Three-dimensional dendritic

G. Dziuk. A boundary element method for curvature flow. Application to crystal growth. In J. E. Taylor, ed. Computational Crystal Growers Workshop, AMS Selected Lectures in Mathematics. Providence, Rhode Island American Mathematical Society, 1992, p. 34 A. Schmidt. Computation of three dimensional dendrites with finite elements. J Comput Phys 125 293, 1996. 

R. Kobayashi. Modeling and numerical simulations of dendritic crystal growth. Physica D (55 410, 1993 R. Kobayashi. A numerical approach to three-dimensional dendritic solidification. Exp Math 5 59, 1994. 

Shen Q, Jiang K, Zhang H et al (2008) Three-dimensional dendritic Pt Nanostructures sonoelectrochemical synthesis and electrochemical applications. J Phys Chem C 112 16385-16392... 

There also exist a variety of syntheses, stabilities, and characteristics, which are unique to each particular material. Further, macromolecules containing metal and metal-like elements can be produced in a variety of geometries, including linear, two-dimensional, three-dimensional, dendritic, and star arrays. 

An increase of the time of mercury exposure up to hours leads to the formation of mercury aggregates in the form of islands or three-dimensional dendritic structures on/in the gold layer [13,14]. Such... 

Jeong, J.-H., N. Goldenfeld, and J. Dantzig. 2001. Phase field model for three dimensional dendritic growth with fluid flow. Phys. Rev. E 64 041602. 

The cauliflower-like agglomerates of copper grains were formed at an overpotential of 550 mV, where there was no hydrogen evolution (Fig. 5.1a). The very branchy 3D (three dimensional) dendrites were formed at an overpotential of 650 mV where hydrogen evolution was very small and corresponds to of... 

Self-assembled, three-dimensional dendritic network structures possessing critical jr-type surface groups have been reported to exhibit unique electrical conducting properties. Miller/Tomalia and coworkers [270] observed unusually high conductivities (i.e., 18 sec/cm at 90% humidity) for... 

It is worth mentioning that when the particle volume fraction is high enough, the three-dimensional network structure instead of fibrillated chain structure may form in ER fluids [5]. Sometimes the three-dimensional dendritic structure may form [6-8]. Figure 1 shows the microstructure of a metal/oil, glass sphere/oil, and nickel coated PMMA/oil under an electric field. Both the metal and metal coated PMMA particles form the dendritic structure, and only the glass spheres form the fibrillated chain structure. The appearance of fractal structure is believed to arise from the huge conductivity difference between the dispersed particle and the dispersed medium. 

Almost 70 of the approximately 115 elements are transition metals. These are elements with electrons successively added to their d or f subshells and have both filled and unfilled orbitals suitable for bonding. They exhibit a variety of oxidation states and bond formations, such as sigma and pi bonds or coordination bonds as are found in typical chelate structures. These characteristics are the reason that transition metal-containing macromolecules exist in a wide variety of structures including linear, two-dimensional, three-dimensional, dendrite, and assemblies. Many of these polymers are often referred to as organometallic polymers. We have, somewhat arbitrarily, separated this class from coordination polymers, which have been covered in Volumes 1, 3, and 5. 

Ravindran K, Brown SGR, Spittle JA (1999) Prediction of the effective thermal conductivity of three-dimensional dendritic regions by the finite element method. Mater Sci Eng 269 A 90-97... 

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