Modeling the growth and branching of plants: A simple rod-based model

Senan, Nur Adila Faruk; O’Reilly, Oliver M.; Tresierras, Timothy N.

doi:10.1016/j.jmps.2008.06.005

Cited by 25 publications

(21 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By treating the growing rod as a one-dimensional continuum that can change its reference length, diameter and stiffness, various authors have formulated a theory for how its shape can vary with time [10,[21][22][23][24]. A general discussion of possible evolution equations for the natural curvature has also been considered [22,25], with autotropism being the primary driver.…”

Section: Introductionmentioning

confidence: 99%

On the growth and form of shoots

Chelakkot

Mahadevan

2017

J. R. Soc. Interface.

View full text Add to dashboard Cite

Growing plant stems and shoots exhibit a variety of shapes that embody growth in response to various stimuli. Building on experimental observations, we provide a quantitative biophysical theory for these shapes by accounting for the inherent observed passive and active effects: (i) the active controllable growth response of the shoot in response to its orientation relative to gravity, (ii) proprioception, the shoot's growth response to its own observable current shape, and (iii) the passive elastic deflection of the shoot due to its own weight, which determines the current shape of the shoot. Our theory separates the sensed and actuated variables in a growing shoot and results in a morphospace diagram in terms of two dimensionless parameters representing a scaled local active gravitropic sensitivity, and a scaled passive elastic sag. Our computational results allow us to explain the variety of observed transient and steady morphologies with effective positive, negative and even oscillatory gravitropic behaviours, without the need for ad hoc complex spatio-temporal control strategies in terms of these parameters. More broadly, our theory is applicable to the growth of soft, floppy organs where sensing and actuation are dynamically coupled through growth processes via shape.

show abstract

Section: Introductionmentioning

confidence: 99%

On the growth and form of shoots

Chelakkot

Mahadevan

2017

J. R. Soc. Interface.

View full text Add to dashboard Cite

show abstract

“…XIX ]. The discussion in Love's classic text [23] is supplemented by material on branching, adhesion and material momentum from recent works (see [19,22,24,25] and references therein). Referring to Figure 4, the centerline of the rod is parameterized by an arc-length coordinate s ∈ [0, ℓ] and the position of a point on the centerline is denoted by the vector-valued function r(s).…”

Section: A Simple Model Of An Adhered Cnt Pairmentioning

confidence: 99%

On Adhesive and Buckling Instabilities in the Mechanics of Carbon Nanotubes Bundles

Zhou

O’Reilly

2015

Journal of Applied Mechanics

View full text Add to dashboard Cite

Many recently synthesized materials feature aligned arrays or bundles of carbon nanotubes (CNTs) whose mechanical properties are partially determined by the van der Waals interactions between adjacent tubes. Of particular interest in this paper are instances where the resulting interaction between a pair of CNTs often produces a fork-like structure. The mechanical properties of this structure are noticeably different from those for isolated individual CNTs. In particular, while one anticipates buckling phenomena in the forked structure, an adhesion instability may also be present. New criteria for buckling and adhesion instabilities in fork-like structures are presented in this paper. The criteria are illuminated with a bifurcation analyses of the response of the fork-like structure to applied compressive and shear loadings.

show abstract

“…Assuming that the Euler-Lagrange differential equation is satisfied by θ * (s), and given that the Weierstrass and Erdmann-Weierstrass conditions are satisfied, it is well-known that satisfaction of either J1 (where applicable) 5 or L1 is sufficient for θ * (s) to be a weak minimum of I (see, e.g., [2,6]). …”

Section: Other Necessary and Sufficient Conditionsmentioning

confidence: 99%

“…Furthermore, the absence of a solution to the Riccati equation for the free-free strut is a clear indication of the degenerate nature of this case and the need for a modified treatment of the type proposed recently by Manning [16] (see also Kuznetsov and Levyakov [10,13]). We close the paper with a discussion of future applications to Legendre's treatment to the stability of branched equilibria of elastic rods such as those discussed in [5,19].…”

mentioning

confidence: 99%

On Stability Analyses of Three Classical Buckling Problems for the Elastic Strut

O’Reilly

Peters

2011

J Elast

View full text Add to dashboard Cite

It is common practice in analyses of the configurations of an elastica to use Jacobi's necessary condition to establish conditions for stability. Analyses of this type date to Born's seminal work on the elastica in 1906 and continue to the present day. Legendre developed a treatment of the second variation which predates Jacobi's. The purpose of this paper is to explore Legendre's treatment with the aid of three classical buckling problems for elastic struts. Central to this treatment is the issue of existence of solutions to a Riccati differential equation. We present two different variational formulations for the buckling problems, both of which lead to the same Riccati equation, and we demonstrate that the conclusions from Legendre and Jacobi's treatments are equivalent for some sets of boundary conditions. In addition, the failure of both treatments to classify stable configurations of a free-free strut are contrasted.

show abstract

Modeling the growth and branching of plants: A simple rod-based model

Cited by 25 publications

References 47 publications

On the growth and form of shoots

On the growth and form of shoots

On Adhesive and Buckling Instabilities in the Mechanics of Carbon Nanotubes Bundles

On Stability Analyses of Three Classical Buckling Problems for the Elastic Strut

Contact Info

Product

Resources

About