arXiv subjects

Mason Haberle

Publications and source records attributed to Mason Haberle.

5 recordsLinked to original sources

arXiv2025

Permanent magnet optimization of stellarators with coupling from finite permeability and demagnetization effects

Permanent magnets provide an attractive path for shaping university-scale stellarator magnetic fields. Previous work has shown that greedy permanent magnet optimization (GPMO) can produce sparse, grid-aligned arrays that match target surfaces with high accuracy under an ideal rigid-remanence model. Here we extend this approach to a greedy permanent magnet optimization with macromagnetic refinement (GPMOmr) by introducing a block-level macromagnetic model that accounts for magnet-magnet and magnet-coil coupling from finite permeability and demagnetizing interactions, and apply it to the published magnet grid from the MUSE stellarator design. Finite-permeability effects produce degree-scale tilts and few-percent magnitude changes in individual magnets and modify the surface-normal field $\mathbf B\cdot\mathbf n$ only at the percent level, yet for a fixed layout they increase the standard squared-flux objective by more than a factor of two. When the same model is embedded in the greedy loop, GPMOmr achieves $f_B$ histories and final errors within a few percent of classical GPMO while producing visibly more nonuniform magnetization patterns. Our formulation provides a fast and practical tool for quantifying and incorporating finite-permeability effects in permanent-magnet stellarator designs, and offers a framework for extending permanent-magnet optimization to higher field strengths and to materials with stronger macromagnetic coupling.

physics.plasm-ph↗

arXiv2024

Weak Diffusive Stability of Roll Solutions at the Zigzag Boundary

Roll solutions at the zigzag boundary, typically selected by patterns and defects in numerical simulations, are shown to be nonlinearly stable. This result also serves as an example that linear decay weaker than the classical diffusive decay, together with quadratic nonlinearity, still gives nonlinear stability of spatially periodic patterns. Linear analysis reveals that, instead of the classical $t^{-1}$ diffusive decay rate, small perturbations of roll solutions at the zigzag boundary decay with a $t^{-3/4}$ rate along with time, due to the degeneracy of the quadratic term of the continuation of the translational mode of the linearized operator in the Bloch-Fourier spaces. The nonlinear stability proof is based on a decomposition of the neutral translational mode and the faster decaying modes in the Bloch-Fourier space, and a fixed-point argument, demonstrating the irrelevancy of the nonlinear terms.

nlin.PS↗

arXiv2023

Nonlinear Stability at the Zigzag Boundary

We investigate the dynamics of roll solutions at the zigzag boundary of the planar Swift-Hohenberg equation. Linear analysis shows an algebraic decay of small perturbation with a $t^{- 1/4}$ rate, instead of the classical $t^{- 1/2}$ diffusive decay rate, due to the degeneracy of the quadratic term of the continuation of the translational mode of the linearized operator in the Bloch-Fourier spaces. The proof is based on a decomposition of the neutral mode and the faster decaying modes in the Bloch-Fourier space, and a fixed-point argument, demonstrating the irrelevancy of the nonlinear terms.

math.AP↗

arXiv2022

Communication Bounds for Convolutional Neural Networks

Convolutional neural networks (CNNs) are important in a wide variety of machine learning tasks and applications, so optimizing their performance is essential. Moving words of data between levels of a memory hierarchy or between processors on a network is much more expensive than the cost of arithmetic, so minimizing communication is critical to optimizing performance. In this paper, we present new lower bounds on data movement for mixed precision convolutions in both single-processor and parallel distributed memory models, as well as algorithms that outperform current implementations such as Im2Col. We obtain performance figures using GEMMINI, a machine learning accelerator, where our tiling provides improvements between 13% and 150% over a vendor supplied algorithm.

cs.DC↗

arXiv2020

A Full Study of the Dynamics on One-Holed Dilation Tori

An open question in the study of dilation surfaces is to determine the typical dynamical behavior of the directional flow on a fixed dilation surface. We show that on any one-holed dilation torus, in all but a measure zero Cantor set of directions, the directional flow has an attracting periodic orbit, is minimal, or is completely periodic. We further show that for directions in this Cantor set, the directional flow is attracted to either a saddle connection or a lamination on the surface that is locally the product of a measure zero Cantor set and an interval.

math.DS↗