arXiv subjects

Xiaodi Zhang

Publications and source records attributed to Xiaodi Zhang.

9 recordsLinked to original sources

arXiv2026

Field-driven nonlinear metasurface: self-adaptive transition between high-selectivity transmission and broadband shielding

The escalating complexity of electromagnetic (EM) environment is posing a significant challenge to the reliability of modern electronic information systems. To address the need for the spatial EM safety of electronic devices, we present a field-driven nonlinear metasurface (NMS) that enables effective protection against out-of-band interference and in-band high-intensity radiation. By constructing a reconfigurable hybrid coupling topology and mapping it to the metasurface geometry, the proposed NMS achieves a self-adaptive transition between its transmission and shielding mode depending on the incident power. The experimental results are in good agreement with theoretical analysis and full-wave simulation. We obtain a highly selective passband with roll-off rate larger than 20.6dB/GHz and a broadband shielding with shielding effectiveness exceeding 23.6dB and 60% bandwidth, demonstrating a significantly enhanced performance relative to the literature. Our findings establish a promising route toward comprehensive EM protection on radio frequency front-end systems.

physics.optics↗

arXiv2026

Time-Varying Directed Interactions in Functional Brain Networks: Modeling and Validation

Understanding the dynamic nature of brain connectivity is critical for elucidating neural processing, behavior, and brain disorders. Traditional approaches such as sliding-window correlation (SWC) characterize time-varying undirected associations but do not resolve directional interactions, limiting inference about time-resolved information flow in brain networks. We introduce sliding-window prediction correlation (SWpC), which embeds a directional linear time-invariant (LTI) model within each sliding window to estimate time-varying directed functional connectivity (FC). SWpC yields two complementary descriptors of directed interactions: a strength measure (prediction correlation) and a duration measure (window-wise duration of information transfer). Using concurrent local field potential (LFP) and fMRI BOLD recordings from rat somatosensory cortices, we demonstrate stable directionality estimates in both LFP band-limited power and BOLD. Using Human Connectome Project (HCP) motor task fMRI, SWpC detects significant task-evoked changes in directed FC strength and duration and shows higher sensitivity than SWC for identifying task-evoked connectivity differences. Finally, in post-concussion vestibular dysfunction (PCVD), SWpC reveals reproducible vestibular-multisensory brain-state shifts and improves healthy-control vs subacute patient (HC-ST) discrimination using state-derived features. Together, these results show that SWpC provides biologically interpretable, time-resolved directed connectivity patterns across multimodal validation and clinical application settings, supporting both basic and translational neuroscience.

q-bio.NC↗

arXiv2025

Reformulated formulation and efficient fully discrete finite element method for a conductive ferrofluid model

In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear, and multiphysics system efficiently, we develop a decoupled, linear, second-order in time, and unconditionally energy stable finite element scheme. We incorporate several distinct numerical techniques, including reformulations of the equations and a scalar auxiliary variable to handle the coupled nonlinear terms,a symmetric implicit-explicit treatment for the symmetric positive definite nonlinearity, and stable finite element approximations. We also prove that the numerical scheme is provably uniquely solvable and unconditionally energy stable rigorously. A series of numerical examples are presented to illustrate the accuracy and performance of our scheme.

math.NA↗

arXiv2023

Sharp-interface limits of the diffuse interface model for two-phase inductionless magnetohydrodynamic fluids

In this paper, we propose and analyze a diffuse interface model for inductionless magnetohydrodynamic fluids. The model couples a convective Cahn-Hilliard equation for the evolution of the interface, the Navier-Stokes system for fluid flow and the possion quation for electrostatics. The model is derived from Onsager's variational principle and conservation laws systematically. We perform formally matched asymptotic expansions and develop several sharp interface models in the limit when the interfacial thickness tends to zero. It is shown that the sharp interface limit of the models are the standard incompressible inductionless magnetohydrodynamic equations coupled with several different interface conditions for different choice of the mobilities. Numerical results verify the convergence of the diffuse interface model with different mobilitiess.

math.AP↗

arXiv2023

Stability and error analysis of the SAV schemes for the inductionless MHD equations

In this paper, we consider numerical approximations for solving the inductionless magnetohydrodynamic (MHD) equations. By utilizing the scalar auxiliary variable (SAV) approach for dealing with the convective and coupling terms, we propose some first- and second-order schemes for this system. These schemes are linear, decoupled, unconditionally energy stable, and only require solving a sequence of differential equations with constant coefficients at each time step. We further derive a rigorous error analysis for the first-order scheme, establishing optimal convergence rates for the velocity, pressure, current density and electric potential in the two-dimensional case. Numerical examples are presented to verify the theoretical findings and show the performances of the schemes.

math.NA↗

arXiv2022

Unconditional stability and error analysis of an Euler IMEX-SAV scheme for the micropolar Navier-Stokes equations

In this paper, we consider numerical approximations for solving the micropolar Navier-Stokes (MNS) equations, that couples the Navier-Stokes equations and the angular momentum equation together. By combining the scalar auxiliary variable (SAV) approach for the convective terms and some subtle implicit-explicit (IMEX) treatments for the coupling terms, we propose a decoupled, linear and unconditionally energy stable scheme for this system. We further derive rigorous error estimates for the velocity, pressure and angular velocity in two dimensions without any condition on the time step. Numerical examples are presented to verify the theoretical findings and show the performances of the scheme.

math.NA↗

arXiv2022

A uniform preconditioner for a Newton algorithm for total-variation minimization and minimum-surface problems

Solution methods for the nonlinear partial differential equation of the Rudin-Osher-Fatemi (ROF) and minimum-surface models are fundamental for many modern applications. Many efficient algorithms have been proposed. First order methods are common. They are popular due to their simplicity and easy implementation. Some second order Newton-type iterative methods have been proposed like Chan-Golub-Mulet method. In this paper, we propose a new Newton-Krylov solver for primal-dual finite element discretization of the ROF model. The method is so simple that we just need to use some diagonal preconditioners during the iterations. Theoretically, the proposed preconditioners are further proved to be robust and optimal with respect to the mesh size, the penalization parameter, the regularization parameter, and the iterative step, essentially it is a parameter independent preconditioner. We first discretize the primal-dual system by using mixed finite element methods, and then linearize the discrete system by Newton\textquoteright s method. Exploiting the well-posedness of the linearized problem on appropriate Sobolev spaces equipped with proper norms, we propose block diagonal preconditioners for the corresponding system solved with the minimum residual method. Numerical results are presented to support the theoretical results.

math.NA↗

arXiv2022

Functional Connectivity of the Brain Across Rodents and Humans

Resting-state functional magnetic resonance imaging (rs-fMRI), which measures the spontaneous fluctuations in the blood oxygen level-dependent (BOLD) signal, is increasingly utilized for the investigation of the brain's physiological and pathological functional activity. Rodents, as a typical animal model in neuroscience, play an important role in the studies that examine the neuronal processes that underpin the spontaneous fluctuations in the BOLD signal and the functional connectivity that results. Translating this knowledge from rodents to humans requires a basic knowledge of the similarities and differences across species in terms of both the BOLD signal fluctuations and the resulting functional connectivity. This review begins by examining similarities and differences in anatomical features, acquisition parameters, and preprocessing techniques, as factors that contribute to functional connectivity. Homologous functional networks are compared across species, and aspects of the BOLD fluctuations such as the topography of the global signal and the relationship between structural and functional connectivity are examined. Time-varying features of functional connectivity, obtained by sliding windowed approaches, quasi-periodic patterns, and coactivation patterns, are compared across species. Applications demonstrating the use of rs-fMRI as a translational tool for cross-species analysis are discussed, with an emphasis on neurological and psychiatric disorders. Finally, open questions are presented to encapsulate the future direction of the field.

q-bio.NC↗

arXiv2022

Decoupled, linear, unconditionally energy stable and charge-conservative finite element method for a inductionless magnetohydrodynamic phase-field model

In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and Poisson equation. We propose a linear and decoupled finite element method to solve this highly nonlinear and multi-physics system. For the time variable, the discretization is a combination of first-order Euler semi-implicit scheme, several first-order stabilization terms and implicit-explicit treatments for coupling terms. For the space variables, we adopt the finite element discretization, especially, we approximate the current density and electric potential by inf-sup stable face-volume mixed finite element pairs. With these techniques, the scheme only involves a sequence of decoupled linear equations to solve at each time step. We show that the scheme is provably mass-conservative, charge-conservative and unconditionally energy stable. Numerical experiments are performed to illustrate the features, accuracy and efficiency of the proposed scheme.

math.NA↗