Three-dimensional interfacial wave theory of dendritic growth： （Ⅰ）. multiple variables expansion solutions

Dendritic pattern formation at the interface between liquid and solid is a commonly observed phenomenon in crystal growth and solidification process. The theoretical investigation of dendritic growth is one of the most profound and highly challenging subjects in the broad areas of interfacial pattern formation, condensed matter physics and materials science, preoccupying many researchers from various areas. Some longstanding key issues on this subject finally gained a breakthrough in the late of last century, via the `{Interfacial Wave} (IFW) Theory' on the ground of systematical global stability analysis of the basic state of dendritic growth. The original form of the IFW theory mainly focus on the investigation of various axi-symmetric unsteady perturbed modes solutions around the axi-symmetric basic state of system of dendritic growth. In reality, the system may allow various non-axi-symmetric, unsteady perturbed states. Whether or not the system of dendritic growth allows some growing non-axi-symmetric modes? Will the stationary dendritic pattern be destroyed by some of such non-axi-symmetric modes? Or, in one word, what is the stability property of the system, once the non-axi-symmetric modes can be evoked? The answers for these questions are important for the solid foundation of IFW theory. The present work attempts to settle down these issues and develop a three-dimensional (3D) interfacial wave theory of dendritic growth. Our investigations verify that dendritic growth indeed allows a discrete set of non-axi-symmetric unstable global wave modes, which gives rise to a set of multiple arms spiral waves propagating along the Ivantsov's paraboloid.     

Multistable selection equations of pattern formation type in the case of inhomogeneous growth rates: With applications to two-dimensional assignment problems

We study the stability of solutions of a particular type of multistable selection equations proposed by Starke, Schanz and Haken in the case of an inhomogeneous spectrum of growth parameters. We determine how the stability of feasible solutions depends on the inhomogeneity of the spectrum. We show that the strength of the competitive interaction between feasible solutions can act as a control parameter that induces bifurcations reducing the degree of multistability.     

Flow waves of hierarchical pattern formation induced by chemical waves: The birth, growth and death of hydrodynamic structures

We introduce a short review of chemically driven convection together with a series of our experiments on hydrodynamic instabilities induced by chemical waves excited in the batch reactor of a Belousov-Zhabotinsky reaction. Several unresolved phenomena are picked out and possible mechanisms are discussed extensively. Interesting features of these phenomena can be summarized as being caused by the ‘global and dynamic hydrodynamic pattern induced by chemical waves’. These chemically induced global pattern of hydrodynamic phenomena may not be simply explained by the reaction-diffusion-convection model based on Marangoni instability (surface tension-driven convection), which produces only a localized structure of the convection pattern. Observed flow waves show global and dynamic patterns of convection that generate a functional structure associated with hierarchical patterns appearing in the reaction-diffusion-convection system. In particular, we clarify the existence of a continuous stream of hydrodynamic flow with growing amplitude and its rotating direction. We find that the flow does not stabilize to a motionless state until the system has self-collapsed. This new picture of the flow waves requires a revision of the reaction-diffusion-convection model. The established flow structure can be regarded as a mixing and/or transport process to supply the substrate from the peripheral region to the centre of the chemical waves to sustain the reaction. This characteristic may be a function of the hierarchical structure. A new mechanism for the viscous-elastic feature of the gas-liquid interface is discussed in order to understand these curious phenomena of interest.     

Synthesis of Au nanorods via autocatalytic growth of Au seeds formed by sonochemical reduction of Au(I): Relation between formation rate and characteristic of Au nanorods

The sonochemical formation of Au seeds and their autocatalytic growth to Au nanorods were investigated in a one-pot as a function of concentration of HAuCl₄, AgNO₃, and ascorbic acid (AA). The effects of ultrasonic power and irradiation time were also investigated. In addition, the formation rate of Au nanorods was analyzed by monitoring the extinction at 400 nm by UV–Vis spectroscopy and compared with the growth behavior of Au seeds to nanorods. Most of the reaction conditions affected the yield, size, and shape of Au nanorods formed. It was confirmed that the concentration balance between HAuCl₄ and AA was important to proceed the formation of Au seeds and nanorods effectively. The formation rate became faster with increasing AA concentration and dog-bone shaped nanorods were formed at high AA concentration. It was also confirmed a unique phenomenon that the shape of Au nanorods changed even after the completion of the reduction of Au(I) in the case of short-time ultrasonic irradiation for Au seed formation.