arXiv subjects

Yueli Yu

Publications and source records attributed to Yueli Yu.

5 recordsLinked to original sources

arXiv2025

Phase Field Study of Exchange Coupling of Hard/Soft Ferrite on Magnetic Permeability

Effective modulation of magnetic permeability plays a vital role in the development of high-performance inductors. Here, phase-field simulations of hard/soft ferrite composites (BaM/NiZn) clarify how exchange coupling and microstructure impact magnetic permeability. We show that particle size, volume fraction, and orientation of the hard phase can effectively control the transition from collinear to non-collinear coupling, with a critical exchange size r_cr approximately 12 nm. Increasing the hard-phase fraction deepens the anisotropy energy well and monotonically suppresses permeability. In contrast, rotating the BaM easy axis to 90 degrees relative to the applied field produces a strong enhancement: at a 10 nm radius and eta = 0.1 volume fraction, the effective permeability can be more than 30 times larger than in the parallel configuration and then saturates for larger particles. This study establishes a microstructure-permeability-based physical framework for designing hard/soft magnetic composite systems.

cond-mat.mtrl-sci↗

arXiv2025

Multifractal analysis of maximal product of consecutive partial quotients in continued fractions

Let $[a_1(x), a_2(x), \ldots, a_n(x), \ldots]$ be the continued fraction expansion of an irrational number $x\in (0,1)$. We study the growth rate of the maximal product of consecutive partial quotients among the first $n$ terms, defined by $L_n(x)=\max_{1\leq i\leq n}\{a_i(x)a_{i+1}(x)\}$, from the viewpoint of multifractal analysis. More precisely, we determine the Hausdorff dimension of the level set \[L(\varphi):=\left\{x\in (0,1):\lim_{n\to \infty}\frac{L_n(x)}{\varphi(n)}=1\right\},\] where $\varphi:\mathbb{R^+}\to\mathbb{R^+}$ is an increasing function such that $\log \varphi$ is a regularly increasing function with index $\rho$. We show that there exists a jump of the Hausdorff dimension of $L(\varphi)$ when $\rho=1/2$. We also construct uncountably many discontinuous functions $\psi$ that cause the Hausdorff dimension of $L(\psi)$ to transition continuously from 1 to 1/2, filling the gap when $\rho=1/2$.

math.NT↗

arXiv2024

Multifractal analysis of the growth rate of digits in Schneider's $p$-adic continued fraction dynamical system

Let $\mathbb{Z}_p$ be the ring of $p$-adic integers and $a_n(x)$ be the $n$-th digit of Schneider's $p$-adic continued fraction of $x\in p\mathbb{Z}_p$. We study the growth rate of the digits $\{a_n(x)\}_{n\geq1}$ from the viewpoint of multifractal analysis. The Hausdorff dimension of the set \[E_{\sup}(\psi)=\Big\{x\in p\mathbb{Z}_p:\ \limsup\limits_{n\to\infty}\frac{a_n(x)}{\psi(n)}=1\Big\}\] is completely determined for any $\psi:\mathbb{N}\to\mathbb{R}^{+}$ satisfying $\psi(n)\to \infty$ as $n\to\infty$. As an application, we also calculate the Hausdorff dimension of the intersection sets \[E^{\sup}_{\inf}(\psi,\alpha_1,\alpha_2)=\left\{x\in p\mathbb{Z}_p:\liminf_{n\rightarrow\infty}\dfrac{a_n(x)}{\psi(n)}=\alpha_1,~\limsup_{n\rightarrow\infty}\dfrac{a_n(x)}{\psi(n)}=\alpha_2\right\}\] for the above function $\psi$ and $0\leq\alpha_1<\alpha_2\leq\infty$.

math.NT↗

arXiv2021

Limit theorems for sums of products of consecutive partial quotients of continued fractions

Let $[a_1(x),a_2(x),\ldots, a_n(x), \ldots]$ be the continued fraction expansion of an irrational number $x\in (0, 1)$. The study of the growth rate of the product of consecutive partial quotients $a_n(x)a_{n+1}(x)$ is associated with the improvements to Dirichlet's theorem (1842). We establish both the weak and strong laws of large numbers for the partial sums $S_n(x)= \sum_{i=1}^n a_i(x)a_{i+1}(x)$ as well as, from a multifractal analysis point of view, investigate its increasing rate. Specifically, we prove the following results: \medskip \begin{itemize} \item For any $\epsilon>0$, the Lebesgue measure of the set $$\left\{x\in(0, 1): \left|\frac{ S_n(x)}{n\log^2 n}-\frac1{2\log2}\right|\geq \epsilon\right\}$$tends to zero as $n$ to infinity. \item For Lebesgue almost all $x\in (0,1)$, $$\lim\limits_{n\rightarrow \infty} \frac{S_n(x)-\max\limits_{1\leq i \leq n}a_i(x)a_{i+1}(x)}{n\log^2n}=\frac{1}{2\log2}.$$ \item The Hausdorff dimension of the set $$E(\phi):=\left\{x\in(0,1):\lim\limits_{n\rightarrow \infty}\frac{S_n(x)}{\phi(n)}=1\right\}$$ is determined for a range of increasing functions $\phi: \mathbb N\to \mathbb R^+$. \end{itemize}

math.NT↗

arXiv2020

Metrical properties for continued fractions of formal Laurent series

Motivated by recent developments in the metrical theory of continued fractions for real numbers concerning the growth of consecutive partial quotients, we consider its analogue over the field of formal Laurent series. Let $A_n(x)$ be the $n$th partial quotient of the continued fraction expansion of $x$ in the field of formal Laurent series. We consider the sets of $x$ such that $\deg A_{n+1}(x)+\cdots+\deg A_{n+k}(x)~\ge~\Phi(n)$ holds for infinitely many $n$ and for all $n$ respectively, where $k\ge1$ is an integer and $\Phi(n)$ is a positive function defined on $\mathbb{N}$. We determine the size of these sets in terms of Haar measure and Hausdorff dimension.

math.NT↗