Analytical model of brittle destruction based on hypothesis of scale similarity

The size distribution of dust particles in nuclear fusion devices is close to the power function. A function of this kind can be the result of brittle destruction. From the similarity assumption it follows that the size distribution obeys the power law with the exponent between -4 and -1. The model of destruction has much in common with the fractal theory. The power exponent can be expressed in terms of the fractal dimension. Reasonable assumptions on the shape of fragments concretize the power exponent, and vice versa possible destruction laws can be inferred on the basis of measured size distributions.Comment: 10 pages, 3 figure

Diffusion-Limited Annihilation with Initially Separated Reactants

A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$. Using this reaction rate we find that the width of the reaction front grows as $t^{1/4}$ in one dimension and as $t^{1/6}(\ln t)^{1/3}$ in two dimensions.Comment: 9 pages, Plain Te

Numerical study of multilayer adsorption on fractal surfaces

We report a numerical study of van der Waals adsoprtion and capillary condensation effects on self-similar fractal surfaces. An assembly of uncoupled spherical pores with a power-law distributin of radii is used to model fractal surfaces with adjustable dimensions. We find that the commonly used fractal Frankel-Halsey-Hill equation systematically fails to give the correct dimension due to crossover effects, consistent with the findings of recent experiments. The effects of pore coupling and curvature dependent surface tension were also studied.Comment: 11 pages, 3 figure

Experiments in vortex avalanches

Avalanche dynamics is found in many phenomena spanning from earthquakes to the evolution of species. It can be also found in vortex matter when a type II superconductor is externally driven, for example, by increasing the magnetic field. Vortex avalanches associated with thermal instabilities can be an undesirable effect for applications, but "dynamically driven" avalanches emerging from the competition between intervortex interactions and quenched disorder constitute an interesting scenario to test theoretical ideas related with non-equilibrium dynamics. However, differently from the equilibrium phases of vortex matter in type II superconductors, the study of the corresponding dynamical phases - in which avalanches can play a role - is still in its infancy. In this paper we critically review relevant experiments performed in the last decade or so, emphasizing the ability of different experimental techniques to establish the nature and statistical properties of the observed avalanche behavior.Comment: To be published in Reviews of Modern Physics April 2004. 17 page

Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series

Notwithstanding the significant efforts to develop estimators of long-range correlations (LRC) and to compare their performance, no clear consensus exists on what is the best method and under which conditions. In addition, synthetic tests suggest that the performance of LRC estimators varies when using different generators of LRC time series. Here, we compare the performances of four estimators [Fluctuation Analysis (FA), Detrended Fluctuation Analysis (DFA), Backward Detrending Moving Average (BDMA), and centred Detrending Moving Average (CDMA)]. We use three different generators [Fractional Gaussian Noises, and two ways of generating Fractional Brownian Motions]. We find that CDMA has the best performance and DFA is only slightly worse in some situations, while FA performs the worst. In addition, CDMA and DFA are less sensitive to the scaling range than FA. Hence, CDMA and DFA remain "The Methods of Choice" in determining the Hurst index of time series.Comment: 6 pages (including 3 figures) + 3 supplementary figure

Fractal Nanotechnology

Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105 nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces

Fabrication Principles and Their Contribution to the Superior In Vivo Therapeutic Efficacy of Nano-Liposomes Remote Loaded with Glucocorticoids

We report here the design, development and performance of a novel formulation of liposome- encapsulated glucocorticoids (GCs). A highly efficient (>90%) and stable GC encapsulation was obtained based on a transmembrane calcium acetate gradient driving the active accumulation of an amphipathic weak acid GC pro-drug into the intraliposome aqueous compartment, where it forms a GC-calcium precipitate. We demonstrate fabrication principles that derive from the physicochemical properties of the GC and the liposomal lipids, which play a crucial role in GC release rate and kinetics. These principles allow fabrication of formulations that exhibit either a fast, second-order (t1/2 ∼1 h), or a slow, zero-order release rate (t1/2 ∼ 50 h) kinetics. A high therapeutic efficacy was found in murine models of experimental autoimmune encephalomyelitis (EAE) and hematological malignancies

Promotion of protocell self-assembly from mixed amphiphiles at the origin of life

Vesicles formed from single-chain amphiphiles (SCAs) such as fatty acids probably played an important role in the origin of life. A major criticism of the hypothesis that life arose in an early ocean hydrothermal environment is that hot temperatures, large pH gradients, high salinity and abundant divalent cations should preclude vesicle formation. However, these arguments are based on model vesicles using 1–3 SCAs, even though Fischer–Tropsch-type synthesis under hydrothermal conditions produces a wide array of fatty acids and 1-alkanols, including abundant C10–C15 compounds. Here, we show that mixtures of these C10–C15 SCAs form vesicles in aqueous solutions between pH ~6.5 and >12 at modern seawater concentrations of NaCl, Mg2+ and Ca2+. Adding C10 isoprenoids improves vesicle stability even further. Vesicles form most readily at temperatures of ~70 °C and require salinity and strongly alkaline conditions to self-assemble. Thus, alkaline hydrothermal conditions not only permit protocell formation at the origin of life but actively favour it