snippets by convex combination of adjacent snippets, and a macro-micro consistency regularization that enforces the model to be invariant to the transformations~\textit{w.r.t.} video semantics, snippet predictions, and snippet representations. Consequently, fine-grained patterns in-between adjacent snippets are enforced to be explored, thereby resulting in a more robust action boundary localization. Experimental results demonstrate the effectiveness of C$^3$BN on top of various baselines for WTAL with video-level and point-level supervisions. Code is at https://github.com/Qinying-Liu/C3BN.

cs.CV↗

arXiv2024

Picotesla-sensitivity microcavity optomechanical magnetometry

Cavity optomechanical systems have enabled precision sensing of magnetic fields, by leveraging the optical resonance-enhanced readout and mechanical resonance-enhanced response. Previous studies have successfully achieved scalable and reproducible microcavity optomechanical magnetometry (MCOM) by incorporating Terfenol-D thin films into high-quality ($Q$) factor whispering gallery mode (WGM) microcavities. However, the sensitivity was limited to 585 pT/Hz$^{1/2}$, over 20 times inferior to those using Terfenol-D particles. In this work, we propose and demonstrate a high-sensitivity and scalable MCOM approach by sputtering a FeGaB thin film onto a high-$Q$ SiO$_2$ WGM microdisk. Theoretical studies are conducted to explore the magnetic actuation constant and noise-limited sensitivity by varying the parameters of the FeGaB film and SiO$_2$ microdisk. Multiple magnetometers with different radii are fabricated and characterized. By utilizing a microdisk with a radius of 355 $μ$m and a thickness of 1 $μ$m, along with a FeGaB film with a radius of 330 $μ$m and a thickness of 1.3 $μ$m, we have achieved a remarkable peak sensitivity of 1.68 pT/Hz$^{1/2}$ at 9.52 MHz. This represents a significant improvement of over two orders of magnitude compared with previous studies employing sputtered Terfenol-D film. Notably, the magnetometer operates without a bias magnetic field, thanks to the remarkable soft magnetic properties of the FeGaB film. Furthermore, as a proof-of-concept, we have demonstrated the real-time measurement of a pulsed magnetic field simulating the corona current in a high-voltage transmission line using our developed magnetometer. These high-sensitivity magnetometers hold great potential for various applications, such as magnetic induction tomography and corona current monitoring.

physics.optics↗

arXiv2023

A Neumann interface optimal control problem with elliptic PDE constraints and its discretization and numerical analysis

We study an optimal control problem governed by elliptic PDEs with interface, which the control acts on the interface. Due to the jump of the coefficient across the interface and the control acting on the interface, the regularity of solution of the control problem is limited on the whole domain, but smoother on subdomains. The control function with pointwise inequality constraints is served as the flux jump condition which we called Neumann interface control. We use a simple uniform mesh that is independent of the interface. The standard linear finite element method can not achieve optimal convergence when the uniform mesh is used. Therefore the state and adjoint state equations are discretized by piecewise linear immersed finite element method (IFEM). While the accuracy of the piecewise constant approximation of the optimal control on the interface is improved by a postprocessing step which possesses superconvergence properties; as well as the variational discretization concept for the optimal control is used to improve the error estimates. Optimal error estimates for the control, suboptimal error estimates for state and adjoint state are derived. Numerical examples with and without constraints are provided to illustrate the effectiveness of the proposed scheme and correctness of the theoretical analysis.

math.NA↗

arXiv2023

Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems

In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods without penalties are not guaranteed to converge optimally if the tangential derivative of the exact solution and the jump of the coefficient are not zero on the interface. A nontrivial counter example is also provided to support our theoretical analysis. To recover the optimal convergence rates, we develop a new nonconforming IFE method with additional terms locally on interface edges. The new method is parameter-free which removes the limitation of the conventional partially penalized IFE method. We show the IFE basis functions are unisolvent on arbitrary triangles which is not considered in the literature. Furthermore, different from multipoint Taylor expansions, we derive the optimal approximation capabilities of both the Crouzeix-Raviart and the rotated-$Q_1$ IFE spaces via a unified approach which can handle the case of variable coefficients easily. Finally, optimal error estimates in both $H^1$- and $L^2$- norms are proved and confirmed with numerical experiments.

math.NA↗

arXiv2023

Magnetoresistance signature of two-dimensional electronic states in Co$_3$Sn$_2$S$_2$

Two-dimensional (2D) Dirac bands and flat bands are characteristics of a kagome lattice. However, experimental studies on their electrical transport are few, because three-dimensional (3D) bulk bands of kagome materials, consisting of stacked 2D kagome layers, dominate the transport. We report a magnetoresistance (MR) study of a kagome material, Co$_3$Sn$_2$S$_2$. Based on analysis of the temperature, magnetic field, and field angle dependence of the resistivity, we obtain a complete anatomy of MR. Besides a magnon MR, a chirality-dependent MR, and a chiral-anomaly-induced MR, the most intriguing feature is an orbital MR that scales only with the out-of-plane field, which strongly indicates its 2D nature. We attribute it to the Dirac band of the kagome lattice.

cond-mat.mes-hall↗

arXiv2023

Magnetotransport induced by anomalous Hall effect

In a magnetic metal, the Hall resistance is generally taken to be the sum of the ordinary Hall resistance and the anomalous Hall resistance. Here it is shown that this empirical relation is no longer valid when either the ordinary Hall angle or the anomalous Hall angle is not small. Using the proper conductivity relation, we reveal an unexpected magnetoresistance (MR) induced by the anomalous Hall effect (AHE). A $B$-linear MR arises and the sign of the slope depends on the sign of the anomalous Hall angle, giving rise to a characteristic bowtie shape. The Hall resistance in a single-band system can exhibit a nonlinearity which is usually considered as a characteristic of a two-band system. A $B$-symmetric component appears in the Hall. These effects reflect the fundamental difference between the ordinary Hall effect and the AHE. Furthermore, we experimentally reproduce the unusual MR and Hall reported before in Co$_3$Sn$_2$S$_2$ and show that these observations can be well explained by the proposed mechanism. MR often observed in quantum anomalous Hall insulators provides further confirmation of the picture. The effect may also account for the large MR observed in non-magnetic three-dimensional topological Dirac semimetals.

cond-mat.mes-hall↗

arXiv2022

Electronic Origin of Half-metal to Semiconductor Transition and Colossal Magnetoresistance in Spinel HgCr2Se4

Half-metals are ferromagnets hosting spin-polarized conducting carriers and crucial for spintronics applications. The chromium spinel HgCr2Se4 represents a unique type of half-metal, which features a half-metal to semiconductor transition (HMST) and exhibits colossal magnetoresistance (CMR) across the ferromagnetic-paramagnetic (FM-PM) transition. Using angle-resolved photoemission spectroscopy (ARPES), we find that the Fermi surface of n-type HgCr2Se4 (n-HgCr2Se4) consists of a single electron pocket which moves above the Fermi level (EF) upon the FM-PM transition, leading to the HMST. Such a Lifshitz transition manifests a giant band splitting which originates from the exchange interaction unveiled with a specific chemical nonstoichiometry. The exchange band splitting and the chemical nonstoichiometry are two key ingredients to the HMST and CMR, consistent with our ab-initio calculation. Our findings provide spectroscopic evidences of the electronic origin of the anomalous properties of HgCr2Se4, which address the unique phase transition in half-metals.

cond-mat.mtrl-sci↗

arXiv2022

Quantum corrections to the magnetoconductivity of surface states in three-dimensional topological insulators

The interplay between quantum interference, electron-electron interaction (EEI), and disorder is one of the central themes of condensed matter physics. Such interplay can cause high-order magnetoconductance (MC) corrections in semiconductors with weak spin-orbit coupling (SOC). However, it remains unexplored how the magnetotransport properties are modified by the high-order quantum corrections in the electron systems of symplectic symmetry class, which include topological insulators (TIs), Weyl semimetals, graphene with negligible intervalley scattering, and semiconductors with strong SOC. Here, we extend the theory of quantum conductance corrections to two-dimensional electron systems with the symplectic symmetry, and study experimentally such physics with dual-gated TI devices in which the transport is dominated by highly tunable surface states. We find that the MC can be enhanced significantly by the second-order interference and the EEI effects, in contrast to suppression of MC for the systems with orthogonal symmetry. Our work reveals that detailed MC analysis can provide deep insights into the complex electronic processes in TIs, such as the screening and dephasing effects of localized charge puddles, as well as the related particle-hole asymmetry.

cond-mat.mes-hall↗

arXiv2022

Numerical integration rules with improved accuracy close to singularities

Sometimes it is necessary to obtain a numerical integration using only discretised data. In some cases, the data contains singularities which position is known but does not coincide with a discretisation point, and the jumps in the function and its derivatives are available at these positions. The motivation of this paper is to use the previous information to obtain numerical quadrature formulas that allow approximating the integral of the discrete data over certain intervals accurately. This work is devoted to the construction and analysis of a new nonlinear technique that allows to obtain accurate numerical integrations of any order using data that contains singularities, and when the integrand is only known at grid points. The novelty of the technique consists in the inclusion of correction terms with a closed expression that depends on the size of the jumps of the function and its derivatives at the singularities, that are supposed to be known. The addition of these terms allows recovering the accuracy of classical numerical integration formulas even close to the singularities, as these correction terms account for the error that the classical integration formulas commit up to their accuracy at smooth zones. Thus, the correction terms can be added during the integration or as post-processing, which is useful if the main calculation of the integral has been already done using classical formulas. The numerical experiments performed allow us to confirm the theoretical conclusions reached in this paper.

math.NA↗

arXiv2022

On the Onsager-Casimir reciprocal relations in a tilted Weyl semimetal

The Onsager-Casimir reciprocal relations are a fundamental symmetry of nonequilibrium statistical systems. Here we study an unusual chirality-dependent Hall effect in a tilted Weyl semimetal Co$_3$Sn$_2$S$_2$ with broken time reversal symmetry. It is confirmed that the reciprocal relations are satisfied. Since two Berry curvature effects, an anomalous velocity and a chiral chemical potential, contribute to the observed Hall effect, the reciprocal relations suggest their intriguing connection.

cond-mat.mes-hall↗

arXiv2022

High order two-grid finite difference methods for interface and internal layer problems

Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal boundaries. In this paper, alternative approaches based on two different grids are developed for some interface and internal layer problems, which are different from adaptive mesh refinement (AMR) techniques. For one dimensional, or two-dimensional problems with straight interfaces or boundary layers that are parallel to one of the axes, the discussion is relatively easy. One of challenges is how to construct a fourth order compact finite difference scheme at boarder grid points that connect two meshes. A two-grid method that employs a second order discretization near the interface in the fine mesh and a fourth order discretization away from the interface in the coarse and boarder grid points is proposed. For two dimensional problems with a curved interface or an internal layer, a level set representation is utilized for which we can build a fine mesh within a tube $|φ({\bf x}) | \le δh$ of the interface. A new super-third seven-point discretization that can guarantee the discrete maximum principle has been developed at hanging nodes. The coefficient matrices of the finite difference equations developed in this paper are M-matrices, which leads to the convergence of the finite difference schemes. Non-trivial numerical examples presented in this paper have confirmed the desired accuracy and convergence.

math.NA↗

arXiv2022

Convergence study of IB methods for Stokes equations with no-slip boundary conditions

Peskin's Immersed Boundary (IB) model and method are among one of the most important modeling tools and numerical methods. The IB method has been known to be first order accurate in the velocity. However, almost no rigorous theoretical proof can be found in the literature for Stokes equations with a prescribed velocity boundary condition. In this paper, it has been shown that the pressure of the Stokes equation has a convergence order $O(\sqrt{h} |\log h| )$ in the $L^2$ norm while the velocity has an $O(h |\log h| )$ convergence order in the infinity norm in two-space dimensions. The proofs are based on splitting the singular source terms, discrete Green functions on finite lattices with homogeneous and Neumann boundary conditions, a new discovered simplest $L^2$ discrete delta function, and the convergence proof of the IB method for elliptic interface problems \cite{li:mathcom}. The conclusion in this paper can apply to problems with different boundary conditions as long as the problems are wellposed. The proof process also provides an efficient way to decouple the system into three Helmholtz/Poisson equations without affecting the order of convergence. A non-trivial numerical example is also provided to confirm the theoretical analysis and the simple new discrete delta function.

math.NA↗

arXiv2022

High order compact schemes for flux type BCs

In this paper new innovative fourth order compact schemes for Robin and Neumann boundary conditions have been developed for boundary value problems of elliptic PDEs in two and three dimensions. Different from traditional finite difference operator approach, which may not work for flux type of boundary conditions, carefully designed undetermined coefficient methods are utilized in developing high order compact (HOC) schemes. The new methods not only can be utilized to design HOC schemes for flux type of boundary conditions but can also be applied to general elliptic PDEs including Poisson, Helmholtz, diffusion-advection, and anisotropic equations with linear boundary conditions. In the new developed HOC methods, the coefficient matrices are generally M-matrices, which guarantee the discrete maximum principle for well-posed problems, so the convergence of the HOC methods. The developed HOC methods are versatile and can cover most of high order compact schemes in the literature. The HOC methods for Robin boundary conditions and for anisotropic diffusion and advection equations with Robin or even Dirichlet boundary conditions are likely the first ones that have ever been developed. With the help of pseudo-inverse, or SVD solutions, we have also observed that the developed HOC methods usually have smaller error constants compared with traditional HOC methods when applicable. Non-trivial examples with large wave numbers and oscillatory solutions are presented to confirm the performance of the new HOC methods.

math.NA↗

arXiv2022

Where to find lossless metals?

Hypothetical metals having optical absorption losses as low as those of the transparent insulators, if found, could revolutionize optoelectronics. We perform the first high-throughput search for lossless metals among all known inorganic materials in the databases of over 100,000 entries. The 381 candidates are identified -- having well-isolated partially-filled bands -- and are analyzed by defining the figures of merit and classifying their real-space conductive connectivity. The existing experimental evidence of most candidates being insulating, instead of conducting, is due to the limitation of current density functional theory in predicting narrow-band metals that are unstable against magnetism, structural distortion, or electron-electron interactions. We propose future research directions including conductive oxides, intercalating layered materials, and compressing these false-metal candidates under high pressures into eventual lossless metals.

cond-mat.mtrl-sci↗