Colloidal ZnO nanostructures and functional coatings: A survey

The past research work devoted to ZnO nanocolloidal sol-gel route is reviewed. It highlights the cluster chemistry of alcoholic ZnAc₂ solutions and the results of ZnO colloid growth investigations performed worldwide. Moreover, the role of doping and co-doping in the processing of functional ZnO coatings is discussed. The possibilities of tuning the optical properties are also reported with a particular attention to luminescence. The last part of this paper deals with electrical and photoelectrochemical properties of ZnO nanocrystals and their aggregates. This contribution is dedicated to the 80th birthday of Prof. Arnim Henglein from the Hahn-Meitner-Institut in Berlin and to the memory of Prof. Jacques Mugnier from the Université Claude-Bernard Lyon 1 in France.     

Thermal and chemical nanofractal relaxation

We studied shape relaxation of nano-fractal islands, during annealing, after their growth from antimony cluster deposition on graphite surface. Annealing at 180^°C shows evidence of an increase of the fractal branch width with time followed by branch fragmentation, without changing the fractal dimension. The time evolution of the width of the arm suggests the surface self-diffusion mechanism as the main relaxation process. With Monte Carlo simulations, we confirmed the observed behavior. Comparison is done with our previous results on fragmentation of nano-fractal silver islands when impurity added to the incident cluster promotes rapid fragmentation by surface self-diffusion enhancement [1].     

Hidden structure in the randomness of the prime number sequence?

We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes, that would eventually appear in applications. Finally, our theory allows us to link with three different but important topics: the Hardy–Littlewood conjecture, the statistical mechanics of spin systems, and the celebrated Sierpinski fractal.     

胶束形成的分形研究

提出了测定胶束质量分维的两种新方法即粘度法和GPC－LALLS联机法，随后从动态光散射数据计算了离子型胶束SDS的分维，这些实验数值之间能互相印证．建立了放束形成过程的Laplace分形理论，计算得分维D＝1.54（二级），作高级计算的分维D＝1.67与前面实测值基本相符，另外，从唯象理论角度，讨论了胶束的多重分形及其热力学行为，发现有两个相变点β_c＝-4和β_c＝-1．并认为这两个转折分别对应着单分子<=>分形胶束<=>经典胶束结构之间的转变．     

Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.     

Squig sheets and some other squig fractal constructions

Squig intervals are a class of hierarchically constructed fractals introduced by the author. They can be visualized as the final outcome upon a straight interval of a suitable cascade of local perturbative eddies ruled by two processes called decimation and separation. Their theory is summarized and their scope is extended in several new directions, especially by introducing new forms of separation. Squig intervals are generalized in two dimensions, with fractal dimensions ranging from 1.2886 to 1.589. Squig sheets are constructed in three dimensional space with fractal dimensions ranging from 8/3 up. They should prove useful in modeling the fractal surfaces associated with turbulence and related phenomena. Squig intervals are constructed in three dimensions. Nonsymmetric eddies and the resulting squigs are tackled. Squig trees and intervals are drawn on unconventional lattices, either in the plane or in a prescribed fractal surface. Peyriére'sM systems are mentioned: their study includes the proof that the informal renormalization argument (involving a transfer matrix) is exact for squigs.Presented at theThird Conference on Fractals: Fractals in the Physical Sciences, held at the National Bureau of Standards, Gaithersburg, Maryland, on November 20–23, 1983.The reader's attention should be drawn to the fact that the second and later printings of this book include an update chapter and additional references. Though it should not have been necessary, it may be useful also to mention here that most of the material in this book that concerns physics, e.g., polymers and percolation clusters, wasnot found in either of my two earlier Essays on fractals,Les objects fractals: forme, hasard et dimension (Flammarion,     

Electric field driven fractal growth dynamics in polymeric medium

This paper reports the extension of earlier work (Dawar and Chandra, 2012) [27] by including the influence of low values of electric field on diffusion limited aggregation (DLA) patterns in polymer electrolyte composites. Subsequently, specified cut-off value of voltage has been determined. Below the cut-off voltage, the growth becomes direction independent (i.e., random) and gives rise to ramified DLA patterns while above the cut-off, growth is governed by diffusion, convection and migration. These three terms (i.e., diffusion, convection and migration) lead to structural transition that varies from dense branched morphology (DBM) to chain-like growth to dendritic growth, i.e., from high field region (A) to constant field region (B) to low field region (C), respectively. The paper further explores the growth under different kinds of electrode geometries (circular and square electrode geometry). A qualitative explanation for fractal growth phenomena at applied voltage based on Nernst–Planck equation has been proposed.     

Incompatibility networks as models of scale-free small-world graphs

We make a mapping from Sierpinski fractals to a new class of networks, the incompatibility networks, which are scale-free, small-world, disassortative, and maximal planar graphs. Some relevant characteristics of the networks such as degree distribution, clustering coefficient, average path length, and degree correlations are computed analytically and found to be peculiarly rich. The method of network representation can be applied to some real-life systems making it possible to study the complexity of real networked systems within the framework of complex network theory.     

Solid structures in a highly agitated bed of granular materials

A series of experiments are described in which bubbles and solid structures are produced in a highly agitated bed of vertically shaken granular materials. To identify the physical mechanisms behind bubbling, three-dimensional simulations of the aforementioned systems are performed on a graphics processing unit (GPU). The gas dynamics above and within shaken granular materials is solved using large-eddy simulations (LES) while the dynamics of grains is described through molecular dynamics. Here, the interaction between the grain surfaces is modeled using the generalized form of contact theory developed by Hertz. In addition, the coefficient of kinetic friction is assumed to depend on the relative velocity of slipping. The results show both a qualitative and a quantitative agreement between simulations and experiments. They imply that the instantaneous formation and failure of granular aggregates could play an important role in the nucleation, growth, departure and collapse of bubbles in shaken granular materials. This promising effort in GPU computing may position the GPU as a compelling future alternative to traditional simulation techniques.     

Thermal conductivity of nanofluids and size distribution of nanoparticles by Monte Carlo simulations

Nanofluids, a class of solid–liquid suspensions, have received an increasing attention and studied intensively because of their anomalously high thermal conductivites at low nanoparticle concentration. Based on the fractal character of nanoparticles in nanofluids, the probability model for nanoparticle’s sizes and the effective thermal conductivity model are derived, in which the effect of the microconvection due to the Brownian motion of nanoparticles in the fluids is taken into account. The proposed model is expressed as a function of the thermal conductivities of the base fluid and the nanoparticles, the volume fraction, fractal dimension for particles, the size of nanoparticles, and the temperature, as well as random number. This model has the characters of both analytical and numerical solutions. The Monte Carlo simulations combined with the fractal geometry theory are performed. The predictions by the present Monte Carlo simulations are shown in good accord with the existing experimental data.