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Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane
Miles H. Wheeler
https://arxiv.org/abs/2509.00455 https://arxi…

Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane
In this note we construct smooth bounded domains $Ω\subset \mathbb R^2$, other than disks, for which the overdetermined problem $$ \left\{ \begin{alignedat}{2} Δu + λu &= 0 &\qquad& \text{ in } Ω, \newline u &= b &\qquad& \text{ on } \partial Ω, \newline \frac{\partial u}{\partial n} &= c &\qquad& \text{ on } \partial Ω \end{alignedat} \right. $$ has a solution for some constants $λ,b,c \ne 0$. These appear to be the first counterexamples to a conjecture of Willms and Gladw…

(2018) Functional MRI of sensory substitution in the blind #blindness

Diffusion of $^{210}\text{Pb}$ and $^{210}\text{Po}$ in Nylon
P. Adhikari, M. G. Boulay, R. Crampton, M. Perry, D. Sinclair
https://arxiv.org/abs/2509.11464 https://

Diffusion of $^{210}\text{Pb}$ and $^{210}\text{Po}$ in Nylon
Radon and its progeny constitute a major source of background in rare-event physics experiments, such as those searching for dark matter, neutrinos, and neutrinoless double beta decay, due to their origin as unavoidable decay products of natural uranium. In particular, $^{222}$Rn and its long-lived daughter $^{210}$Pb can diffuse from detector material surfaces, resulting in sustained background contributions. To investigate this process, a system was developed using a controlled radon source, …