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The separation of micro and nanoscale colloids is a necessary step in most biological microassay techniques, and is a common practice in microchemical processing. Chemical waves are frequently encountered in biochemical systems driven far from equilibrium. Here, we put forward a strategy for separating small suspending colloids by means of their surfing on substrate chemical wavefronts. The colloids with catalytic activities sensitive to the substrates are activated to show self-propulsion and consequently exhibit a chemotactic response to the traveling wavefronts, which results in their spontaneous separation from the multicomponent complex mixture via self-diffusiophoresis. The dynamics of the process is analyzed through a particle-based simulation. In addition, it is found that separation can be carried out according to particle size. The mechanisms underpinning the chemical and physical separation processes are discussed, and the dependencies on the reaction rate constant and particle size are presented. The results may prove relevant for further experimental and theoretical studies of separation in complex active environments.

The dynamics of chemically powered sphere dimers at the micro- and nano-scales confined in a quasi-two-dimensional geometry are investigated. The dimer consists of a Janus particle and a non-catalytic sphere. A chemical reaction taking place on the catalytic surface of the Janus particle creates asymmetric concentration gradients that give rise to the self-propulsion of both rotation and translation of the dimer. Due to the chemical interactions, ensembles of dimers spontaneously form anti-parallel aligned doublets that exhibit the same rotation direction and lose translational motion. The chirality of the dimer plays an important role in the process of doublet formation. The study displays new collective dynamics and structures when both translational and rotational self-propulsion occur.

Information transmission delay can be widely observed in various systems. Here, we study the dynamics of scroll waves with time-delay propagation among slices in excitable media. Weak time delay induces scroll waves to meander. Through increasing the time delay, we find a series of dynamical transitions. Firstly, the straight filament of a scroll wave becomes twisted. Then, the scroll wave breaks and forms interesting patterns. With long time delay, loosed scroll waves are maintained while their period are greatly decreased. Also, cylinder waves appears. The influences of diffusively coupling strength on the time-delay-induced scroll waves are studied. It is found that the critical time delay characterizing those transitions decreases as the coupling strength is increased. A phase diagram in the diffusive coupling-time delay plane is presented.

The folding and unfolding of the carbon chain, which is the basic constitutional unit of polymers, are important to the performance of the material. However, it is difficult to regulate conformational transition of the carbon chain, especially in an aqueous environment. In this paper, we propose a strategy to regulate the conformational transition of the carbon chain in water based on the all-atom molecular dynamics simulations. It is shown that the unfolded carbon chain will spontaneously collapse into the folded state, while the folded carbon chain will unfold with an external electric field. The regulation ability of the electric field is attributed to the electric field-induced redistribution of interface water molecules near the carbon chain. The demonstrated method of regulating conformational transition of the carbon chain in water in this study provides an insight into regulating hydrophobic molecules in water, and has great potential in drug molecule design and new polymer material development.

Synthetic chemically powered nanomotors possessing the ability of chemotaxis are desirable for target cargo delivery and self-assembly. The chemotactic properties of a sphere dimer motor, composed of linked catalytic and inactive monomers, are studied in a gradient field of fuel. Particle-based simulation is carried out by means of hybrid molecular dynamics/multiparticle collision dynamics. The detailed tracking and motion analysis describing the running and tumbling of the sphere dimer motor in the process of chemotaxis are investigated. Physical factors affecting chemotactic velocity are discussed, and quantitative relations are presented. The influence of the geometry of sphere dimer motors on the chemotactic dynamics is explored, which is beneficial for the design of motors with high sensitivity for detecting the surrounding environment.

Active matter, some of whose constituent elements are active agents that can move autonomously, behaves very differently from matter without such agents. The active agents can self-assemble into structures with a variety of forms and dynamical properties. Swarming, where groups of living agents move cooperatively, is commonly observed in the biological realm, but it is also seen in the physical realm in systems containing small synthetic motors. The existence of diverse forms of self-assembled structures has stimulated the search for new applications that involve active matter. We consider active systems where the agents are synthetic chemically powered motors with various shapes and sizes that operate by phoretic mechanisms, especially self-diffusiophoresis. These motors are able to move autonomously in solution by consuming fuel from their environment. Chemical reactions take place on catalytic portions of the motor surface and give rise to concentration gradients that lead to directed motion. They can operate in this way only if the chemical composition of the system is maintained in a nonequilibrium state since no net fluxes are possible in a system at equilibrium. In contrast to many other active systems, chemistry plays an essential part in determining the properties of the collective dynamics and self-assembly of these chemically powered motor systems. The inhomogeneous concentration fields that result from asymmetric motor reactions are felt by other motors in the system and strongly influence how they move. This chemical coupling effect often dominates other interactions due to fluid flow fields and direct interactions among motors and determines the form that the collective dynamics takes. Since we consider small motors with micrometer and nanometer sizes, thermal fluctuations are strong and cannot be neglected. The media in which the motors operate may not be simple and may contain crowding agents or molecular filaments that influence how the motors assemble and move. The collective motion is also influenced by the chemical gradients that arise from reactions in the surrounding medium. By adopting a microscopic perspective, where the motors, fluid environment, and crowding elements are treated at the coarse-grained molecular level, all of the many-body interactions that give rise to the collective behavior naturally emerge from the molecular dynamics. Through simulations and theory, this Account describes how active matter made from chemically powered nanomotors moving in simple and more complicated media can form different dynamical structures that are strongly influenced by interactions arising from cooperative chemical reactions on the motor surfaces.

In this paper, a novel lattice Boltzmann (LB) model based on the Allen-Cahn phase-field theory is proposed for simulating axisymmetric multiphase flows. The most striking feature of the model is that it enables to handle multiphase flows with large density ratio, which are unavailable in all previous axisymmetric LB models. The present model utilizes two LB evolution equations, one of which is used to solve fluid interface, and another is adopted to solve hydrodynamic properties. To simulate axisymmetric multiphase flows effectively, the appropriate source term and equilibrium distribution function are introduced into the LB equation for interface tracking, and simultaneously, a simple and efficient forcing distribution function is also delicately designed in the LB equation for hydrodynamic properties. Unlike many existing LB models, the source and forcing terms of the model arising from the axisymmetric effect include no additional gradients, and consequently, the present model contains only one non-local phase field variable, which in this regard is much simpler. We further conducted the Chapman-Enskog analysis to demonstrate the consistencies of our present MRT-LB model with the axisymmetric Allen-Cahn equation and hydrodynamic equations. A series of numerical examples, including static droplet, oscillation of a viscous droplet, breakup of a liquid thread, and bubble rising in a continuous phase, are used to test the performance of the proposed model. It is found that the present model can generate relatively small spurious velocities and can capture interfacial dynamics with higher accuracy than the previously improved axisymmetric LB model. Besides, it is also found that our present numerical results show excellent agreement with analytical solutions or available experimental data for a wide range of density ratios, which highlights the strengths of the proposed model., Comment: 50 pages, 7 figure

We study the pair dynamics of two self-propelled sphere dimers in the chemically active medium in which a cubic autocatalytic chemical reaction takes place. Concentration gradient around the dimer, created by reactions occurring on the catalytic sphere surface and responsible for the self-propulsion, is greatly influenced by the chemical activities of the environment. Consequently, the pair dynamics of two dimers mediated by the concentration field are affected. In the particle-based mesoscopic simulation, we combine molecular dynamics (MD) for potential interactions and reactive multiparticle collision dynamics (RMPC) for solvent flow and bulk reactions. Our results indicate three different configurations between a pair of dimers after the collision, i.e., two possible scenarios of bound dimer pairs and one unbound dimer pair. A phase diagram is sketched as a function of the rate coefficients of the environment reactions. Since the pair interactions are the basic elements of larger scale systems, we believe the results may shed light on the understanding of the collective dynamics.

In this paper, a wetting boundary scheme used to describe the interactions among ternary fluids and solid is proposed in the framework of the lattice Boltzmann method. This scheme for three-phase fluids can preserve the reduction consistency property with the diphasic situation such that it could give physically relevant results. Combining this wetting boundary scheme and the lattice Boltzmann (LB) ternary fluid model based on the multicomponent phase-field theory, we simulated several ternary fluid flow problems involving solid substrate, including the spreading of binary drops on the substrate, the spreading of a compound drop on the substrate, and the shear of a compound liquid drop on the substrate. The numerical results are found to be good agreement with the analytical solutions or some available results. Finally, as an application, we use the LB model coupled with the present wetting boundary scheme to numerically investigate the impact of a compound drop on a solid circular cylinder. It is found that the dynamics of a compound drop can be remarkably influenced by the wettability of the solid surface and the dimensionless Weber number., Comment: 32 pages, 14 figures

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A novel forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and Spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocities in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. At last, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomenon of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature., Comment: 31 pages, 8 figures

Based on a reactive multiple particle collision method, we construct a mesoscopic dynamics model to simulate chemical system. The validity of the reactive multiple particle collision method under various conditions in a double-feedback bi-stable chemical system is studied. Then, we extend it to simulate diffusion-limited reactions with fast reaction rate in cellular environment. Using the improved method, we observe bi-stable behavior with randomly distributed reactants and spatial domain separation of opposite phases. The particle-based mesoscopic method is computationally efficient, although hydrodynamic interactions and fluctuation are both properly accounted for. Stochastic effects shown to play dominant roles in biochemical dynamics are also considered. The improved method could be used to explore a variety of reactions with disparate scale of reaction rates.

We study the behavior of spiral wave under the driving of a rotating electric field. The rotating electric field can drive a spiral wave to be synchronous, depending on four factors: its frequency and amplitude, chirality, and polarized modes. Rotation-synchronization characterized by the rotating direction is focused on. We discuss the behavior of synchronization, such as the dependence of angle-differences between the spiral tip and the electric field on ratio of frequency, the influences of different polarized modes of the electric field, the radius of synchronous spiral wave, and so on. A circularly polarized electric fields (CPEF) can suppress meandering spiral to rigid one and prevent breakup of spiral in medium with low excitability. The phase diagram describing the controllable region in excitability-period plane is presented. The influences of polarized modes of electric field on minimum excitability of medium are also studied.

The collective behavior of synthetic micro- and nano-scale motors powered by catalytic reactions has been an active research area for understanding the fundamental principles in active matter as well as their prominent applications. In many situations, small motors should operate in out-of-equilibrium complex chemically reacting media. By making use of particle-based simulations, we study the collective dynamics of chemically powered sphere-dimer motors in a chemically oscillating medium which can supply fuels to the motors and remove the products they produce. In collections of such motors, the interactions among individual motors that arise from concentration gradients and hydrodynamic coupling, are greatly influenced by the properties of the oscillation. It is shown how oscillations of the concentrations in chemical species in the environment give rise to a periodic dispersion-aggregation transition of motor clusters. The susceptibility of the transition to the oscillation is found to be changed by the manner of fuel supplies, from the time-delay response in a harmonic oscillating medium to the synchronous response in a bistable medium. The dynamical process of clusters formation, which exhibits different regimes involving propulsive and diffusive behaviors, as well as the structure of transiently formed clusters, is analyzed. The dependence of dispersion-aggregation transition on the dimer density and the frequency of periodic oscillation is presented in a phase diagram. The results presented here will contribute to the applications when an ensemble of dimers performs their tasks in complex chemical media.

In this paper, we present a formulas of rational ratios between the frequency of external stimulus and its paced target waves, considering the existence of the absolute refractory period and the relative refractory period. Based on this, we design a self-sustained high-frequency target waves by feeding back few periphery field points to the center to responsibly play the role of source for pacemaker. Such constructed target waves, to all appearances, are shown as a repetition of their initial condition. We explore further in application that those feedback-sustained targets can eliminate both a freely rotating spiral waves and a pinned ones only if frequencies, feedback lengths and radius of obstacles are appropriately chosen. After feedback stimuli are removed, the system eventually returns to the rest state.

The dynamics of a scroll wave in an excitable medium with gradient excitability is studied in detail. Three parameter regimes can be distinguished by the degree of gradient. For a small gradient, the system reaches a simple rotating synchronization. In this regime, the rigid rotating velocity of spiral waves is maximal in the layers with the highest filament twist. As the excitability gradient increases, the scroll wave evolutes into a meandering synchronous state. This transition is accompanied by a variation in twisting rate. Filament twisting may prevent the breakup of spiral waves in the bottom layers with a low excitability with which a spiral breaks in a 2D medium. When the gradient is large enough, the twisted filament breaks up, which results in a semi-turbulent state where the lower part is turbulent while the upper part contains a scroll wave with a low twisting filament.

The drift of rigidly rotating spiral waves in an excitable medium induced by synchronous and asynchronous mechanical deformation is investigated numerically and analytically. The resonant drift of spiral waves induced by a mechanical deformation with ω = ω0 and ω = 3ω0 is observed. At ω = ω0, synchronous and greatest degree of asynchronous mechanical deformations are specially investigated. For the case ω = 3ω0, synchronous mechanism deformation locks the spiral while decreasing of degree of synchronization increases the drift velocity. We derive an approximate but explicit formula of the spiral drift velocity and direction which is consistent with the numerical results.

Very small synthetic motors that use chemical reactions to drive their motion are being studied widely because of their potential applications, which often involve active transport and dynamics on nanoscales. Like biological molecular machines, they must be able to perform their tasks in complex, highly fluctuating environments that can form chemical patterns with diverse structures. Motors in such systems can actively assemble into dynamic clusters and other unique nonequilibrium states. It is shown how chemical patterns with small characteristic dimensions may be utilized to suppress rotational Brownian motions of motors and guide them to move along prescribed paths, properties that can be exploited in applications. In systems with larger pattern length scales, domains can serve as catch basins for motors through chemotactic effects. The resulting collective motor dynamics in such confining domains can be used to explore new aspects of active particle collective dynamics or promote specific types of active self-assembly. More generally, when chemically self-propelled motors operate in far-from-equilibrium active chemical media the variety of possible phenomena and the scope of their potential applications are substantially increased.

We study pattern formation induced by a spiral wave developing from heterogeneities in an excitable medium. Turbulence can be suppressed by a spiral wave from the heterogeneity, forming multiple coexistent systems of regular geometrical patterns. We find that the types of these patterns depend critically on the degree of heterogeneity. The underlying mechanism is due to dispersion relation which is characterized by excitability.

Influences of periodic mechanical deformation (PMD) on spiral breakup that results from Doppler instability in excitable media are investigated. We present a new effect: a high degree of homogeneous PMD is favored to prevent the low-excitability-induced breakup of spiral waves. The frequency and amplitude of PMD are also significant for achieving this purpose. The underlying mechanism of successful control is also discussed, which is believed to be related to the increase of the minimum temporal period of the meandering spiral when the suitable PMD is applied.

The growth mechanism and characteristic ordered patterns of iron ( Fe ) films deposited on the silicone oil surfaces by a DC-magnetron sputtering method are presented in this paper. It is found that as the film thickness increases, the iron atoms deposited on the oil surface first form compact clusters, then transfer to ramified aggregates and web-shaped structures, and finally form a continuous iron film. The average branch width of the ramified aggregates is about 0.34 μm, which is almost independent of the sputtering power, i.e., the deposition rate. In the continuous iron films, large spatially disk-shaped patterns are observed, which result from spontaneous ordered organization of the iron atoms and atomic clusters driven by the internal stress in this nearly free sustained film system.

The growth mechanism and characteristic ordered patterns of iron (Fe) films deposited on the silicone oil surfaces by a DC-magnetron sputtering method are presented in this paper. It is found that as the film thickness increases, the iron atoms deposited on the oil surface first form compact clusters, then transfer to ramified aggregates and web-shaped structures, and finally form a continuous iron film. The average branch width of the ramified aggregates is about 0.34 μm, which is almost independent of the sputtering power, i.e., the deposition rate. In the continuous iron films, large spatially disk-shaped patterns are observed, which result from spontaneous ordered organization of the iron atoms and atomic clusters driven by the internal stress in this nearly free sustained film system.

A nearly free sustained aluminum (Al) film system has been successfully fabricated by vapor phase deposition of Al atoms on silicone oil surfaces and an unusual type of ordered patterns at the micrometer scale has been systematically studied. The ordered patterns are composed of a large number of parallel key-shaped domains and possess a sandwiched structure. The nucleation and growth of the patterns are very susceptible to the growth period, deposition rate, nominal film thickness and location of the film. The experiment shows that the ordered patterns are induced by the residual compressive stress in the film owing to contraction of the liquid surface after deposition. The appearance of these stress relief patterns generally represents the stress distribution in the nearly free sustained Al films, which mainly results from the characteristic boundary condition and the nearly zero adhesion of the solid–liquid interface.

In this paper, we present the spontaneous formation of an unusual type of ordered structures in thin metal film systems deposited on silicon oil surfaces by a thermal evaporation method. These structures are composed of a large number of parallel rectangular-shaped domains and exhibit anti-symmetric characteristic. The experiment shows that thin solid films can move freely on liquid surfaces due to the near-zero adhesion of the solid–liquid interface, resulting in superposition of the films and formation of the ordered structures. Compressive stress gradient in the films is shown to be the driving force for self-organization. All characteristics of the ordered structures are discussed in detail based on special mechanical behaviors of these near-free sustained films.

In this paper, we present the spontaneous formation of an unusual type of ordered structures in thin metal film systems deposited on silicon oil surfaces by a thermal evaporation method. These structures are composed of a large number of parallel rectangular-shaped domains and exhibit anti-symmetric characteristic. The experiment shows that thin solid films can move freely on liquid surfaces due to the near-zero adhesion of the solid–liquid interface, resulting in superposition of the films and formation of the ordered structures. Compressive stress gradient in the films is shown to be the driving force for self-organization. All characteristics of the ordered structures are discussed in detail based on special mechanical behaviors of these near-free sustained films.

The Young's modulus ( E ) of Cu–Ni sheathed MgB 2 monofilament tape was measured using electric method. It is about 8.05 × 10 10 Pa, the same order of Cu and its alloys. We found that the lower E value of the MgB 2 component seemed to relate to the lower filament density. The benefits of pre-compression in filaments were discussed in terms of improving stress distribution in the wires and tapes during winding and operation of superconducting magnets. The magnetic field dependence of J c was investigated on the sample subjected to various strain levels through bending with different radii at 4.2 K.

Using Langevin simulations, we numerically investigate the dynamics phases of driven two-dimensional colloids subject to randomly distributed point-like pinning centers and present phase diagram. For weak disorder strength, the colloid systems form an ordered state and depin into moving Bragg glass phase by increasing driving force. With increasing the strength of pinning, we find a sharp crossover from elastic to plastic depinning where a substantial increase in the depinning force is observed, accompanied by an order to disorder state transition. Increasing the strength of pinning further, a transition to a smectic 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.

Using Langevin simulations, we investigate numerically the dynamics of driven 2D colloids on disordered substrate. For weak disorder or strong colloid–colloid interaction, the colloid systems form an ordered state and depin elastically. The scaling relationship between velocity and applied drive force is obtained. With decreasing the strength of particle–particle interaction as well as increasing substrate strength, we find a sharp crossover from elastic to plastic depinning where a substantial increase in the depinning force is observed, accompanied by an order to disorder state transition. In inhomogeneous depinning regime, history dependence of depinning process is found. Furthermore, peaks in the differential curves of velocity force dependence and obvious transverse diffusion above depinning start to appear.

In a generic model of excitable media, we simulate wave emission from a heterogeneity (WEH) induced by an electric field. Based on the WEH effect, a rotating electric field is proposed to terminate existed spatiotemporal turbulence. Compared with the effects resulted by a periodic pulsed electric field, the rotating electric field displays several improvements, such as lower required intensity, emitting waves on smaller obstacles, and shorter suppression time. Furthermore, due to rotation of the electric field, it can automatically source waves from the boundary of an obstacle with small curvature.

The termination of pinned spirals on a defect by means of local stimuli is studied. On a completely unexcitable defect, the elimination process is discussed and its corresponding mechanism is presented. Especially, the mechanism of unpinning spirals on a partially unexcitable defect, which has not been investigated so far, is explored. With fixed pacing frequency ω L , there exists a maximal radius R max above which the pinned spiral cannot be removed. It is found that the value of R max does not increase as ω L in a dynamical regime, forming a platform in the curves. Based on analyzing the dispersion relation on the spiral tip around the obstacle, the underlying mechanism is clarified. Also, it is found that when multiple spirals are pinned, the value of R max decreases on a partially unexcitable defect while the change is very slight on a completely unexcitable one.

A mesoscopic model is set up to study the predator-prey-like phenomenon between two chemically active objects. A target sphere (T) secretes chemical signal molecules that are detected and traced by a hunter sphere (H). The distribution of signal molecules diffusing around the target is simulated and analyzed. The chemotactic behavior of the hunter along the gradient of signal molecules results in the capture of the target. The dependences of capture time tc on different conditions are focused on. It is found that the values of capture time rely on their initial separation d as a power law tc ∞ dα. The exponent α depends on decay rate of signal molecules. The capture time increases with the decay rate. The increases of target and hunter size both lead to the decrease of the capture time, which is also shown by the power law behavior. The detailed chemotaxis process is investigated.

Control of turbulence in two kinds of typical heterogeneous excitable media by applying a combined method is investigated. It is found that local-low-amplitude and high-frequency pacing (LHP) is effective to suppress turbulence if the deviation of the heterogeneity is minor. However, LHP is invalid when the deviation is large. Studies show that an additional radial electric field can greatly increase the efficiency of LHP. The underlying mechanisms of successful control in the two kinds of cases are different and are discussed separately. Since the developed strategy of combining LHP with a radial electric field can terminate turbulence in excitable media with a high degree of inhomogeneity, it has the potential contribution to promote the practical low-amplitude defibrillation approach.

We study the nonequilibrium dynamics of colloidal system with short-range depletion attraction and screened electrostatic repulsion on a disordered substrate. We find a growth-melting process of the clusters as the temperature is increased. By strengthening the screened electrostatic repulsion, a depinning transition from moving cluster to plastic flow is observed, which is characterized by a peak in threshold depinning force. The corresponding phase diagram is then mapped out. Due to the influences of disorder from substrate, the clusters are polarized by the strong external force, accompanied by the appearance of interesting orientational order parallel to the force and translational order perpendicular to the force. Under the condition of strong external force, the influences of density of pins and temperature are also studied.

We study analytically and numerically the anomalous diffusion across periodically modulated parabolic potential within Langevin and Fokker-Planck descriptions. We find that the probability of particles passing over the saddle is affected strikingly by the periodical modulation with average zero bias. Particularly, the initial phase plays an important role in the modulation effect. The effect of the correlation time of external Ornstein-Uhlenbeck noise on dynamical process is also discussed. A reduction in overpassing probability is observed due to finite correlation time.

Suppression of spiral and turbulence in inhomogeneous media due to local heterogeneity with higher excitability is investigated numerically. When the inhomogeneity is small, control tactics by boundary periodic forcing (BPF) is effective against the existing spiral and turbulence. When the inhomogeneity of excitability is large, a rotating electric field (REF) is utilized to "smooth" regional heterogeneity based on driven synchronization. Consequently, a control approach combining BPF with REF is proposed to suppress the spiral and turbulence. The underlying mechanism of successful suppression is discussed in terms of dispersion relation.

Synchronization of a spiral by a circularly polarized electric field (CPEF) in reaction-diffusion systems is investigated since they both possess rotation symmetry. It is found that spirals in different regimes (including rigidly rotating, meandering, and drifting spirals) can be forced to be rigidly rotating ones by CPEFs. Moreover, the rotational frequency of the entrained spiral is found to be synchronized with the frequency of the electric field in a ratio of 1:1.

The motion of spiral waves in excitable media driven by a weak pacing around the spiral tip is investigated numerically as well as theoretically. We presented a Bifurcations diagram containing four types of the spiral motion induced by different frequencies of pacing: rigidly rotating, inward-petal meandering, resonant drift, and outward-petal meandering spiral. Simulation shows that the spiral resonantly drifts when the frequency of pacing is close to that of the spiral rotation. We also find that the speed and direction of the drift can be efficiently controlled by means of the strength and phase of the local pacing, which is consistent with analytical results based on the framework of the weak deformation approximation.

The control of spiral breakup due to Doppler instability is investigated. It is found that applying an alternating advective field with suitable amplitude and period can prevent the breakup of spiral waves. Further numerical simulations show that the growing meandering behavior of a spiral tip caused by decreasing the excitability of the medium can be efficiently suppressed by the alternating advective field, which inhibits the breakup of spiral waves eventually.