arXiv subjects

Liyu Zhong

Publications and source records attributed to Liyu Zhong.

6 recordsLinked to original sources

arXiv2026

Wrinkling of Randomly Heterogeneous Film-Substrate Systems

Wrinkling instabilities in stiff films on compliant substrates are strongly affected by spatial fluctuations in film stiffness. We develop a homogenized instability theory for one-dimensional film--substrate systems with random bending stiffness. The heterogeneous stability equation is reformulated as a Lippmann--Schwinger equation for the curvature field, and a strong-contrast expansion is derived using a local--nonlocal kernel decomposition and a cavity-field formulation. Truncation at third order yields an effective polarizability and a Dyson-type dispersion relation for predicting the critical load and wavenumber. The stiffness is modeled as an exponentially mapped Gaussian random field, allowing the required two- and three-point connected statistics to be obtained analytically. The theory is validated against generalized eigenvalue calculations and Fourier spectral simulations. Increasing stiffness contrast lowers the critical load and shifts the instability toward higher wavenumbers, producing shorter wrinkles. At weak contrast, the threshold follows the universal scaling $N_c^{(0)}-N_c\sim\varepsilon^2$, whereas at moderate and strong contrast the third-order approximation is more accurate than the second-order theory. Wavelength selection is controlled by the ratio of the dominant material wavelength $λ^\ast$ to the harmonic-mean reference wavelength $λ_H$. For $λ^\ast/λ_H<1$, the harmonic-mean model accurately predicts the wrinkle wavelength. The framework provides a mechanics-based tool for reliability assessment and design of statistically heterogeneous film--substrate systems.

cond-mat.mtrl-sci↗

arXiv2026

Response-Selected Hidden Hyperuniformity in Hydrodynamic Active Matter

Hyperuniformity in active matter is usually treated as a property of a prescribed density or continuum field. This view misses a basic feature of hydrodynamic active matter: an incompressible fluid does not respond equally to every microscopic force. Longitudinal forcing is absorbed into pressure, whereas transverse forcing drives flow. The relevant question is therefore not only whether particles are uniformly arranged or whether the total activity is small, but which sector of the active forcing is selected by the physical response. Here we introduce response-selected hyperuniformity, in which long-wavelength order is a property of a source-response pair. In a reversible valence-one fluid with no prescribed partners, locally neutral clusters screen the signed active-moment sector that controls transverse flow, producing a first-moment spectrum that vanishes quadratically at low wavenumber. Locally unscreened moments instead generate a nonzero infrared plateau. The resulting transverse-force spectrum has a universal crossover from fourth- to sixth-order scaling, with the crossover set by the ratio of the unscreened residual to the screened analytic contribution. Complete partner renewal preserves this normal form, establishing exchangeable multipole inheritance, while turnover tunes the residual through an independently measured local defect density. The zero-residual limit yields strictly hyperuniform velocity fluctuations; any finite residual causes defect-controlled infrared leakage and sets a finite screening length. Thus microscopic exchange need not destroy hidden hyperuniform flow order, but rare unscreened moments determine how far the quiet-flow regime survives.

cond-mat.soft↗

arXiv2026

Ordinary Disordered Materials Can Carry Hyperuniform Physical Fields

Fluctuations in disordered matter play a central role in determining material properties and physical responses. Recent studies have identified an exotic class of systems known as structurally hyperuniform materials, in which large-scale density fluctuations are anomalously suppressed through special spatial organization of particles, phases, or microstructural features. Here we demonstrate that ordinary, structurally nonhyperuniform disordered materials can nevertheless support hyperuniform physical scalar, vector, and tensor fields such as charge, bound current, vorticity, defect density, and stress. We develop a general theoretical framework in which a physical field is generated from a more primitive parent field through a local physical operator. In Fourier space, the spectrum of the derived field is determined by the product of the parent-field spectrum and the Fourier symbol of the operator. When the operator embodies a local gauge-like constraint, its Fourier symbol possesses zeros at small wavenumber, eliminating the corresponding long-wavelength fluctuations. As a consequence, the derived field exhibits complete suppression of infinite-wavelength intensity fluctuations, irrespective of the large-scale disorder and nonhyperuniformity of the parent field. We demonstrate this mechanism in elastic, electrostatic, and magnetostatic settings, showing that operator-generated incompatibility, bound charge, and bound-current fields can become hyperuniform even when their parent eigenstrain, polarization, or magnetization fields remain conventionally disordered. These findings broaden the notion of hyperuniformity from a structural property of matter to a universal field phenomenon generated by local physical constraints.

cond-mat.mtrl-sci↗

arXiv2025

Exact Expansion Formalism for Transport Properties of Heterogeneous Materials Characterized by Arbitrary Continuous Random Fields

We derive an exact contrast-expansion formalism for the effective conductivity of heterogeneous materials (media) with local properties described by arbitrary continuous random fields, significantly generalizing the widely used binary-field models. The theory produces a rapidly convergent Neumann-series that, upon Gaussian closure via a Hermite expansion, yields closed-form first-, second- and third-order approximations, which achieve percent-level accuracy at first order for isotropic media. For anisotropic media, second-order approximations achieve sub-2% accuracy across a wide range of local property contrasts and correlations. Our formalism provides mathematically rigorous structure-property closures, with significant implications for the discovery and design of novel graded and architected materials with tailored transport properties.

cond-mat.mtrl-sci↗

arXiv2025

Ultra-Efficient Reconstruction of Anisotropic Hyperuniform Continuous Random Fields in 2D and 3D via Generalized Spectral Filtering

Hyperuniform continuous random fields suppress large-scale fluctuations while preserving rich local disorder, making them highly attractive for next-generation photonic, thermal and mechanical materials. However, traditional reconstruction techniques often suffer from limited spectral control or excessive computational cost, especially in high-resolution 2D and 3D settings. In this work, we present an ultra-efficient generative algorithm based on generalized superellipse spectral filtering, which allows independent tuning of isotropic and anisotropic spectral envelopes without resorting to costly iterative schemes. We demonstrate our method on a comprehensive set of 2D and 3D examples, showing precise manipulation of spectral band shape and orders-of-magnitude speedup compared to existing approaches. Furthermore, we explore the effect of simple thresholding on the generated fields, analyzing the morphological features and power-spectrum characteristics of the resulting two-phase maps. Our results confirm that the proposed framework not only accelerates hyperuniform field synthesis but also provides a versatile platform for systematic study of binary microstructures derived from continuous designs. This work opens new avenues for large-scale simulation and optimized design of advanced hyperuniform materials.

cond-mat.mtrl-sci↗

arXiv2025

Structure-Property Relationship in Disordered Hyperuniform Materials: Microstructure Representation, Field Fluctuations and Effective Properties

Disordered hyperuniform (DHU) materials are an emerging class of exotic heterogeneous material systems characterized by a unique combination of disordered local structures and a hidden long-range order, which endow them with unusual physical properties. Here, we consider material systems possessing continuously varying local material properties $\mathcal{K}({\bf x})$ modeled via a random field. We devise quantitative microstructure representation of the material systems based on a class of analytical spectral density function ${\tilde χ}_{_\mathcal{K}}({k})$ associated with $\mathcal{K}({\bf x})$, possessing a power-law small-$k$ scaling behavior ${\tilde χ}_{_\mathcal{K}}({k}) \sim k^α$. By controlling the exponent $α$ and using a highly efficient forward generative model, we obtain realizations of a wide spectrum of distinct material microstructures spanning from hyperuniform ($α>0$) to nonhyperuniform ($α=0$) to antihyperuniform ($α<0$) systems. We perform a comprehensive perturbation analysis to quantitatively connect the fluctuations of the local material property to the fluctuations of the resulting physical fields. In the weak-contrast limit, our first-order perturbation theory reveals that the physical fields associated with Class-I hyperuniform materials (characterized by $α\ge 2$) are also hyperuniform, albeit with a lower hyperuniformity exponent ($α-2$). As one moves away from this weak-contrast limit, the fluctuations of the physical field develop a diverging spectral density at the origin. We also establish an end-to-end mapping connecting the spectral density of the local material property to the overall effective conductivity of the material system via numerical homogenization.

cond-mat.mtrl-sci↗