144
4. SIMULATING GROWTH AND FORM
The body diameter of these cells is within the range 10. 106 m-20 . 106 m.
They estimate the value of D, in which an estimate of the swimming speed
of the individual cells is also included, at 2.5' 108 rrr's'". In our model, simulation of nutrient distributions representing Chlamydomonas suspensions
would require a Pe number of 600000.
The objects generated with the k(c) · (1- i(c»h 2 ( •• ) model (4.30) in
which the nutrient-driven growth is regulated by a simple suppression mechanism, shown in Fig. 4.49, differ in several aspects from the objects formed
in a process exclusively driven by the supply of nutrients (Fig.4.41). In
Fig. 4.49b, where there is a relatively low decay rate of the suppressing agent
(decay_isomone = 0.01)compared with Fig. 4.49a (decay_isomone =0.1), this
difference is particularly visible. The simulated form, when compared with
the object shown in Fig. 4.41 for the same Pe number (Pe = 3.0), has become
somewhat more regular. The branches tend to grow more upwards, away
from the substrate, since the older part of the object produces relatively more
growth-suppressing agent (see also Fig. 4.48). Although the objects shown
in Fig. 4.49 represent only a few realizations and a further, systematic exploration for different parameter settings (various settings for decay_isomone,
delay_isomone, and Pe numbers) is required, this demonstrates the important role of possible regulation mechanisms. Compared with the growth
forms of actual stony corals (see for example Figs. 2.39 and 3-18) where an
isomone regulation mechanism might playa fundamental role in the emergence of colony shapes with a highly regular branch spacing, the objects in
Fig. 4.49 do not show an obvious regular branch formation. As mentioned
above in the discussion on the k(c) · h 2 ( •• ) objects, a poss ible explanation
for this is that growth velocities in a growth layer depend only to a limited
extent on the previous growth velocities.
4-7 Gastrovascular Dynamics of Hydractiniid Hydrozoans
In Sect. 2.2.3 the characteristics of fluid transport in the gastrovascular system
and redox chemistry were identified as the physiological mechanisms in colonial hydrozoans that control morphological plasticity. As shown in Fig. 2.27
hydractiniid polyps prior to feeding, or long after regurgitation, behave simply. Contractions are infrequent, they lack periodicity, and the amplitude of
volume exchange with the stolon is small. The behaviors of polyps between
ingestion and regurgitation can be classified into three distinct phases. These
phases of behavior reflect differing input-output relationships between the
polyp and either the external (via the mouth) or internal (via the polypstolon junction) environment. Moreover, these phases carry the signatures
of characteristic dynamical behavior that can be expressed in terms of frequencies and amplitudes of polyp and stolon oscillations (Dudgeon et al.
1999). Wagner et al. (1998) used this conceptualization of post-feeding behavior to develop a model of the following ordinary differential equations to
characterize the dynamical behavior of a single isolated polyp :
~: = !s(s, u)
dx = xgtn, x
2 , f ) - y
dt
dn = !n(S, n)
dt
dy = yg(n,x 2 , f ) + x
dt
4. SIMULATING GROWTH AND FORM
The body diameter of these cells is within the range 10. 106 m-20 . 106 m.
They estimate the value of D, in which an estimate of the swimming speed
of the individual cells is also included, at 2.5' 108 rrr's'". In our model, simulation of nutrient distributions representing Chlamydomonas suspensions
would require a Pe number of 600000.
The objects generated with the k(c) · (1- i(c»h 2 ( •• ) model (4.30) in
which the nutrient-driven growth is regulated by a simple suppression mechanism, shown in Fig. 4.49, differ in several aspects from the objects formed
in a process exclusively driven by the supply of nutrients (Fig.4.41). In
Fig. 4.49b, where there is a relatively low decay rate of the suppressing agent
(decay_isomone = 0.01)compared with Fig. 4.49a (decay_isomone =0.1), this
difference is particularly visible. The simulated form, when compared with
the object shown in Fig. 4.41 for the same Pe number (Pe = 3.0), has become
somewhat more regular. The branches tend to grow more upwards, away
from the substrate, since the older part of the object produces relatively more
growth-suppressing agent (see also Fig. 4.48). Although the objects shown
in Fig. 4.49 represent only a few realizations and a further, systematic exploration for different parameter settings (various settings for decay_isomone,
delay_isomone, and Pe numbers) is required, this demonstrates the important role of possible regulation mechanisms. Compared with the growth
forms of actual stony corals (see for example Figs. 2.39 and 3-18) where an
isomone regulation mechanism might playa fundamental role in the emergence of colony shapes with a highly regular branch spacing, the objects in
Fig. 4.49 do not show an obvious regular branch formation. As mentioned
above in the discussion on the k(c) · h 2 ( •• ) objects, a poss ible explanation
for this is that growth velocities in a growth layer depend only to a limited
extent on the previous growth velocities.
4-7 Gastrovascular Dynamics of Hydractiniid Hydrozoans
In Sect. 2.2.3 the characteristics of fluid transport in the gastrovascular system
and redox chemistry were identified as the physiological mechanisms in colonial hydrozoans that control morphological plasticity. As shown in Fig. 2.27
hydractiniid polyps prior to feeding, or long after regurgitation, behave simply. Contractions are infrequent, they lack periodicity, and the amplitude of
volume exchange with the stolon is small. The behaviors of polyps between
ingestion and regurgitation can be classified into three distinct phases. These
phases of behavior reflect differing input-output relationships between the
polyp and either the external (via the mouth) or internal (via the polypstolon junction) environment. Moreover, these phases carry the signatures
of characteristic dynamical behavior that can be expressed in terms of frequencies and amplitudes of polyp and stolon oscillations (Dudgeon et al.
1999). Wagner et al. (1998) used this conceptualization of post-feeding behavior to develop a model of the following ordinary differential equations to
characterize the dynamical behavior of a single isolated polyp :
~: = !s(s, u)
dx = xgtn, x
2 , f ) - y
dt
dn = !n(S, n)
dt
dy = yg(n,x 2 , f ) + x
dt