arXiv subjects

Xiangyu Ding

Publications and source records attributed to Xiangyu Ding.

6 recordsLinked to original sources

arXiv2026

Porosity Effects on Cyclic Gas Invasion and Trapping in Deformable Porous Media

Fluid transport in deformable porous media is central to many biophysical and geophysical processes. While extensive studies exist, how porosity governs fluid behaviour in deformable systems during cyclic injection remains elusive. Here, we investigate gas-liquid multiphase flow in a quasi-2D Hele-Shaw cell packed with soft hydrogel particles at different initial porosities. Alternative gas and water injection experiments, combined with high-resolution imaging and continuous pressure monitoring, are used to quantify gas dynamics and pressure evolution. Results show that the gas entry pressure increases as porosity decreases, consistent with a Young-Laplace estimation based on effective pore-throat width. After entry, invasion shifts from cavity-dominated expansion in high porosity packings to localised pore invasion in low porosity packings, with a mixed cavity-fingering regime at intermediate porosity. Pressure fluctuations are linked to pore-scale gas escape and internal gas redistribution. Low porosity packings produce frequent small-amplitude pressure drops, whereas higher porosity packings produce more discrete pressure relaxations. Across cycles, the decreasing mean pressure suggests preferential-pathway reuse and reduced local capillary constraints. Residual gas saturation increases systematically with injection cycles and reaches higher terminal values as porosity decreases. Specific interfacial length increases as available pore space decreases and follows a power-law relationship with gas cluster size, with scaling exponent decreases as porosity decreases and cycling progresses. Together, these results demonstrate that gas trapping in deformable porous media depends on both initial packing structure and cyclically evolving gas-solid interactions. This study provides insights for interpreting porosity-dependent trapping and reinvasion during repeated gas injection.

cond-mat.soft↗

arXiv2026

A combinatorial proof for the positivity of the normalized Jacobi triple product tails

For $k\geq 1$, we prove that \[ [q^n z^s]J_k(z,q)\geq 0, \qquad (n\geq 0,\ s\in\mathbb Z) \] for the normalized Jacobi triple product tails \[ J_k(z,q) = \frac{ \sum_{j=k}^{\infty}(-1)^{j-k} q^{\binom{j+1}{2}}(z^{-j}+\cdots+z^j)} {(zq,q/z;q)_\infty}. \] This result not only implies Merca's stronger nonnegativity conjecture on truncated Jacobi triple product series in full generality, but also yields infinite families of linear inequalities for two-colored partitions and partitions with parts in the residue classes $\pm S \pmod{R}$. We present a combinatorial proof wherein a sign-reversing involution reduces the normalized Jacobi triple product tails to the invariant subsets according to the generalized minimal-excludant of partitions. Furthermore, by combing an invertible lift operator on Frobenius arms with Konan's size- and length-preserving bijection, an injection is constructed between the consecutive invariant subsets, which implies the coefficientwise positivity of the normalized Jacobi triple product tails.

math.CO↗

arXiv2026

Interlayer Error Calibration for Stacked Intelligent Metasurfaces:Modeling, Algorithms, and Future Perspectives

Stacked intelligent metasurfaces (SIMs) have recently emerged as a key enabler for realizing electromagnetic wave-domain signal processing in next-generation wireless networks. However, practical SIM implementations often suffer from noticeable mismatches between theoretical models and measured responses due to fabrication and assembly imperfections. This article systematically investigates the problem of interlayer error calibration in SIMs. We first classify representative modeling and hardware-induced imperfections. Then, we outline the major challenges in SIM calibration and further develop a general framework that integrates a calibration protocol with the relevant solution strategies. Moreover, we investigate the effectiveness of the multi-stage calibration approach in mitigating geometric deviations and improving the alignment between the calibrated and practical propagation coefficients. Finally, we elaborate on key research opportunities and practical challenges toward realizing physically consistent and hardware-compliant SIM implementations for future research.

eess.SP↗

arXiv2024

Proof of Merca's stronger conjecture on truncated Jacobi triple product series

In the study of theta series and partition functions, Andrews and Merca, Guo and Zeng independently conjectured that a truncated Jacobi triple product series has nonnegative coefficients. This conjecture was proved analytically by Mao and combinatorially by Yee. In 2021, Merca proposed a stronger version of the conjecture, that is, for positive integers $1\leq S<R$ with $k\geq 1$, the coefficient of $q^n$ in the theta series \[ \frac{(-1)^{k} \sum_{j=k}^{\infty}(-1)^j q^{R j(j+1) / 2}\left(q^{-Sj}-q^{( j+1) S}\right)}{\left(q^S, q^{R-S}; q^R\right)_{\infty}} \] is nonnegative. Recently, some very special cases of this conjecture have been proved and studied. For any given $R, S$ and $k$, we take $s=S/(S,R), r=R/(S,R)$ which are coprime, equivalently. In this paper, we confirm Merca's stronger conjecture for sufficiently large $n$. Furthermore, for given $r, s$ and $k$, we provide a systematic method to determine an integer $N(r, s, k)$ such that Merca's stronger conjecture holds for $ n\geq N(r,s,k) $. More precisely, we decompose the infinite product in the denominator of the above theta series into two parts, one of which can be interpreted as the generating function of partitions with certain restricted parts and the other is a nonmodular infinite product. We derive the general upper and lower bounds for the coefficients of these two parts by using the partition theoretical method and the circle method, respectively. Further multiplying the partition part by the numerator of the theta series and considering the convolution with the nonmodular infinite product, we obtain the constant $N(r,s,k)$ and confirm Merca's stronger conjecture when $n\geq N(r,s,k)$. Moreover, we also show that when $k$ is sufficiently large, this conjecture holds directly for any $n\geq 0$.

math.NT↗

arXiv2024

Truncated theta series from the Bailey lattice

In 2012, Andrews and Merca obtained a truncated version of Euler's pentagonal number theorem and showed the nonnegativity related to partition functions. Meanwhile, Andrews-Merca and Guo-Zeng independently conjectured that the truncated Jacobi triple product series has nonnegative coefficients, which has been confirmed analytically and also combinatorially. In 2022, Merca proposed a stronger version for this conjecture. In this paper, by applying Agarwal, Andrews and Bressoud's Bailey lattice, we derive a truncated version for the Jacobi triple product series with odd basis which reduces to the Andrews-Gordon identity as a special instance. As consequences, we obtain new truncated forms for Euler's pentagonal number theorem, Gauss'theta series on triangular numbers and square numbers, which lead to inequalities for certain partition functions. Moreover, by considering a truncated theta series involving $\ell$-regular partitions, we confirm a conjecture proposed by Ballantine and Merca about 6-regular partitions and show that Merca's stronger conjecture on truncated Jacobi triple product series holds when $R = 3S$ for $S \geq 1.$

math.CO↗

arXiv2023

Multiple Access Design for Symbiotic Radios: Facilitating Massive IoT Connections with Cellular Networks

Symbiotic radio (SR) has emerged as a spectrum- and energy-efficient paradigm to support massive Internet of Things (IoT) connections. Two multiple access schemes are proposed in this paper to facilitate the massive IoT connections using the cellular network based on the SR technique, namely, the simultaneous access (SA) scheme and the selection diversity access (SDA) scheme. In the SA scheme, the base station (BS) transmits information to the receiver while multiple IoT devices transmit their information simultaneously by passively backscattering the BS signal to the receiver, while in the SDA scheme, only the IoT device with the strongest backscatter link transmits information to the receiver. In both of the schemes, the receiver jointly decodes the information from the BS and the IoT devices. To evaluate the above two schemes, in this paper, we have derived the closed-form expressions of the ergodic rates and the outage probabilities for the cellular and IoT transmissions. Finally, numerical results are provided to verify the theoretical analysis and compare the two proposed multiple access schemes. When the number of IoT devices is small, the SDA scheme is more appealing since it can significantly reduce the computational complexity while achieving equivalent performance to the SA scheme. When the number of IoT devices is large, the SA scheme is preferable since it guarantees a significantly better rate performance and a lower outage probability.

cs.IT↗