We study a model for a thin liquid film dewetting from a periodic heterogeneous substrate (template). The amplitude and periodicity of a striped template heterogeneity necessary to obtain a stable ...periodic stripe pattern, i.e. pinning, are computed. This requires a stabilization of the longitudinal and transversal modes driving the typical coarsening dynamics during dewetting of a thin film on a homogeneous substrate. If the heterogeneity has a larger spatial period than the critical dewetting mode, weak heterogeneities are sufficient for pinning. A large region of coexistence between coarsening dynamics and pinning is found.
Physica D 160, 127 (2001) The transition from phase chaos to defect chaos in the complex
Ginzburg-Landau equation (CGLE) is related to saddle-node bifurcations of
modulated amplitude waves (MAWs). ...First, the spatial period P of MAWs is shown
to be limited by a maximum P_SN which depends on the CGLE coefficients;
MAW-like structures with period larger than P_SN evolve to defects. Second,
slowly evolving near-MAWs with average phase gradients $\nu \approx 0$ and
various periods occur naturally in phase chaotic states of the CGLE. As a
measure for these periods, we study the distributions of spacings p between
neighboring peaks of the phase gradient. A systematic comparison of p and P_SN
as a function of coefficients of the CGLE shows that defects are generated at
locations where p becomes larger than P_SN. In other words, MAWs with period
P_SN represent ``critical nuclei'' for the formation of defects in phase chaos
and may trigger the transition to defect chaos. Since rare events where p
becomes sufficiently large to lead to defect formation may only occur after a
long transient, the coefficients where the transition to defect chaos seems to
occur depend on system size and integration time. We conjecture that in the
regime where the maximum period P_SN has diverged, phase chaos persists in the
thermodynamic limit.
Phys. Rev. Lett. 85, 86 (2000) The mechanism for transitions from phase to defect chaos in the
one-dimensional complex Ginzburg-Landau equation (CGLE) is presented. We
introduce and describe periodic ...coherent structures of the CGLE, called
Modulated Amplitude Waves (MAWs). MAWs of various period P occur naturally in
phase chaotic states. A bifurcation study of the MAWs reveals that for
sufficiently large period P, pairs of MAWs cease to exist via a saddle-node
bifurcation. For periods beyond this bifurcation, incoherent near-MAW
structures occur which evolve toward defects. This leads to our main result:
the transition from phase to defect chaos takes place when the periods of MAWs
in phase chaos are driven beyond their saddle-node bifurcation.
We study a recent model for calcium signal transduction. This model displays spiking, bursting and chaotic oscillations in accordance with experimental results. We calculate bifurcation diagrams and ...study the bursting behaviour in detail. This behaviour is classified according to the dynamics of separated slow and fast subsystems. It is shown to be of the Fold-Hopf type, a type which was previously only described in the context of neuronal systems, but not in the context of signal transduction in the cell.
The transition from phase chaos to defect chaos in the complex Ginzburg-Landau equation (CGLE) is related to saddle-node bifurcations of modulated amplitude waves (MAWs). First, the spatial period P ...of MAWs is shown to be limited by a maximum P_SN which depends on the CGLE coefficients; MAW-like structures with period larger than P_SN evolve to defects. Second, slowly evolving near-MAWs with average phase gradients \(\nu \approx 0\) and various periods occur naturally in phase chaotic states of the CGLE. As a measure for these periods, we study the distributions of spacings p between neighboring peaks of the phase gradient. A systematic comparison of p and P_SN as a function of coefficients of the CGLE shows that defects are generated at locations where p becomes larger than P_SN. In other words, MAWs with period P_SN represent ``critical nuclei'' for the formation of defects in phase chaos and may trigger the transition to defect chaos. Since rare events where p becomes sufficiently large to lead to defect formation may only occur after a long transient, the coefficients where the transition to defect chaos seems to occur depend on system size and integration time. We conjecture that in the regime where the maximum period P_SN has diverged, phase chaos persists in the thermodynamic limit.
The mechanism for transitions from phase to defect chaos in the one-dimensional complex Ginzburg-Landau equation (CGLE) is presented. We introduce and describe periodic coherent structures of the ...CGLE, called Modulated Amplitude Waves (MAWs). MAWs of various period P occur naturally in phase chaotic states. A bifurcation study of the MAWs reveals that for sufficiently large period P, pairs of MAWs cease to exist via a saddle-node bifurcation. For periods beyond this bifurcation, incoherent near-MAW structures occur which evolve toward defects. This leads to our main result: the transition from phase to defect chaos takes place when the periods of MAWs in phase chaos are driven beyond their saddle-node bifurcation.
PDF