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• MCN/SI-FC composite coatings with micro and nano hierarchical structure were prepared. • At one solar intensity, the temperature of the coating quickly rises to 97.5 °C. • The water contact Angle of the coating reaches 155.79°, and the mechanical properties are excellent. • The coating can be applied to a variety of substrates. Solar collector coatings can solve the current energy shortage and environmental pollution by converting clean solar energy into thermal energy. However, once the coating is adhered to a liquid, the performance of the solar thermal conversion will be seriously affected. Here, a cost-effective photothermal superhydrophobic coating was designed by modulating the microstructure of a highly solar-absorbing material (MCN), followed by a simple spraying method combined with polyvinylidene fluoride resin (PVDF). The MCN in the coating provides excellent photothermal conversion performance, hence, the surface temperature of the coating can be rapidly increased to 97.5 °C at 1 kW/m2. In addition, the coating achieves a water contact angle (WCA) of 155.79° due to the combined micro-nano structure of MCN and PVDF coupled with the low surface energy of PVDF. More importantly, the coating possesses excellent mechanical properties and can be applied to different substrates. This cost-effective photothermal superhydrophobic coating has promising applications in outdoor environments such as insulated tents and waterproof insulation packaging. In this work, MCN/SI-FC composite coatings with micro-nano hierarchical structure were prepared by a simple and cost-effective method. The composite not only heats up quickly to 97.5 °C under 1 sunlight intensity, but also has super hydrophobic properties and can be applied to a variety of substrates. [Display omitted] [ABSTRACT FROM AUTHOR]

Hierarchical programming is being increasingly recognized as helpful in the construction of large programs. Users of hierarchical techniques claim or predict substantial increases in productivity and in the reliability of the programs produced. In this paper we describe a formal method for hierarchical program specification, implementation, and proof. We apply this method to a significant list processing problem and also discuss a number of extensions to current programming languages that ease hierarchical program design and proof. [ABSTRACT FROM AUTHOR]

We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allows CAs in rule space to be classified according to their hierarchy of layers. Since the method is valid for any discrete operator and only depends on the alphabet size, the resulting conclusions, of general validity, apply to CAs in any dimension or order in time, arbitrary neighborhood ranges and topology. We provide several examples of the method, illustrating how it can be applied to the mathematical modeling of the emergence of systems composed of parts of different sizes. Specifically, we use the majority CA rule as a building block to construct more complex cellular automata in which separate domains (with substructures having different dynamical properties) are able to emerge out of disorder and coexist in a stable manner. [ABSTRACT FROM AUTHOR]

The mechanical properties of nacre (mother-of-pearl), which are superior to those of its constituent materials, derive from a micro-architecture formed by the arrangement into parallel laminae of individual aragonite tiles with surface asperities, bonded by organic interlayers. A mechanical model is developed to determine how the contact profile that defines the geometry of the tile surface affects the constitutive response of hierarchical metamaterials of this type when they are strained in the lamellar plane. We consider the structured character of the deformation, consisting of elastic distortion of the tiles and the inelastic contribution from the disarrangements produced by relative sliding of the lamellar interfaces, which is formulated within the thermodynamic framework for irreversible processes in generalized materials. The resistance to sliding associated with constrained shear-induced dilatation of the tiles and the bridging of the organic interlayers are represented by a generalized cohesive-frictional law, effective at the level of averaged separation plane, providing a phenomenological approach that by-passes the difficulty in analytically solving the contact problem at asperities. The nominal stress–strain curves of the nacreous structure are shown to be highly dependent, qualitatively and quantitatively, on the geometry of the contact profiles. The model not only produces results that are in excellent agreement with experiments on nacre, but it can also describe complex stress–strain curves with pinched hysteresis loops having branches of various shapes, as well as serrated inelastic regimes. The versatility of this theoretical approach offers promise as a design tool for innovative metamaterials. [ABSTRACT FROM AUTHOR]

The problem of the most probable distributions on energy is studied in a combinatorial formulation, under the natural hypotheses regarding conservation laws, such as conservation of the total number of particles, total energy, etc. The particle distributions on the maximum and minimum energies are obtained and coincide with those found in the framework of the original combinatorial treatment. Two types of energy distributions for delimited particles are obtained. The results can be interpreted as sorting of particles based on their statistical mechanics behavior observed in various experiments. An effective Pauli principle arises in a non-contradictory way in one-particle observations both for once- and twice-delimited systems in the combinatorial formulation as well as in the problem of distributions on maximum and minimum energies. Many of the distributions obtained describe particles that do not have negative energy states. • Coincidence of most probable distributions over energy with distributions of extremes • Once- and twice-delimited hierarchical particle systems • Emergency of particles statistical sorting with effective Pauli principle • Appearance of distributions with negligible probability of negative-energy particles [ABSTRACT FROM AUTHOR]

ZnO nanosheets and nanoflakes were grown on alumina particles in the absence of surfactants via heterogeneous precipitation using urea, zinc acetate and bayerite as precursors. Thermo-gravimetric analysis (TGA), X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) were used and the results indicated the formation of only two phases: wurtzite-type ZnO and γ-Al2O3. ZnO nanoflakes were grown on alumina particles in the samples with ZnO content of 40 and 60 wt%. By increasing the ZnO content to 80 wt%, a porous hierarchical structure of ZnO with nanosheet arrays appeared. Both of these nanoflakes and nanosheets were about 40–80 nm in thickness and about 1–2 μm in diameter. It was proposed that Zn5(CO3)2(OH)6 nuclei undergo higher growth rates in thin sheets at edges of bayerite particles with a higher surface energy. The Brunauer–Emmett–Teller (BET) measurements proved a reachable high surface area for hierarchical structures of ZnO nanosheets, which could mainly be attributed to their unique growth on alumina particles. Also, UV absorption results revealed that ZnO–Al2O3 compositions still show the UV characteristic absorption of ZnO, which can evidence the presence of photocatalytic properties in ZnO–Al2O3 compositions. [ABSTRACT FROM AUTHOR]

Abstract: Let k and m be two fixed positive integers with and . Let which is the th smallest value of k real numbers . We call this f the th order function of k real numbers . Let be a nonconstant random variable with cumulative distribution . Let be the unique solution in (0, 1) to the equation where , which is the (cumulative) Beta distribution function with parameters m and . Write and . Define the hierarchical sequence of random variables by with being independent random variables identically distributed as . In this note it is shown that and a.s. and a.s. It follows that a.s. if and only if . This result generalizes and improves Propositions 4.3 and 4.4 of Li and Rogers [1999. Asymptotic behavior for iterated functions of random variables. Ann. Appl. Probab. 9, 1175–1201]. [Copyright &y& Elsevier]