arXiv subjects

Jiayu Wan

Publications and source records attributed to Jiayu Wan.

6 recordsLinked to original sources

arXiv2025

Extending Azumaya algebras associated to arithmetic 2-bridge links

Let {\Gamma} be a finitely generated group and consider the set of all characters of representations of {\Gamma} into SL2(C). This set, denoted by X({\Gamma}), admits an algebraic structure and is called the character variety of {\Gamma}. When {\Gamma} is the fundamental group of a hyperbolic 3-manifold M, X({\Gamma}) turns out to be a powerful tool in the study of the geometry and topology of M. Chinburg-Reid-Stover have borrowed tools from algebraic and arithmetic geometry to understand algebraic and number-theoretic properties of the canonical curves of X({\Gamma}). In this paper, we will partly generalize their results to certain hyperbolic link complements, and prove that the associated canonical quaternion algebra will not extend to an Azumaya algebra over the canonical surfaces.

math.GT↗

arXiv2025

Asymptotic-preserving semi-Lagrangian discontinuous Galerkin schemes for the Boltzmann equation

In this work, we present an asymptotic-preserving semi-Lagrangian discontinuous Galerkin scheme for the Boltzmann equation that effectively handles multi-scale transport phenomena. The main challenge lies in designing appropriate moments update for penalization within the semi-Lagrangian framework. Inspired by [M. Ding, J. M. Qiu, and R. Shu, Multiscale Model. Simul. 21 (2023), no. 1, 143--167], the key ingredient is utilizing the Shu-Osher form of the scheme in the implicit-explicit Runge-Kutta (IMEX-RK) setting, which enables us to capture the correct limiting system by constructing an appropriate moments update procedure. Our theoretical analysis establishes accuracy order conditions for both the IMEX-RK time integration and the new moments update step. We also employ hypocoercivity techniques to establish stability for the linearized model. Numerical experiments for various test problems validate our proposed scheme's accuracy, asymptotic-preserving property, and robustness in various regimes, which demonstrates its effectiveness for multi-scale kinetic simulations.

math.NA↗

arXiv2025

Hypocoercivity for the Linear Semiconductor Boltzmann Equation with Boundaries and Uncertainties

In this paper, we establish hypocoercivity for the semiconductor Boltzmann equation with the presence of an external electrical potential under the Maxwell boundary condition. We will construct a modified entropy Lyapunov functional, which is proved to be equivalent to some weighted norm of the corresponding function space. We then show that the entropy functional dissipates along the solutions, and the exponential decay to the equilibrium state of the system follows by a Gronwall type inequality. We also generalize our arguments to situations where uncertainties in our model arise,and the hypocoercivity method we have established is adopted to analyze the regularity of the solutions along the random space.

math.AP↗

arXiv2025

Error estimates of asymptotic-preserving neural networks in approximating stochastic linearized Boltzmann equation

In this paper, we construct an asymptotic-preserving neural networks (APNNs) [21] for the linearized Boltzmann equation in the acoustic scaling and with uncertain parameters. Utilizing the micro-macro decomposition, we design the loss function based on the stochastic-Galerkin system conducted from the micro-macro equations. Rigorous analysis is provided to show the capability of neural networks in approximating solutions near the global Maxwellian. By employing hypocoercivity techniques, we demonstrate two key results: the existence of APNNs when the loss function approaches zero, and the convergence of the APNN approximated solution as the loss tends to zero, with the error exhibiting an exponential decay in time.

math.NA↗

arXiv2024

Machine learning-based moment closure model for the linear Boltzmann equation with uncertainties

The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving closed macroscopic moment systems from the Boltzmann equation remains a long-standing challenge due to the intrinsic non-closure of the moment hierarchy. In this paper, we propose a machine learning (ML)-based moment closure model for the linear Boltzmann equation, addressing both the deterministic and stochastic settings. Our approach leverages neural networks to learn the spatial gradient of the unclosed highest-order moment, enabling effective training through natural output normalization. For the deterministic problem, to ensure global hyperbolicity and stability, we derive and apply the constraints that enforce symmetrizable hyperbolicity of the system. For the stochastic problem, we adopt the generalized polynomial chaos (gPC)-based stochastic Galerkin method to discretize the random variables, resulting in a system for which the approach in the deterministic case can be used similarly. Several numerical experiments are shown to demonstrate the effectiveness and accuracy of our ML-based moment closure model for the linear Boltzmann equation with or without uncertainties.

math.NA↗

arXiv2014

Approaching the Limits of Transparency and Conductivity in Graphitic Materials through Lithium Intercalation

Various bandstructure engineering methods have been studied to improve the performance of graphitic transparent conductors; however none demonstrated an increase of optical transmittance in the visible range. Here we measure in situ optical transmittance spectra and electrical transport properties of ultrathin-graphite (3-60 graphene layers) simultaneously via electrochemical lithiation/delithiation. Upon intercalation we observe an increase of both optical transmittance (up to twofold) and electrical conductivity (up to two orders of magnitude), strikingly different from other materials. Transmission as high as 91.7% with a sheet resistance of 3.0 Ω per square is achieved for 19-layer LiC6, which corresponds to a figure of merit σ_dc/σ_opt = 1400, significantly higher than any other continuous transparent electrodes. The unconventional modification of ultrathin-graphite optoelectronic properties is explained by the suppression of interband optical transitions and a small intraband Drude conductivity near the interband edge. Our techniques enable the investigation of other aspects of intercalation in nanostructures.

cond-mat.mtrl-sci↗