Nonmagnetic microspheres confined in a ferrofluid layer are denoted by magnetic holes. They form aggregates due to dipolar interactions when an external magnetic field is exerted. Their cluster-cluster aggregation was studied for various magnetic fields using optical microscopy, both for small spheres of diameters, d=1.9 and 4 microm, for which Brownian motion was important and for large spheres of diameter, d=14 microm, for which Brownian motion was not important. The results for the two smaller sizes were in agreement with standard dynamic scaling theory and the dynamic scaling exponent z for the average cluster length S(t) approximately t(z) was found to be slightly smaller than 0.5, while for the largest spheres the z exponent showed a strong dependence on the magnetic-field strength.
We investigate a deterministic, conservative, undirected, critical height sandpile model with dissipation of an energy at boundaries that can simulate avalanche dynamics. It was derived from the Bak-Tang-Wiesenfeld model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)] introducing an additional second-higher threshold so the model has two distinct thresholds. Our computer simulations for a two-dimensional lattice show that scaling properties of the model depend on the higher-threshold values and site concentrations. These results are not therefore consistent with the present self-organized criticality hypothesis where the scaling properties are independent of the model parameters.
A value of about 20% relative change of the dielectric constant of mineral-oil-based ferrofluids was observed in an external magnetic field. The cluster model, based on a long-chain model, was proposed for the explanation of experimental data.
Is it possible to reverse the low total fertility rate (TFR) in the developed world? Using a hypothetical model of population we have analyzed the decline of the TFR which have took place in the background of ongoing global economic changes, and a liberalization process after the end of the Cold War. These phenomena have affected more that 110 millions of inhabitants of Central Europe and the Baltics and approximately 80 millions of inhabitants in Germany. The model has features of complex and evolving system of interacting individuals, and it enables to investigate a broad spectrum of input factors on individual decisions to limit the offspring. In the case of the TFR < 1.5, our initial analysis show a need of radical changes of the global economy that will stimulate series of self-regulations of demographic processes and evolution toward the safe TFR > 2.1. The changes should stimulate more uniform spatial distribution of wealth, capital, and usage. They will increase a number of self-sufficient and cooperative territories, to decrease the income inequality, to decrease labor and social mobilities. Societies should investigate the impacts of economic regulations and actions on the TFR trends in advance and take into account a biological nature of women more responsible.
We have experimentally investigated field induced aggregation of nonmagnetic particles confined in a magnetic fluid layer when rotating magnetic fields were applied. After application of a magnetic field rotating in the plane of the fluid layer, the single particles start to form two-dimensional (2D) clusters, like doublets, triangels, and more complex structures. These clusters aggregated again and again to form bigger clusters. During this nonequilibrium process, a broad range of cluster sizes was formed, and the scaling exponents, z and z ′ , of the number of clusters N (t) ∼ t z ′ and average cluster size S(t) ∼ t z were calculated. The process could be characterized as diffusion limited clustercluster aggregation. We have found that all sizes of clusters that occured during an experiment, fall on a single curve as the dynamic scaling theory predicts. Hovewer, the characteristic scaling exponents z ′ , z and crossover exponents ∆ were not universal. A particle tracking method was used to find the dependence of the diffusion coefficients D s on cluster size s. The cluster motions show features of Brownian motion. The average diffusion coefficients < D s > depend on the cluster sizes s as a power law < D s >∝ s γ where values of γ as different as γ = −0.62 ± 0.19 and γ = −2.08 ± 0.51 were found in two of the experiments.
The appearance and growth process of needle-like aggregates in thin films of magnetic fluid within a magnetic field are investigated. The results show that the average length of aggregates in a given magnetic field depends on the method of application of the magnetic field. However, the full needle length per unit area as a first approximation to a condensed phase volume is approximately the same.
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