Sanjay Pradeep | Search arXiv

arXiv2026

Equivariant Neural Prediction of the Stokes Resistance Tensors for Arbitrary Microparticle Shapes

The Stokes-flow hydrodynamics of an irregular microparticle is encoded by its grand resistance matrix, a 6x6 tensor whose translational and rotational blocks (A and C) govern settling, diffusion, and orientational transport. Empirical drag correlations compress these tensors to a single scalar, discarding drag's orientation dependence and the rotational response. We present an SO(3)-equivariant neural network that predicts the full symmetric positive-definite A and C blocks from a particle's spherical-harmonic surface representation, equivariant by construction to floating-point precision. Trained on 1.1x10^5 random shapes from near-spherical to very rough, with a sealed test set of 18,000, it achieves 1.4% and 2.7% mean relative error on the two blocks while evaluating each shape 4-5 orders of magnitude faster than the regularised-Stokeslet solver that generated its labels. A spectral-convergence study confirms the representation is faithful: truncating a shape at spherical-harmonic degree 15 changes its resistance by a median of 0.14% (translation) and 0.38% (rotation), while the training shapes, generated band-limited at degree 15, carry no truncation error. Across 1.16x10^6 orientation-sampled settling, rotation and diffusion events, the surrogate reveals lateral drift up to 11 deg, rotational misalignment up to 46 deg, and shape-induced diffusion spreads of 30% (translational) and 2.4x (rotational), all identically zero under any scalar or spheroid reduction. Even the orientation-averaged scalar friction the correlations target, accurate to 1.7-2.8% (median; 2.2-3.2% mean), carries no tensor orientation, whereas the surrogate reproduces that scalar to ~1% while supplying the full anisotropic tensors. A fast, equivariant tensor surrogate can replace both solver and scalar approximation in atmospheric dust transport, microplastic fate and colloidal Brownian dynamics.

physics.flu-dyn↗

arXiv2026

Quantification and Classification of Carbon Nanotubes in Electron Micrographs using Vision Foundation Models

Accurate characterization of carbon nanotube morphologies in electron microscopy images is vital for exposure assessment and toxicological studies, yet current workflows rely on slow, subjective manual segmentation. This work presents a unified framework leveraging vision foundation models to automate the quantification and classification of CNTs in electron microscopy images. First, we introduce an interactive quantification tool built on the Segment Anything Model (SAM) that segments particles with near-perfect accuracy using minimal user input. Second, we propose a novel classification pipeline that utilizes these segmentation masks to spatially constrain a DINOv2 vision transformer, extracting features exclusively from particle regions while suppressing background noise. Evaluated on a dataset of 1,800 TEM images, this architecture achieves 95.5% accuracy in distinguishing between four different CNT morphologies, significantly outperforming the current baseline despite using a fraction of the training data. Crucially, this instance-level processing allows the framework to resolve mixed samples, correctly classifying distinct particle types co-existing within a single field of view. These results demonstrate that integrating zero-shot segmentation with self-supervised feature learning enables high-throughput, reproducible nanomaterial analysis, transforming a labor-intensive bottleneck into a scalable, data-driven process.

cs.CV↗