arXiv subjects

Yichen Fu

Publications and source records attributed to Yichen Fu.

15 recordsLinked to original sources

arXiv2026

Fast and Provable Nonconvex Robust Matrix Completion

We study the robust matrix completion (RMC) problem subject to both sparse outliers and stochastic noise. A non-convex method termed Accelerated Robust Matrix Completion (ARMC) is proposed, which accelerates a prior non-convex approach by incorporating an explicit subspace projection step into the low-rank update, leading to significantly improved computational efficiency. Through a delicate analysis based on the leave-one-out technique, the entrywise linear convergence guarantee of ARMC has been established. Notably, the derived bounds for sample complexity and outlier sparsity improve upon existing guarantees of the convex relaxation approach that also accounts for both sparse outliers and stochastic noise. Moreover, numerical experiments on synthetic and real data show that ARMC is superior to existing non-convex RMC methods.

cs.IT↗

arXiv2025

Statistical inference of anomalous thermal transport with uncertainty quantification for interpretive 2-D SOL models

The critical task of inferring anomalous cross-field transport coefficients is addressed in simulations of boundary plasmas with fluid models. A workflow for parameter inference in the UEDGE fluid code is developed using Bayesian optimization with parallelized sampling and integrated uncertainty quantification. In this workflow, transport coefficients are inferred by maximizing their posterior probability distribution, which is generally multidimensional and non-Gaussian. Uncertainty quantification is integrated throughout the optimization within the Bayesian framework that combines diagnostic uncertainties and model limitations. As a concrete example, we infer the anomalous electron thermal diffusivity $\chi_\perp$ from an interpretive 2-D model describing electron heat transport in the conduction-limited region with radiative power loss. The workflow is first benchmarked against synthetic data and then tested on H-, L-, and I-mode discharges to match their midplane temperature and divertor heat flux profiles. We demonstrate that the workflow efficiently infers diffusivity and its associated uncertainty, generating 2-D profiles that match 1-D measurements. Future efforts will focus on incorporating more complicated fluid models and analyzing transport coefficients inferred from a large database of experimental results.

physics.plasm-ph↗

arXiv2025

Wave Topology in Hall MHD

Hall Magnetohydrodynamics (HMHD) extends ideal MHD by incorporating the Hall effect via the induction equation, making it more accurate for describing plasma behavior at length scales below the ion skin depth. Despite its importance, a comprehensive description of the eigenmodes in HMHD has been lacking. In this work, we derive the complete spectrum and eigenvectors of HMHD waves and identify their underlying topological structure. We prove that the HMHD wave spectrum is homotopic to that of ideal MHD, consisting of three distinct branches: the slow magnetosonic-Hall waves, the shear Alfv\'en-Hall waves, and the fast magnetosonic-Hall waves, which continuously reduce to their ideal MHD counterparts in the limit of vanishing Hall parameter. Contrary to a recent claim, we find that HMHD does not admit any additional wave branches beyond those in ideal MHD. The key qualitative difference lies in the topological nature of the HMHD wave structure: it exhibits nontrivial topology characterized by a Weyl point-an isolated eigenmode degeneracy point-and associated nonzero Chern numbers of the eigenmode bundles over a 2-sphere in k-space surrounding the Weyl point.

physics.plasm-ph↗

arXiv2025

An Underwater, Fault-Tolerant, Laser-Aided Robotic Multi-Modal Dense SLAM System for Continuous Underwater In-Situ Observation

Existing underwater SLAM systems are difficult to work effectively in texture-sparse and geometrically degraded underwater environments, resulting in intermittent tracking and sparse mapping. Therefore, we present Water-DSLAM, a novel laser-aided multi-sensor fusion system that can achieve uninterrupted, fault-tolerant dense SLAM capable of continuous in-situ observation in diverse complex underwater scenarios through three key innovations: Firstly, we develop Water-Scanner, a multi-sensor fusion robotic platform featuring a self-designed Underwater Binocular Structured Light (UBSL) module that enables high-precision 3D perception. Secondly, we propose a fault-tolerant triple-subsystem architecture combining: 1) DP-INS (DVL- and Pressure-aided Inertial Navigation System): fusing inertial measurement unit, doppler velocity log, and pressure sensor based Error-State Kalman Filter (ESKF) to provide high-frequency absolute odometry 2) Water-UBSL: a novel Iterated ESKF (IESKF)-based tight coupling between UBSL and DP-INS to mitigate UBSL's degeneration issues 3) Water-Stereo: a fusion of DP-INS and stereo camera for accurate initialization and tracking. Thirdly, we introduce a multi-modal factor graph back-end that dynamically fuses heterogeneous sensor data. The proposed multi-sensor factor graph maintenance strategy efficiently addresses issues caused by asynchronous sensor frequencies and partial data loss. Experimental results demonstrate Water-DSLAM achieves superior robustness (0.039 m trajectory RMSE and 100\% continuity ratio during partial sensor dropout) and dense mapping (6922.4 points/m^3 in 750 m^3 water volume, approximately 10 times denser than existing methods) in various challenging environments, including pools, dark underwater scenes, 16-meter-deep sinkholes, and field rivers. Our project is available at https://water-scanner.github.io/.

cs.RO↗

arXiv2024

Energy-momentum-conserving stochastic differential equations and algorithms for nonlinear Landau-Fokker-Planck equation

Coulomb collision is a fundamental diffusion process in plasmas that can be described by the Landau-Fokker-Planck (LFP) equation or the stochastic differential equation (SDE). While energy and momentum are conserved exactly in the LFP equation, they are conserved only on average by the conventional corresponding SDEs, suggesting that the underlying stochastic process may not be well-defined by such SDEs. In this study, we derive new SDEs with exact energy-momentum conservation for the Coulomb collision by factorizing the collective effect of field particles into individual particles and enforcing Newton's third law. These SDEs, when interpreted in the Stratonovich sense, have a particularly simple form that represents pure diffusion between particles without drag. Numerical algorithms that preserve discrete conservation laws are developed and benchmarked in various relaxation processes. Techniques to reduce computational complexity are also discussed.

physics.plasm-ph↗

arXiv2024

Moment-preserving Monte-Carlo Coulomb collision method for particle codes

Binary-pairing Monte-Carlo methods are widely used in particle-in-cell codes to capture effects of small angle Coulomb collisions. These methods preserve momentum and energy exactly when the simulation particles have equal weights. However, when the interacting particles are of varying weight, these physical conservation laws are only preserved on average. Here, we 1) extend these methods to weighted particles such that the scattering physics is correct on average, and 2) describe a new method for adjusting the particle velocities post scatter to restore exact conservation of momentum and energy. The efficacy of the model is illustrated with various test problems.

physics.comp-ph↗

arXiv2023

Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media

In classical Hermitian continuous media, the spectral-flow index of topological modes is linked to the bulk topology via index theorem. However, the interface between two bulks is usually non-Hermitian due to the inhomogeneities of system parameters. We show that the connection between topological modes and bulk topology still exists despite the non-Hermiticity at the interface if the system is endowed with PT symmetry. The theoretical framework developed is applied to the Hall magnetohydrodynamic model to identify a topological mode called topological Alfv\'{e}n-sound wave in magnetized plasmas.

physics.plasm-ph↗

arXiv2022

Spin Hall effect of radiofrequency waves in magnetized plasmas

In inhomogeneous media, electromagnetic-wave rays deviate from the trajectories predicted by the leading-order geometrical optics. This effect, called the spin Hall effect of light, is typically neglected in ray-tracing codes used for modeling waves in plasmas. Here, we demonstrate that the spin Hall effect can be significant for radiofrequency waves in toroidal magnetized plasmas whose parameters are in the ballpark of those used in fusion experiments. For example, an electron-cyclotron wave beam can deviate by as large as ten wavelengths ($\sim 0.1\,\text{m}$) relative to the lowest-order ray trajectory in the poloidal direction. We calculate this displacement using gauge-invariant ray equations of extended geometrical optics, and we also compare our theoretical predictions with full-wave simulations.

physics.plasm-ph↗

arXiv2022

Topological Langmuir-cyclotron wave

A theoretical framework is developed to describe the Topological Langmuir-Cyclotron Wave (TLCW), a recently identified topological surface excitation in magnetized plasmas. As a topological wave, the TLCW propagates unidirectionally without scattering in complex boundaries. The TLCW is studied theoretically as a spectral flow of the Hamiltonian Pseudo-Differential-Operator (PDO) $\hat{H}$ for waves in an inhomogeneous plasma. The semi-classical parameter of the Weyl quantization for plasma waves is identified to be the ratio between electron gyro-radius and the inhomogeneity scale length of the system. Hermitian eigenmode bundles of the bulk Hamiltonian symbol H for plasma waves are formally defined. Because momentum space in classical continuous media is contractible in general, the topology of the eigenmode bundles over momentum space is trivial. This is in stark contrast to condensed matters. Nontrivial topology of the eigenmode bundles in classical continuous media only exists over phase space. A boundary isomorphism theorem is established to facilitate the calculation of Chern numbers of eigenmode bundles over non-contractible manifolds in phase space. It also defines a topological charge of an isolated Weyl point in phase space without adopting any connection. Using these algebraic topological techniques and an index theorem formulated by Faure, it is rigorously proven that the nontrivial topology at the Weyl point of the Langmuir wave-cyclotron wave resonance generates the TLCW as a spectral flow. It is shown that the TLCW can be faithfully modeled by a tilted Dirac cone in phase space. An analytical solution of the entire spectrum of the PDO of a generic tilted phase space Dirac cone, including its spectral flow, is given. The spectral flow index of a tilted Dirac cone is one, and its mode structure is a shifted Gaussian function.

physics.plasm-ph↗

arXiv2022

The dispersion and propagation of topological Langmuir-cyclotron waves in cold magnetized plasmas

Topological Langmuir-Cyclotron Wave (TLCW) is a recently identified topological surface excitation in magnetized plasmas. We show that TLCW originates from the topological phase transition at the Langmuir wave-cyclotron wave resonance. By isofrequency surface analysis and 2D and 3D time-dependent simulations, we demonstrate that the TLCW can propagate robustly along complex phase transition interfaces in a unidirectional manner and without scattering. Because of these desirable features, the TLCW could be explored as an effective mechanism to drive current and flow in magnetized plasmas. The analysis also establishes a close connection between the newly instituted topological phase classification of plasmas and the classical CMA diagram of plasma waves.

physics.plasm-ph↗

arXiv2020

Topological phases and bulk-edge correspondence of magnetized cold plasmas

Plasmas have been recently studied as topological materials. However, a comprehensive picture of topological phases and topological phase transitions in cold magnetized plasmas is still missing. Here we systematically map out all the topological phases and establish the bulk-edge correspondence in cold magnetized plasmas. We find that for the linear eigenmodes, there are 10 topological phases in the parameter space of density $n$, magnetic field $B$, and parallel wavenumber $k_{z}$, separated by the surfaces of Langmuir wave-L wave resonance, Langmuir wave-cyclotron wave resonance, and zero magnetic field. For fixed $B$ and $k_{z}$, only the phase transition at the Langmuir wave-cyclotron wave resonance corresponds to edge modes. A sufficient and necessary condition for the existence of this type of edge modes is given and verified by numerical solutions. We demonstrate that edge modes exist not only on a plasma-vacuum interface but also on more general plasma-plasma interfaces. This finding broadens the possible applications of these exotic excitations in space and laboratory plasmas.

physics.plasm-ph↗

arXiv2020

An Explicitly Solvable Energy-Conserving Algorithm for Pitch-Angle Scattering in Magnetized Plasmas

We develop an Explicitly Solvable Energy-Conserving (ESEC) algorithm for the Stochastic Differential Equation (SDE) describing the pitch-angle scattering process in magnetized plasmas. The Cayley transform is used to calculate both the deterministic gyromotion and stochastic scattering, affording the algorithm to be explicitly solvable and exactly energy conserving. An unusual property of the SDE for pitch-angle scattering is that its coefficients diverge at the zero velocity and do not satisfy the global Lipschitz condition. Consequently, when standard numerical methods, such as the Euler-Maruyama (EM), are applied, numerical convergence is difficult to establish. For the proposed ESEC algorithm, its energy-preserving property enables us to overcome this obstacle. We rigorously prove that the ESEC algorithm is order 1/2 strongly convergent. This result is confirmed by detailed numerical studies. For the case of pitch-angle scattering in a magnetized plasma with a constant magnetic field, the numerical solution is benchmarked against the analytical solution, and excellent agreements are found.

physics.plasm-ph↗

arXiv2020

Spontaneous and explicit parity-time-symmetry breaking in drift wave instabilities

A method of Parity-Time (PT)-symmetry analysis is introduced to study the high dimensional, complicated parameter space of drift wave instabilities. We show that spontaneous PT-symmetry breaking leads to the Ion Temperature Gradient (ITG) instability of drift waves, and the collisional instability is the result of explicit PT-symmetry breaking. A new unstable drift wave induced by finite collisionality is identified. It is also found that gradients of ion temperature and density can destabilize the ion cyclotron waves when PT symmetry is explicitly broken by a finite collisionality.

physics.plasm-ph↗

arXiv2020

Simulating Pitch Angle Scattering Using An Explicitly Solvable Energy Conserving Algorithm

Particle distribution functions evolving under the Lorentz operator can be simulated with the Langevin equation for pitch angle scattering. This approach is frequently used in particle based Monte-Carlo simulations of plasma collisions, among others. However, most numerical treatments do not guarantee energy conservation, which may lead to unphysical artifacts such as numerical heating and spectra distortions. We present a novel structure-preserving numerical algorithm for the Langevin equation for pitch angle scattering. Similar to the well-known Boris algorithm, the proposed numerical scheme takes advantage of the structure-preserving properties of the Cayley transform when calculating the velocity-space rotations. The resulting algorithm is explicitly solvable, while preserving the norm of velocities down to machine precision. We demonstrate that the method has the same order of numerical convergence as the traditional stochastic Euler-Maruyama method. The numerical scheme is benchmarked by simulating the pitch angle scattering of a particle beam, and comparing with the analytical solution. Benchmark results show excellent agreement with theoretical predictions, showcasing the remarkable long time accuracy of the proposed algorithm.

physics.comp-ph↗

arXiv2020

The Physics of Spontaneous Parity-Time Symmetry Breaking in the Kelvin-Helmholtz Instability

We show that the dynamics, in particular the Kelvin-Helmholtz (KH) instability, of an inviscid fluid with velocity shear admits Parity-Time (PT) symmetry, which provides a physical explanation to the well-known observation that the spectrum of the perturbation eigenmodes of the system is symmetric with respect to the real axis. It is found that the KH instability is triggered when and only when the PT symmetry is spontaneously broken. The analysis of PT symmetry also reveals that the relative phase between parallel velocity and pressure perturbations needs to be locked at $\pi/2$ when the instability is suppressed.

physics.plasm-ph↗