⭐New preprint: "A multiscale theory for network advection-reaction-diffusion"

with @alaingoriely.bsky.social and Emilia Cozzolino

arxiv.org/abs/2509.06546

In this endearing 1923 caricature by his mother, 11-year-old Alan Turing gazes at daisies instead of playing hockey. Decades later, he’d explore phyllotaxis—the spiral patterns in plants—using a 'digital computer', in one of his final works, cut short by his untimely death in 1954.

But who is to reverse the left-handed DNA? Now we know:

D'Arcy Thompson described himself as 'no skilled mathematician'; yet, he evidently clearly grasped the essence of mathematical modelling in biology, as well as the root of some common misapprehensions about it (On Growth and Form, 1917)

🧵 Ultimately, this work seeks to contribute to a comprehensive theory of growth, where growth emerges from the underlying (multi)physics of the material, a key problem of "formidable mathematical complexity". For more, check out the paper in #openaccess:
www.sciencedirect.com/science/arti...

In this theory, regions can grow in various ways, but fundamentally correspond to water sink (regions of lower water potential). This generates fascinating emergent effects, such as water competition dynamics and water gradients. 🫗

Combining *morphoelasticity* (a successful mechanical theory of growth) and *poroelasticity*, a theory of fluid saturated solids, we describe the plant as a growing material whose growth is linked to pressure and water transport across the medium. This extends Lockhart's model to continuum media.

At the scale of an entire tissues, things get a bit more complicated and we need a *field* theory, that is, a continuum theory which describes the behaviour of the material in terms of partial differential equations expressing the various balance relations and constitutive laws.

Plants grow because their cells absorb water and mechanically deform under pressure 🌱 a well-known process described (for a single cell) by the celebrated Lockhart's model and its various extensions.

🚨Hot off the press!

With Ibrahim Cheddadi, we tackled a key challenge: building a field theory of plant morphogenesis, based on fundamental balance laws and capturing cell wall remodelling and water dynamics in tissues🌿💧Check out our paper at www.sciencedirect.com/science/arti...

🧵👇

Combining morphoelasticity (my fav theory of growth) and poroelasticity, a theory of fluid saturated solids, we describe the tissue as a growing solid, whose growth is linked to water intake and transport across the medium. This extends Lockhart's model to continuum media.

At the scale of an entire tissues, things get a bit more complicated and we need a field theory, that is, a continuum theory which describes the behaviour of the material in terms of partial differential equations expressing the different balance relations and constitutive laws.

Plants grow because their cells absorb water and mechanically deform under pressure, a well-known process described by the celebrated Lockhart's model and its various extensions.