arXiv subjects

Berian James

Publications and source records attributed to Berian James.

2 recordsLinked to original sources

arXiv2025

The magnetic scalar potential for a rectangular prism

We analytically solve Poisson's equation for the magnetic scalar potential generated by a uniformly magnetized rectangular prism and determine a closed-form solution for the magnetic scalar potential given only in terms of arctan and natural logarithmic functions. We show that the magnetic scalar potential can be written as a demagnetization vector, containing all the geometric information, multiplied with the magnetization, analogous to demagnetization tensors. We validate the derived analytical expression for the magnetic scalar potential by comparing with a finite element simulation and show that these agree perfectly. We finally extend the concept of the demagnetization vector and tensor, which contains the geometric information for the source generating the potential, to gravitational objects.

physics.class-ph↗

arXiv2024

Scalable physical source-to-field inference with hypernetworks

We present a generative model that amortises computation for the field and potential around e.g.~gravitational or electromagnetic sources. Exact numerical calculation has either computational complexity $\mathcal{O}(M\times{}N)$ in the number of sources $M$ and evaluation points $N$, or requires a fixed evaluation grid to exploit fast Fourier transforms. Using an architecture where a hypernetwork produces an implicit representation of the field or potential around a source collection, our model instead performs as $\mathcal{O}(M + N)$, achieves relative error of $\sim\!4\%-6\%$, and allows evaluation at arbitrary locations for arbitrary numbers of sources, greatly increasing the speed of e.g.~physics simulations. We compare with existing models and develop two-dimensional examples, including cases where sources overlap or have more complex geometries, to demonstrate its application.

cs.LG↗