Studies On Spiral Wave And Colloid Dynamics

In this thesis, we investigated spiral pattern and colloid dynamics under the influence of external electric field. There are seven chapters including a general introduction in chapter 1; a review of progress in chapter 2; From chapter 3 to 7, we report our main results:the investigation of drift behavior induced by polarized electric field in chapter 3; studies on controlling spiral breakup by ac electric field in chapter 4; Elimination of second Hopf Bifurcation by phase synchronization induced by polarized electric field in chapter 5; simulations of depinning properties in colloid systems in chapter 6; presentation of phase diagram depending on driving force and strength of pins in Chapter 7; investigation of dynamical phase transition induced by temperature in chapter 8.The topic of spiral waves has attracted wide interests in physics, chemistry, biology and other fields of natural science. In particular, they play an essential role in heart diseases such as arrhythmia and fibrillation. Thus, how to eliminate and control spiral waves is important for practical applications. Studies on spiral waves and turbulence in physics will greatly contribute to the development of cardiology in preventing and controlling the cardiac arrhythmias and fibrillation.There has been considerable interest in colloidal crystals during the past two decades, since they provide ideal model systems for studies of various problems in material science, physical chemistry, and condensed matter physics. Especially, it shows a rich variety of patterns and phases under the influence of electric field. Thus, it attracts widely attention. We studied the dynamics of two-dimensional colloids system on a disordered substrate using Langevin simulation.In the light that both the polarised electric field and the spiral waves possess rotation symmetry, we investigated the drift behavior of spiral waves under the influence of a polarized electric field for the first time. Numerical simulations show that the drift velocity of spiral tip can be controlled by changing the polarization-mode of the polarized electric field and some interesting drift phenomena are observed. When the electric field is circularly polarized and its rotation follows that of the spiral, the drift speed of spiral tip reaches its maximal value. On the contrary, opposite rotation between spiral and electric field locks the drift of spiral tip. The drift direction can also be tuned by changing the phase difference of the polarized electric field。The sum of drift angle of two opposite rotating spiral waves at fixed phase differences is equal to kπ+π/2. Analytical results based on the weak deformation approximation are consistent with the numerical results. Since a polarized electric field can be easily applied to practical systems, such as BZ reaction, we expect that our theoretical results will be observed in experiments. Besides the drift of spiral waves, we hope that other effects of the polarized electric field on spiral waves, Turing patterns, etc., will be studied in the future.A new effect induced by ac electric field on spiral is detected for the first time. We apply it as a method to control spiral breakup. The controlling of spiral wave breakup has attracted considerable attention. However, the controlling approach to prevent spiral wave breakup is still poor and open. It is necessary to develop some efficient and practical control schemes. Generally, the influence of electric field is studied widely. Ac field can induce two effects on spiral wave:drift and breakup (far deformation). With suitable amplitude and frequency of the ac electric field, spiral breakup can efficiently be suppressed. The underling mechanism is studied and presented:it is due to the efficient modulation of spiral meandering that prevent spiral breakup. We expect that our theoretical results will be observed in experiments.The phase synchronization between circular polarised electric and spiral eliminates the second Hopf bifurcation. We find the spiral is efficient modulated and become zero phase synchronization with the superimposed circular polarized electric field. The critical value of breakup is increased due to the vanishing of second Hopf bifurcation and tempering of meandering behavior. It is the rotating symmetry of the spiral that favoring the circular polarized electric field and leads to the striking behavior. Varying polarized modes shows that more ideal symmetry lead to higher critical value of breakup. Opposite rotation between spiral and electric field induces the spiral breakup and recover to rigid spiral again.We investigated depinning dynamics of 2D colloid system driven by external field in detail. At First, we studied the role of disorder on substrate. With increasing strength of disorder, we found a sharp crossover from elastic to plastic depinning associated with the order-disorder state transition and substantial increase of the depinning force. In the elastic regime, no peaks are found in the differential curves of the velocity-force dependence (VFD) and the transverse motion is forbidden. In addition, the scaling relationship between velocity and force is found to be valid with exponent about 1.0. In inhomogeneous depinning regimes, history dependence of depinning process is found. Peaks in the differential curves of VFD and transverse diffusion occur above depinning.We studied the influence of colloid-colloid interaction on depinning behavior. Through tuning the interparticle potential, we also can observe the disorder-order transition. Thus, it is possible to crystallize colloid system by strengthen interaction of colloid particles in experiments. The underlying mechanism of dynamics properties mentioned above is proposed:it is the competition of several types of force on colloid system that leads to the softness and fracture of colloid lattice which adjusts individual colloid particles to the lowest energy positions, inducing a series of interesting phenomena.We proposed the phase diagram depending on pinning strength and driving force. For weak disorder strength, the colloid systems form an ordered state and depin into moving Bragg glass phase by increasing driving force. Increasing the strength of pinning, a transition to a semtic flow phase occurs where longitudinal order is lost while transverse order remains. Four dynamic phases are found in strong pinning regime upon increasing applied driving force:creeping disordered, plastic flow, smectic flow, and moving Bragg glass phase.We found a dynamical phase transition from the moving liquid to the moving smectic at high drivingforces by decreasing the temperature. The dynamical properties in high driving force region are still less known. Thus, we considered influence of the temperature on the dynamical behavior of 2D colloids at high velocity for the first time. Across the observed dynamical transition, peak effect occurs in the dynamical critical driving force, accompanied by a clear crossing of velocity-force dependence curves.