arXiv subjects

Yufei Bai

Publications and source records attributed to Yufei Bai.

3 recordsLinked to original sources

arXiv2026

The irrationality measure of {\pi} is at most 7.101862832357

We introduce two independent numerator exponents into the Zeilberger--Zudilin integral and specialize them to \[ A_1=A_2=\frac{1857}{2785}. \] The resulting integer linear forms in $1$ and $\pi$ prove \[ \mu(\pi)<7.101862832357. \] This lowers the Zeilberger--Zudilin upper bound $7.103205334137\ldots$ by more than $0.001342501780$; the difference between the unrounded bounds is $0.0013425017806509\ldots$, approximately $0.01890\%$. The same parameter point is a strict two-dimensional local minimizer of the explicit auxiliary upper-bound function in its admissible arithmetic chamber. This is a local statement about that function, not a claim that the point is a global optimizer among all constructions.

math.NT↗

arXiv2026

The irrationality measure of arctan1/2 is at most 8.585166

This paper establishes a new upper bound for the irrationality measure of arctan(1/2), namely 8.585166... Following the strategy and proof techniques of Zudilin and Zeilberger (who improved the bound for pi), we use a family of complex contour integrals with symmetric integrands. The integrality and divisibility of the partial-fraction coefficients are derived via p-adic valuations and a specially defined prime set P_n. Combined with saddle-point asymptotics, the growth rates of the integral sequence and its rational/logarithmic components yield the desired irrationality measure.

math.NT↗

arXiv2025

Maze-Bubble Pattern Magnetic Domain Simulation Based on the Lengyel-Epstein Model

This study is based on the Lengyel-Epstein (LE) model, governed by a system of nonlinear partial differential equations, to simulate the maze-bubble pattern magnetic domains in magnetic thin films with perpendicular magnetic anisotropy (PMA). Through numerical simulations, we successfully reproduce the maze, bubble, and intermediate-state magnetic domains observed in PMA multilayer films under the influence of material thickness and external magnetic fields. The topological structures of the magnetic domains shown in the simulation closely resemble those observed under a microscope, demonstrating the effectiveness of the LE model in simulating changes in the magnetic domain topology of magnetic thin films. This study also innovatively applies the concept of reaction-diffusion, commonly used in biochemistry, by drawing an analogy to electromagnetism. This approach holds significant implications for the study of magnetic domains.

cond-mat.mtrl-sci↗