Thomas Lessinnes

Morphomechanical Innovation Drives Explosive Seed Dispersal

Summary How mechanical and biological processes are coordinated across cells, tissues, and organs to produce complex traits is a key question in biology. Cardamine hirsuta, a relative of Arabidopsis thaliana, uses an explosive mechanism to disperse its seeds. We show that this trait evolved through morphomechanical innovations at different spatial scales. At the organ scale, tension within the fruit wall generates the elastic energy required for explosion. This tension is produced by differential contraction of fruit wall tissues through an active mechanism involving turgor pressure, cell geometry, and wall properties of the epidermis. Explosive release of this tension is controlled at the cellular scale by asymmetric lignin deposition within endocarp b cells—a striking pattern that is strictly associated with explosive pod shatter across the Brassicaceae plant family. By bridging these different scales, we present an integrated mechanism for explosive seed dispersal that links evolutionary novelty with complex trait innovation. Video Abstract

A biomechanical model of anther opening reveals the roles of dehydration and secondary thickening.

Summary Understanding the processes that underlie pollen release is a prime target for controlling fertility to enable selective breeding and the efficient production of hybrid crops. Pollen release requires anther opening, which involves changes in the biomechanical properties of the anther wall. In this research, we develop and use a mathematical model to understand how these biomechanical processes lead to anther opening. Our mathematical model describing the biomechanics of anther opening incorporates the bilayer structure of the mature anther wall, which comprises the outer epidermal cell layer, whose turgor pressure is related to its hydration, and the endothecial layer, whose walls contain helical secondary thickening, which resists stretching and bending. The model describes how epidermal dehydration, in association with the thickened endothecial layer, creates forces within the anther wall causing it to bend outwards, resulting in anther opening and pollen release. The model demonstrates that epidermal dehydration can drive anther opening, and suggests why endothecial secondary thickening is essential for this process (explaining the phenotypes presented in the myb26 and nst1nst2 mutants). The research hypothesizes and demonstrates a biomechanical mechanism for anther opening, which appears to be conserved in many other biological situations where tissue movement occurs.

Energy transfers in shell models for magnetohydrodynamics turbulence

A systematic procedure to derive shell models for magnetohydrodynamic turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross helicity, and the magnetic helicity, as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest-neighbor shells, this procedure reproduces well-known models but suggests a reinterpretation of the energy fluxes.

Dissipation scales of kinetic helicities in turbulence

A systematic study of the influence of the viscous effect on both the spectra and the nonlinear fluxes of conserved as well as nonconserved quantities in Navier–Stokes turbulence is proposed. This analysis is used to estimate the helicity dissipation scale which is shown to coincide with the energy dissipation scale. However, it is shown using the decomposition of helicity into eigenmodes of the curl operator that viscous effects have to be taken into account for wave vectors smaller than the Kolmogorov wave number in the evolution of these eigencomponents of the helicity.

The elastic secrets of the chameleon tongue

The ballistic projection of the chameleon tongue is an extreme example of quick energy release in the animal kingdom. It relies on a complicated physiological structure and an elaborate balance between tissue elasticity, collagen fibre anisotropy, active muscular contraction, stress release and geometry. A general biophysical model for the dynamics of the chameleon tongue based on large deformation elasticity is proposed. The model involves three distinct coupled subsystems: the energetics of the intralingual sheaths, the mechanics of the activating accelerator muscle and the dynamics of tongue extension. Together, these three systems elucidate the key physical principles of prey-catching among chameleonides.

Dynamo transition in low-dimensional models

Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and current helicity. The velocity modes are forced in both these models. These low-dimensional models exhibit a dynamo transition at a critical forcing amplitude that depends on the Prandtl number. In the nonhelical model, dynamo exists only for magnetic Prandtl number beyond 1, while the helical model exhibits dynamo for all magnetic Prandtl number. Although the model is far from reproducing all the possible features of dynamo mechanisms, its simplicity allows a very detailed study and the observed dynamo transition is shown to bear similarities with recent numerical and experimental results.

Geometric conditions for the positive definiteness of the second variation in one-dimensional problems

Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is, in general, analytically untractable. However, we show here that a global geometric analysis of the phase-plane trajectories associated with the stationary solutions leads to generic conditions for minimality. These results provide a straightforward and direct proof of positive definiteness, or lack thereof, in many important cases. In particular, when applied to mechanical systems, the stability or instability of entire classes of solutions can be obtained effortlessly from their geometry in phase-plane, as illustrated on a problem of a mass hanging from an elastic rod with intrinsic curvature.

Design and Stability of a Family of Deployable Structures

A large family of deployable filamentary structures can be built by connecting two elastic rods along their length. The resulting structure has interesting shapes that can be stabilized by tuning the material properties of each rod. To model this structure and study its stability, we show that the equilibrium equations describing unloaded states can be derived from a variational principle. We then use a novel geometric method to study the stability of the resulting equilibria. As an example we apply the theory to establish the stability of all possible equilibria of the Bristol ladder.

Direct numerical simulation of dynamo transition for nonhelical MHD

Pseudospectral Direct Numerical Simulation (DNS) has been performed to simulate dynamo transition for nonhelical magnetohydrodynamics turbulence. The numerical results are compared with a recent low-dimensional model [Verma et al. [13]]. The forcing in DNS is the same as that used in the low-dimensional model. Dynamo transition is observed in DNS, but the forcing required for the transition is higher than that for the model. A qualitative similarity is observed between DNS and model results. The difference is due to the presence of large number of modes present in the DNS.

Shell models of MHD turbulence

Understanding the existence and the dynamics of the magnetic field of the Earth, of the Sun and, in general, of other celestial bodies (dynamo effect) remains one of the most challenging problems of classical physics. Analytical approaches of this problem are extremely complicated while numerical efforts are limited to a range of parameter space that is often quite distant from the realistic systems. For instance, in certain astrophysical bodies as well as in laboratory experiments, the kinematic viscosity ν of the fluid is six orders of magnitude smaller than its resistivity η. The two dissipation processes therefore take place at very different time scales. This property makes direct numerical simulations of dynamo intractable. Due to these reasons, we resort to simplified models.