arXiv subjects

Zhiyuan Dai

Publications and source records attributed to Zhiyuan Dai.

4 recordsLinked to original sources

arXiv2026

Asymptotics for two-dimensional parabolic vectorial Allen-Cahn systems

We study the parabolic vectorial Allen--Cahn equation in two space dimensions for a fixed smooth potential with finitely many non-degenerate wells. Our result provides a parabolic extension of Bethuel's elliptic compactness theorem: at almost every positive time, the diffuse energy, potential energy, and gradient tensor converge to measures concentrated on a countably $1$-rectifiable interface and satisfy all the Bethuel-type relations. In the scalar case, the tangential defect vanishes and the usual mean-curvature-flow structure is recovered. For general vectorial potentials, the limiting stress and dissipation yield a two-mobility system: the normal energy flux balances weighted curvature, while a tangential internal mobility transports residual tangential energy. Thus the result extends the Allen--Cahn-to-Brakke framework of Ilmanen from scalar to vector-valued systems, with an additional non-negative dissipation defect in the localized energy inequality.

math.AP↗

arXiv2026

Boundary asymptotics for two-dimensional vectorial Allen-Cahn systems

We study asymptotic properties of critical points of the two-dimensional vectorial Allen-Cahn energy with finitely many non-degenerate wells, subject to a homogeneous Neumann boundary condition. For any sequence with uniformly bounded energy, we prove that the limiting full and potential measures are supported on a closed countably 1-rectifiable set up to the boundary and satisfy the discrepancy relations. The potential measure defines a free-boundary stationary rectifiable varifold. Boundary mass may occur: weights are constant on regular boundary arcs, finite-type junctions obey projected balance, and the sole non-boundary branch meets the boundary orthogonally. This provides a Neumann-boundary extension of Bethuel's planar interior theory. The key idea is to read the boundary geometry from the limiting stress-energy tensor, which identifies the potential-energy measure as the stationary interfacial measure even in the presence of boundary concentration.

math.AP↗

arXiv2026

Boundary regularity for Oseen-Frank minimizers with arbitrary positive splay, twist, and bend constants

Let $Ω\subset\mathbb R^3$ be a smooth bounded domain and let $g:\partialΩ\to\mathbb S^2$ be smooth. We prove that any global minimizer of the Oseen--Frank energy subject to the strong anchoring condition $n=g$ is smooth in a full neighborhood of $\partialΩ$. The result holds for arbitrary positive splay, twist, and bend constants, without any small-anisotropy assumption. It resolves the boundary-regularity part of Lin and Liu's Problem~(c) for the pure Oseen--Frank problem and for its prescribed smooth magnetic-field perturbation.

math.AP↗

arXiv2024

Machine Learning Co-pilot for Screening of Organic Molecular Additives for Perovskite Solar Cells

Machine learning (ML) has been extensively employed in planar perovskite photovoltaics to screen effective organic molecular additives, while encountering predictive biases for novel materials due to small datasets and reliance on predefined descriptors. Present work thus proposes an effective approach, Co-Pilot for Perovskite Additive Screener (Co-PAS), an ML-driven framework designed to accelerate additive screening for perovskite solar cells (PSCs). Co-PAS overcomes predictive biases by integrating the Molecular Scaffold Classifier (MSC) for scaffold-based pre-screening and utilizing Junction Tree Variational Autoencoder (JTVAE) latent vectors to enhance molecular structure representation, thereby enhancing the accuracy of power conversion efficiency (PCE) predictions. Leveraging Co-PAS, we integrate domain knowledge to screen an extensive dataset of 250,000 molecules from PubChem, prioritizing candidates based on predicted PCE values and key molecular properties such as donor number, dipole moment, and hydrogen bond acceptor count. This workflow leads to the identification of several promising passivating molecules, including the novel Boc-L-threonine N-hydroxysuccinimide ester (BTN), which, to our knowledge, has not been explored as an additive in PSCs and achieves a device PCE of 25.20%. Our results underscore the potential of Co-PAS in advancing additive discovery for high-performance PSCs.

cs.LG↗