Bernardo González | Searcharxiv

arXiv2026

Macroscopic bioinspired magnetic active matter and the physical limits of magnetotaxis

Magnetotactic bacteria (MTB) are endowed with an exquisite orientation mechanism allowing them to swim along the geomagnetic field lines. This mechanism consists of a chain of bio-synthesized magnetic nano-crystals that endow MTB with a permanent magnetic moment. Although the physics behind the minimum size of this biological compass is well understood, it is yet unclear what sets its maximum size. Here we combine macroscopic bioinspired experiments, calibrated simulations, and analytic estimates to show that increasing dipolar strength can drive magnetic active matter from a freely swimming regime into clustered states. Using a physical model with parameters relevant to MTB, we infer a plausible physical upper bound on useful magnetosome-chain magnetic moments: beyond a threshold, clustering and the formation of compound bodies are expected to hinder effective swimming and reduce magnetotactic performance. Our macroscopic bio-inspired experiment and physical model show how long-range magnetic interactions reshape the phase behavior of anisotropic active matter and provide a programmable platform for studying magnetic active matter across scales.

cond-mat.soft↗

arXiv2013

Volume inequalities for the $i$-th-Convolution bodies

We obtain a new extension of Rogers-Shephard inequality providing an upper bound for the volume of the sum of two convex bodies $K$ and $L$. We also give lower bounds for the volume of the $k$-th limiting convolution body of two convex bodies $K$ and $L$. Special attention is paid to the $(n-1)$-th limiting convolution body, for which a sharp inequality, which is equality only when $K=-L$ is a simplex, is given. Since the $n$-th limiting convolution body of $K$ and $-K$ is the polar projection body of $K$, these inequalities can be viewed as an extension of Zhang's inequality.

math.MG↗