Fractal formation and ordering in random sequential adsorption

We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered as $\alpha$ increases, and that the Apollonian packing is obtained at $\alpha \to \infty$ limit. We introduce the entropy production rate as a quantitative criteria of regularity and observe a transition from an irregular regime of the pattern formation to a regular one. We develop a scaling theory that relates kinetic and structural properties of the system.Comment: 4 pages, RevTex, 4 postscript figures. To appear in Phys.Rev.Let

Polydisperse Adsorption: Pattern Formation Kinetics, Fractal Properties, and Transition to Order

We investigate the process of random sequential adsorption of polydisperse particles whose size distribution exhibits a power-law dependence in the small size limit, $P(R)\sim R^{\alpha-1}$. We reveal a relation between pattern formation kinetics and structural properties of arising patterns. We propose a mean-field theory which provides a fair description for sufficiently small $\alpha$. When $\alpha \to \infty$, highly ordered structures locally identical to the Apollonian packing are formed. We introduce a quantitative criterion of the regularity of the pattern formation process. When $\alpha \gg 1$, a sharp transition from irregular to regular pattern formation regime is found to occur near the jamming coverage of standard random sequential adsorption with monodisperse size distribution.Comment: 8 pages, LaTeX, 5 figures, to appear in Phys.Rev.

Exact results for nucleation-and-growth in one dimension

We study statistical properties of the Kolmogorov-Avrami-Johnson-Mehl nucleation-and-growth model in one dimension. We obtain exact results for the gap density as well as the island distribution. When all nucleation events occur simultaneously, the island distribution has discontinuous derivatives on the rays x_n(t)=nt, n=1,2,3... We introduce an accelerated growth mechanism where the velocity increases linearly with the island size. We solve for the inter-island gap density and show that the system reaches complete coverage in a finite time and that the near-critical behavior of the system is robust, i.e., it is insensitive to details such as the nucleation mechanism.Comment: 9 pages, revtex, also available from http://arnold.uchicago.edu/~ebn

Influence of alloying elements and heat treatment on the mechanical properties of chromium cast iron

The results of experimental studies to determine the effect of alloying and heat treatment on the mechanical properties of the high-chromium cast iron are described. When alloying the melt with nickel, molybdenum and manganese, as well as during heat treatment by quenching, specific wear, tensile strength in bending of the obtained samples, their hardness and microhardness were studied. A comparative analysis of the influence of alloying elements and heat treatment methods has been performed. When alloying Ni, Mo, and Mn, cast specimens that have not undergone heat treatment have the highest specific wear. It was established that the hardened Ni alloyed samples have the greatest bending strength. It was found that cast samples that were not subjected to heat treatment have much lower hardness and microhardness. The approximate composition of chromium cast iron was determined for further studies to increase its wear resistance. The research results are used in the manufacturing process of parts for crushing and grinding equipment

The performance properties of chromium cast irons with different degree of eutectic

The influence of carbon and the type of forms on the wear resistance, hardness and strength of samples from chromium iron made of ИЧХ18ВМ cast iron was investigated. The analysis of the structural structure of the samples of cast iron ИЧХ18ВМ depending on the type of shape and amount of carbon was made. It is established that regardless of the type of forms with increasing carbon content the formation of large primary carbides is observed, and then the emergence of particularly large trigonal carbides in a hypereutectic iron was confirmed. It is shown that regardless of the type of forms the formation and growth of carbides are influenced by such factors as an increase in the carbon content and the rate of solidification. A comparison was made between the hardness, strength, and wear resistance of samples obtained at different heat exchange and solidification rates