JEB desktop wallpaper calendar 2016

JEB desktop wallpaper calendar 2016

The mechanics of explosive dispersal and self-burial in the seeds of the filaree, Erodium cicutarium (Geraniaceae)
Dennis Evangelista, Scott Hotton, Jacques Dumais

SUMMARY

The filaree (Erodium cicutarium), a small, flowering plant related to geraniums, possesses a unique seed dispersal mechanism: the plant can fling its seeds up to half a meter away; and the seeds can bury themselves by drilling into the ground, twisting and untwisting in response to changes in humidity. These feats are accomplished using awns, helical bristles of dead but hygroscopically active tissue attached to the seeds. Here, we describe the kinematics of explosive dispersal and self-burial based on detailed high-speed and time-lapse videos. We use these observations to develop a simple mechanical model that accounts for the coiling behavior of the awn and allows comparison of the strain energy stored in the awn with the kinetic energy at launch. The model is used to examine tradeoffs between dispersal distance and reliability of the dispersal mechanism. The mechanical model may help in understanding the invasive potential of this species and provides a framework for examining other evolutionary tradeoffs in seed dispersal mechanisms among the Geraniaceae.

FOOTNOTES

  • LIST OF SYMBOLS AND ABBREVIATIONS

    A
    reference area (m2)
    b
    section width (m)
    b
    unit binormal vector in Frenet equations
    CD
    drag coefficient (dimensionless
    D
    maximum awn diameter (m)
    e
    base for natural logarithms (2.71828)
    E
    Young's modulus (Pa)
    EI
    flexural stiffness (N m2)
    FD
    drag force (N)
    G
    shear modulus
    Gc
    work of fracture (J m–2)
    g
    gravitational acceleration (9.81 m s–2)
    h
    section height (m)
    h0
    initial height (m)
    I
    second moment of area (m4)
    L
    awn height (m)
    m
    mass (kg)
    M
    bending moment (N m)
    n
    number of turns
    p
    unit principal normal vector in Frenet equations
    r=(r, θ, z)
    cylindrical coordinates of awn finite element, radial (m), tangential (rad), and vertical (m), parameterized over awn coordinates [0,1] or arc length s (m)
    Re
    Reynolds number (dimensionless)
    RI
    range index (dimensionless)
    s
    arc length along awn neutral axis (m)
    t
    position, from proximal to distal, along awn neutral axis [0,1]
    td
    time (s) in desiccation model
    u
    tangential vector of awn finite element, pointing along neutral axis, in Frenet equations
    u
    horizontal component of velocity (m s–1)
    Uelastic
    elastic strain energy (J)
    Ulaunch
    energy at launch (J)
    Usurf
    surface energy of crack (J)
    v
    vertical component of velocity (m s–1)
    vT
    terminal velocity during drop test (m s–1)
    Embedded Image
    applied wetting or drying, [0,1], in desiccation model
    xd
    dessication factor [0,1]
    α
    awn spiral angle (rad)
    β
    launch angle (rad)
    δrecoil
    fraction of energy lost to recoil during launch, dimensionless
    δrotation
    fraction of energy lost to rotation during launch, dimensionless
    κ
    curvature in Frenet equations (m–1)
    ν
    Poisson's ratio (dimensionless
    ξ
    dummy variable of integration
    ρ
    air density (1.2 kg m–3)
    τ
    torsion in Frenet equations (dimensionless)
    τd
    time constant for wetting/drying (s) in desiccation model
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