arXiv subjects

Eric Lang

Publications and source records attributed to Eric Lang.

7 recordsLinked to original sources

arXiv2026

Delaunay surfaces with free boundary on the unit $2$-sphere

We characterize all symmetric, embedded surfaces of revolution with constant mean curvature that meet the unit sphere orthogonally. It is well known that there exists a unique free boundary catenoid inside of the unit ball. By analogy, we prove the existence of a unique free boundary nodoid inside of the unit ball with constant mean curvature equal to $-1$. Moreover, there exists a unique compact free boundary nodoid \emph{outside} of the unit ball with constant mean curvature equal to $-1$. However, there exists no symmetric surface of revolution with constant mean curvature $1$ that meets the unit sphere orthogonally.

math.DG↗

arXiv2026

Fragmenting Diffusion Pathways Confers Extraordinary Radiation Resistance in Refractory Multicomponent Alloys

The accumulation and growth of vacancy clusters under irradiation is a pivotal degradation mode for structural materials in extreme environments. Even tungsten undergoes rapid defect coarsening compromising its integrity. Here we show a tungsten multicomponent alloy that effectively fragments the vacancy diffusion network, kinetically trapping defects within localized domains. This effect originates from a broad spectrum of migration barriers and substantial vacancy-jump heterogeneity, which drives the interconnectivity of diffusion paths below the percolation threshold. Starving clusters of the necessary vacancy supply, irradiation experiments and atomic-scale defect characterizations confirm negligible defect growth as radiation doses increase by four orders of magnitude. These results provide a fundamental paradigm for percolation-engineered kinetics, offering a predictive pathway for tailoring defect diffusion and discovering inherently radiation-tolerant materials.

cond-mat.mtrl-sci↗

arXiv2026

Perish or Flourish? A Holistic Evaluation of Large Language Models for Code Generation in Functional Programming

Functional programming provides strong foundations for developing reliable and secure software systems, yet its adoption remains not widespread due to the steep learning curve. Recent advances in Large Language Models (LLMs) for code generation present new opportunities to lower these barriers. However, extensive evaluations of LLMs largely focus on imperative programming languages, and their capabilities in functional programming languages (FP) remain underexplored. To address this gap, we introduce FPEval, a holistic evaluation framework built on FPBench, a new benchmark of 721 programming tasks across three difficulty levels on three mainstream FP languages: Haskell, Ocaml and Scala. FPEval provides compehensive evaluation infrastructures with both test validations with comprehensive test suites and static analysis tools to assess both functional correctness and code style and maintainability. Using this framework, we evaluate state-of-the-art LLMs, including GPT-3.5, GPT-4o, and GPT-5, for code generation in functional programming languages and Java as an imperative baseline. Our results demonstrate that LLM performance in functional programming improves substantially with model advancement; however, error rates remain significantly higher in purely functional languages (Haskell and OCaml) than in hybrid (Scala) or imperative (Java) languages. Moreover, LLMs frequently generate non-idiomatic functional code that follows imperative patterns, raising concerns about code style and long-term maintainability. Finally, we show that LLMs can partially self-repair both correctness and quality issues when provided with static analysis feedback and hand-crafted instructions for common types of issues.

cs.PL↗

arXiv2024

Revealing the Evolution of Order in Materials Microstructures Using Multi-Modal Computer Vision

The development of high-performance materials for microelectronics, energy storage, and extreme environments depends on our ability to describe and direct property-defining microstructural order. Our present understanding is typically derived from laborious manual analysis of imaging and spectroscopy data, which is difficult to scale, challenging to reproduce, and lacks the ability to reveal latent associations needed for mechanistic models. Here, we demonstrate a multi-modal machine learning (ML) approach to describe order from electron microscopy analysis of the complex oxide La$_{1-x}$Sr$_x$FeO$_3$. We construct a hybrid pipeline based on fully and semi-supervised classification, allowing us to evaluate both the characteristics of each data modality and the value each modality adds to the ensemble. We observe distinct differences in the performance of uni- and multi-modal models, from which we draw general lessons in describing crystal order using computer vision.

cond-mat.mtrl-sci↗

arXiv2023

Unsupervised segmentation of irradiation$\unicode{x2010}$induced order$\unicode{x2010}$disorder phase transitions in electron microscopy

We present a method for the unsupervised segmentation of electron microscopy images, which are powerful descriptors of materials and chemical systems. Images are oversegmented into overlapping chips, and similarity graphs are generated from embeddings extracted from a domain$\unicode{x2010}$pretrained convolutional neural network (CNN). The Louvain method for community detection is then applied to perform segmentation. The graph representation provides an intuitive way of presenting the relationship between chips and communities. We demonstrate our method to track irradiation$\unicode{x2010}$induced amorphous fronts in thin films used for catalysis and electronics. This method has potential for "on$\unicode{x2010}$the$\unicode{x2010}$fly" segmentation to guide emerging automated electron microscopes.

cond-mat.mtrl-sci↗

arXiv2023

Alloying Effects on the Microstructure and Properties of Laser Additively Manufactured Tungsten Materials

A large body of literature within the additive manufacturing (AM) community has focused on successfully creating stable tungsten (W) microstructures due to significant interest in its application for extreme environments. However, solidification cracking and additional embrittling features at grain boundaries have resulted in poorly performing microstructures, stymying the application of AM as a manufacturing technique for W. Several alloying strategies, such as ceramic particles and ductile elements, have emerged with the promise to eliminate solidification cracking while simultaneously enhancing stability against recrystallization. In this work, we provide new insights regarding the defects and microstructural features that result from the introduction of ZrC for grain refinement and NiFe as a ductile reinforcement phase - in addition to the resulting thermophysical and mechanical properties. ZrC is shown to promote microstructural stability with increased hardness due to the formation of ZrO2 dispersoids. Conversely, NiFe forms into micron-scale FCC phase regions within a BCC W matrix, producing enhanced toughness relative to pure AM W. A combination of these effects is realized in the WNiFe+ZrC system and demonstrates that complex chemical environments coupled with the tuning of AM microstructures provides an effective pathway for enabling laser AM W materials with enhanced stability and performance.

cond-mat.mtrl-sci↗

arXiv2021

Thermal conductivity reduction in (Zr$_{0.25}$Ta$_{0.25}$Nb$_{0.25}$Ti$_{0.25}$)C high entropy carbide from extrinsic lattice defects

High entropy carbides ceramics with randomly-distributed multiple principal cations have shown high temperature stability, low thermal conductivity, and possible radiation tolerance. While chemical disorder has been shown to suppress thermal conductivity in these materials, little investigation has been made on the effects of additional, extrinsically-generated structural defects on thermal transport. Here, (Zr$_{0.25}$Ta$_{0.25}$Nb$_{0.25}$Ti$_{0.25}$)C is exposed to Zr ions to generate a micron-scale, structural-defect-bearing layer. The reduction in lattice thermal transport is measured using laser thermoreflectance. Conductivity changes from different implantation temperatures suggest dislocation loops contribute little to phonon scattering while nanoscale defects serve as effective scatterers, offering a pathway for thermal engineering.

cond-mat.mtrl-sci↗