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Yuan Cai

Publications and source records attributed to Yuan Cai.

At least 19 recordsLinked to original sources
arXiv2026

Global nonlinear stability of the plasma-vacuum free boundary problem for the 2D ideal incompressible MHD

We address the plasma-vacuum interface problem in the two dimensional space. The plasma region is governed by the ideal incompressible magnetohydrodynamic equations. The vacuum region is described by the pre-Maxwell dynamics, with the unknowns set to zero for simplicity. This is a free boundary problem of ideal Euler type equations. Under the strong horizontal magnetic field in the plasma region, we prove the global in time nonlinear stability of the two dimensional plasma-vacuum interface. The proof relies on understanding the interplay between the dynamics of the fluids inside the domain and those on the free interface, as well as the inherent structures of the problem.

math.AP↗
arXiv2026

Global nonlinear stability of the 2D incompressible viscous non-resistive MHD under sheared magnetic field

We study the two-dimensional incompressible viscous non-resistive magnetohydrodynamics in the periodic strip $\mathbb T\times\mathbb R$, subject to a smooth sheared background magnetic field $(\xi(x_2),0)^{\top}$, where $\xi(x_2)$ is bounded and away from zero. For sufficiently smooth perturbations satisfying even-odd symmetry, we prove global-in-time well-posedness and nonlinear stability in Lagrangian coordinates. The spatial inhomogeneity of the shear profile generates persistent linear contributions, most critically a nontrivial pressure term that precludes the uniform-in-time estimates. We straighten the integral curves of the initial magnetic field and construct a volume-preserving corrector. This geometric reduction transforms the intractable linear pressure into a quadratic nonlinearity. These structures yield the global energy bounds and the anisotropic algebraic decay rate for the system. This mechanism appears to provide the first rigorous framework for establishing global nonlinear stability for viscous non-resistive magnetohydrodynamics near the genuinely nonuniform sheared magnetic profile.

math.AP↗
arXiv2026

The Dynamics of Attention across Automated and Manual Driving Modes: A Driving Simulation Study

This study aims to explore the dynamics of driver attention to various zones, including the road, the central mirror, the embedded Human-Machine Interface (HMI), and the speedometer, across different driving modes in AVs. The integration of autonomous vehicles (AVs) into transportation systems has introduced critical safety concerns, particularly regarding driver re-engagement during mode transitions. Past accidents underscore the risks of overreliance on automation and highlight the need to understand dynamic attention allocation to support safety in autonomous driving. A high-fidelity driving simulation was conducted. Eye-tracking technology was used to measure fixation duration, fixation count, and time to first fixation across distinct driving modes (automated, manual, and transition), which were then used to assess how drivers allocated attention to various areas of interest (AOIs). Findings show that drivers' attention varies significantly across driving modes. In manual mode, attention consistently focuses on the road, while in automated mode, prolonged fixation on the embedded HMI was observed. During the handover and takeover phases, attention shifts dynamically between environmental and technological elements. The study reveals that driver attention allocation is mode-dependent. These findings inform the design of adaptive HMIs in AVs that align with drivers' attention patterns. By presenting relevant information according to the driving context, such systems can enhance driver-vehicle interaction, support effective transitions, and improve overall safety. Systematic analysis of visual attention dynamics across driving modes is gaining prominence, as it informs adaptive HMI designs and driver readiness interventions. The GLMM findings can be directly applied to the design of adaptive HMIs or driver training programs to enhance attention and improve safety.

cs.ET↗
arXiv2025

Small Alfv\'en Number Limit for the Global-in-time Solutions of Incompressible MHD Equations with General Initial Data

The small Alfv\'en number (denoted by $\varepsilon$) limit (one type of large parameter limits, i.e. singular limits) in magnetohydrodynamic (abbr. MHD) equations was first proposed by Klainerman--Majda in (Comm. Pure Appl. Math. 34: 481--524, 1981). Recently Ju--Wang--Xu mathematically verified that the \emph{local-in-time} solutions of three-dimensional (abbr. 3D) ideal (i.e. the absence of the dissipative terms) incompressible MHD equations with general initial data in $\mathbb{T}^3$ (i.e. a spatially periodic domain) tend to a solution of 2D ideal MHD equations in the distribution sense as $\varepsilon\to 0$ by Schochet's fast averaging method in (J. Differential Equations, 114: 476--512, 1994). In this paper, we revisit the small Alfv\'en number limit in $\mathbb{R}^n$ with $n=2$, $3$, and develop another approach, motivated by Cai--Lei's energy method in (Arch. Ration. Mech. Anal. 228: 969--993, 2018), to establish a new conclusion that the \emph{global-in-time} solutions of incompressible MHD equations (including the viscous resistive case) with general initial data converge to zero as $\varepsilon\to 0$ for any given time-space variable $(x,t)$ with $t>0$. In addition, we find that the large perturbation solutions and vanishing phenomenon of the nonlinear interactions also exist in the \emph{viscous resistive} MHD equations for small Alfv\'en numbers, and thus extend Bardos et al.'s results of the \emph{ideal} MHD equations in (Trans Am Math Soc 305: 175--191, 1988).

math.AP↗
arXiv2024

Global current-vortex sheets in the two-dimensional ideal incompressible MHD

The magnetohydrodynamic current-vortex sheet is a free boundary problem involving a moving free surface separating two plasma regions. We prove the global nonlinear stability of current-vortex sheet in the two dimensional ideal incompressible magnetohydrodynamics under the strong horizontal background magnetic field. This appears to be the first result on the global solutions of the free boundary problems for the ideal (inviscid and non-resistive) incompressible rotational fluids. The strong magnetic field plays a crucial role in the global in time stabilization effect. The proof relies on the understanding of the interplay between the dynamics of the fluids inside the domain and on the free interface, a design of multiple-level energy estimates with different weights, and the inherent structures of the problem.

math.AP↗
arXiv2024

Large data global existence for coupled massive-massless wave-type systems

We consider 3D Klein-Gordon-Zakharov (KGZ) and Dirac-Klein-Gordon (DKG) systems, where a common feature is that there exist both massless and massive fields in each system. We establish global existence and asymptotic behavior for both systems with a class of large data. More precisely, in the KGZ system, we allow the massless field to be large, while in the DKG system we allow the massive field to be large.

math.AP↗
arXiv2023

On the energy method for the global solutions to the three dimensional incompressible non-resistive MHD near equilibrium

We prove the global existence of the smooth solutions near equilibrium to the Cauchy problem of the incompressible non-resistive magnetohydrodynamic equations in the whole three dimensional space under some admissible condition. The result has been obtained by Xu and Zhang (SIAM J. Math. Anal. 47: 26--65, 2015) in anisotropic Besov space framework. In this paper, we provide a new proof based on the temporal weighted energy method.

math.AP↗
arXiv2021

Bridging the gap between atomically thin semiconductors and metal leads

Electrically interfacing atomically thin transition metal dichalcogenide semiconductors (TMDSCs) with metal leads is challenging because of undesired interface barriers, which have drastically constrained the electrical performance of TMDSC devices for exploring their unconventional physical properties and realizing potential electronic applications. Here we demonstrate a strategy to achieve nearly barrier-free electrical contacts with few-layer TMDSCs by engineering interfacial bonding distortion. The carrier-injection efficiency of such electrical junction is substantially increased with robust ohmic behaviors from room to cryogenic temperatures. The performance enhancements of TMDSC field-effect transistors are well reflected by the ultralow contact resistance (down to 90 Ohm um in MoS2, towards the quantum limit), the ultrahigh field-effect mobility (up to 358,000 cm2V-1s-1 in WSe2) and the prominent transport characteristics at cryogenic temperatures. This method also offers new possibilities of the local manipulation of structures and electronic properties for TMDSC device design.

cond-mat.mtrl-sci↗
arXiv2020

Uniform Bound of the Highest-order Energy of the 2D Incompressible Elastodynamics

This paper concerns the time growth of the highest-order energy of the systems of incompressible isotropic elastodynamics in two space dimensions. The global well-posedness of smooth solutions near equilibrium was first obtained by Lei [31] where the highest-order generalized energy may have certain growth in time. We improve above result and show that the highest-order generalized energy is uniformly bounded for all the time. The two dimensional incompressible elastodynamics is a system of nonlocal quasilinear wave equations where the unknowns decay as $\langle t\rangle^{-\frac12}$. This suggests the problem is supercritical in the sense that the decay rate is far from integrable. Surprisingly, we showed that in the highest-order energy estimate, the temporal decay can be strongly enhanced to be subcritical $\langle t \rangle^{-\frac54}$. The analysis is based on the ghost weight energy method by Alinhac [5], the inherent strong null structure by Lei [31] and the inherent div-curl structure of the system.

math.AP↗
arXiv2019

Vanishing Viscosity Limit for Incompressible Viscoelasticity in Two Dimensions

This paper studies the inviscid limit of the two-dimensional incompressible viscoelasticity, which is a system coupling a Navier-Stokes equation with a transport equation for the deformation tensor. The existence of global smooth solutions near the equilibrium with a fixed positive viscosity was known since the work of F. H. Lin, C. Liu, and P. Zhang in "On hydrodynamics of viscoelastic fluids". The inviscid case was solved recently by the second author Z. Lei. in "Global well-posedness of incompressible elastodynamics in two dimensions". While the latter was solely based on the techniques from the studies of hyperbolic equations, and hence the 2D problem is in general more challenge than that in higher dimensions, the former was relied crucially upon a dissipative mechanism. Indeed, after a symmetrization and a linearization around the equilibrium, the system of the incompressible viscoelasticity reduces to an incompressible system of damped wave equations for both the fluid velocity and the deformation tensor. These two approaches are not compatible. In this paper, we prove global existence of solutions, uniformly in both time $t \in [0, \infty)$ and viscosity $μ\geq 0$. This allows us to justify in particular the vanishing viscosity limit for all time. In order to overcome difficulties coming from the incompatibility between the purely hyperbolic limiting system and the systems with additional parabolic viscous perturbations, we introduce in this paper a rather robust method which may apply to a wide class of physical systems of similar nature. Roughly speaking, the method works in two dimensional case whenever the hyperbolic system satisfies intrinsically a "Strong Null Condition". For dimensions not less than three, the usual null condition is sufficient for this method to work.

math.AP↗
arXiv2017

Global Well-posedness for 2D Nonlinear Wave Equations without Compact Support

In the significant work of [2], Alinhac proved the global existence of small solutions for 2D quasilinear wave equations under the null conditions. The proof heavily relies on the fact that the initial data have compact support [22]. Whether this constraint can be removed or not is still unclear. In this paper, for fully nonlinear wave equations under the null conditions, we prove the global well-posedness for small initial data without compact support. Moreover, we apply our result to a class of quasilinear wave equations.

math.AP↗
arXiv2017

Isolation and Characterization of Few-layer Manganese Thiophosphite

This work reports an experimental study on an antiferromagnetic honeycomb lattice of MnPS$_3$ that couples the valley degree of freedom to a macroscopic antiferromagnetic order. The crystal structure of MnPS$_3$ is identified by high resolution scanning transmission electron microscopy. Layer dependent angle resolved polarized Raman fingerprints of the MnPS$_3$ crystal are obtained and the Raman peak at 383 cm$^{-1}$ exhibits 100% polarity. Temperature dependences of anisotropic magnetic susceptibility of MnPS$_3$ crystal are measured in superconducting quantum interference device. Magnetic parameters like effective magnetic moment, and exchange interaction are extracted from the mean field approximation mode. Ambipolar electronic transport channels in MnPS$_3$ are realized by the liquid gating technique. The conducting channel of MnPS$_3$ offers a unique platform for exploring the spin/valleytronics and magnetic orders in 2D limitation.

cond-mat.mes-hall↗
arXiv2017

Quantum Transport in Ambipolar Few-layer Black Phosphorus

Few-layer black phosphorus possesses unique electronic properties giving rise to distinct quantum phenomena and thus offers a fertile platform to explore the emergent correlation phenomena in low dimensions. A great progress has been demonstrated in improving the quality of hole-doped few-layer black phosphorus and its quantum transport studies, whereas the same achievements are rather modest for electron-doped few-layer black phosphorus. Here, we report the ambipolar quantum transport in few-layer black phosphorus exhibiting undoubtedly the quantum Hall effect for hole transport and showing clear signatures of the quantum Hall effect for electron transport. By bringing the spin-resolved Landau levels of the electron-doped black phosphorus to the coincidence, we measure the spin susceptibility $χ_s=m^\ast g^\ast=1.1\pm0.03$. This value is larger than for hole-doped black phosphorus and illustrates an energetically equidistant arrangement of spin-resolved Landau levels. Evidently, the n-type black phosphorus offers a unique platform with equidistant sequence of spin-up and spin-down states for exploring the quantum spintronic.

cond-mat.mes-hall↗
arXiv2017

Gate-tunable strong-weak localization transition in few-layer black phosphorus

Atomically thin black phosphorus (BP) field-effect transistors show strong-weak localization transition which is tunable through gate voltages. Hopping transports through charge impurity induced localized states are measured at low-carrier density regime. Variable-range hopping model is applied to simulate the charge carrier scattering behavior. In the high-carrier concentration regime, a negative magnetoresistance signals the weak localization effect. The extracted phase coherence length is power-law temperature dependent ($\sim T^{-0.48\pm0.03}$) and demonstrates electron-electron interactions in few-layer BP. The competition between the Strong localization length and phase coherence length is proposed and discussed based on the observed gate tunable strong-weak localization transition in few-layer BP.

cond-mat.mes-hall↗
arXiv2017

Odd-integer quantum Hall states and giant spin susceptibility in p-type few-layer WSe2

We fabricate high-mobility p-type few-layer WSe2 field-effect transistors and surprisingly observe a series of quantum Hall (QH) states following an unconventional sequence predominated by odd-integer states under a moderate strength magnetic field. By tilting the magnetic field, we discover Landau level (LL) crossing effects at ultra-low coincident angles, revealing that the Zeeman energy is about three times as large as the cyclotron energy near the valence band top at Γ valley. This result implies the significant roles played by the exchange interactions in p-type few-layer WSe2, in which itinerant or QH ferromagnetism likely occurs. Evidently, the Γ valley of few-layer WSe2 offers a unique platform with unusually heavy hole-carriers and a substantially enhanced g-factor for exploring strongly correlated phenomena.

cond-mat.mes-hall↗
arXiv2016

Charge Density Wave Phase Transition on the Surface of Electrostatically Doped Multilayer Graphene

We demonstrate that charge density wave (CDW) phase transition occurs on the surface of electronically doped multilayer graphene when the Fermi level approaches the M points (also known as van Hove singularities where the density of states diverge) in the Brillouin zone of graphene band structure. The occurrence of such CDW phase transitions are supported by both the electrical transport measurement and optical measurements in electrostatically doped multilayer graphene. The CDW transition is accompanied with the sudden change of graphene channel resistance at T$_m$= 100K, as well as the splitting of Raman G peak (1580 cm$^{-1}$). The splitting of Raman G peak indicats the lifting of in-plane optical phonon branch degeneracy and the non-degenerate phonon branches are correlated to the lattice reconstructions of graphene -- the CDW phase transition.

cond-mat.mes-hall↗