Morphoelastic rods Part 1: A single growing elastic rod

A theory for the dynamics and statics of growing elastic rods is presented. First, a single growing rod is considered and the formalism of three-dimensional multiplicative decomposition of morphoelasticity is used to describe the bulk growth of Kirchhoff elastic rods. Possible constitutive laws for growth are discussed and analysed. Second, a rod constrained or glued to a rigid substrate is considered, with the mismatch between the attachment site and the growing rod inducing stress. This stress can eventually lead to instability, bifurcation, and buckling

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 non conserved 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 eigen modes of the curl operator, that viscous effects have to be taken into account for wave vector smaller than the Kolomogorov wave number in the evolution of these eigen components of the helicity.Comment: 6 pages, 2 figures, submited to Po

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

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

MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales

Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research

Helical shell models for MHD turbulence

Based on the helical decomposition of both the magnetic and the velocity fields, a helical shell model for MHD turbulence is introduced. It is used to study the influence of the forcing helicity on the onset of dynamo. It is shown that the well-known GOY shell model is not well adapted for such a study and that additional interactions between the shell variables have to be taken into account

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

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

Uniclass Unified classification for the construction industry

SIGLEAvailable from British Library Document Supply Centre-DSC:98/18087 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

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

Morphoelastic rods Part II: Growing birods

The general problem of determining the shape and response of two attached growing elastic Kirchhoff rods is considered. A description of the kinematics of the individual interacting rods is introduced. Each rod has a given intrinsic shape and constitutive laws, and a map associating points on the two rods is defined. The resulting filamentary structure, a growing birod, can be seen as a new filamentary structure. This kinematic description is used to derive the general equilibrium equations for the shape of the rods under loads, or equivalently, for the new birod. It is shown that, in general, the birod is not simply a Kirchhoff rod but rather, due to the internal constraints, new effects can appear. The two-dimensional restriction is then considered explicitly and the limit for small deformation is shown to be equivalent to the classic Timsohenko bi-metallic strip problem. A number of examples and applications are presented. In particular, the problem of two attached rods with intrinsic helical shape and uniform growth is computed in detail and a host of new interesting solutions and bifurcations are observed. </p