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Precipitated ammonium aluminium carbonate hydroxide (NH4Al(OH)2CO3) is a promising precursor for preparation of nanostructured Al2O3. However, the experimental conditions, such as the low concentration of Al3+ salt solution, high temperature and/or pressure, long reaction time, and excessive amount of the (NH4)2CO3 precipitating agent, make this process expensive for large-scale production. Here, we report a simpler and cheaper route to prepare nanostructured alumina by partial neutralisation of a nearly saturated aqueous solution of Al(NO3)3 with (NH4)2CO3 as a base at pH < 4. Synthesis in the acidic region led to formation of a polynuclear aluminium cluster (Al13), which is an important “green” solution precursor for large-area preparation of Al2O3 thin films and nanoparticles. Control of the textural properties of the final alumina product during calcination of the prepared aluminium (oxy)hydroxide gel was accomplished by adding low-solubility aluminium acetate hydroxide (Al(OH)(CH3COO)2) as a seed to the Al(NO3)3 solution before neutralisation. The large Brunauer–Emmett–Teller specific surface area (376 m2 g−1) and narrow pore size distribution (2–20 nm) of the prepared compact alumina suggest that the chelating effect of the acetate ions affects the structures of the forming transition aluminas, and the evolved gases produced by decomposition of Al(OH)(CH3COO)2 and NH4NO3 as a by-product of the reaction during calcination prevent particle agglomeration. Other advantages of the proposed process are its versatility and the ability to obtain high purity materials without producing large amounts of by-products without the need for washing and energy saving by using a low processing temperature, and the possibility of recycling the generated CO2 and NH3 gases as the (NH4)2CO3 reagent.

A generalized non-porous shrinking particle model (G NSPM) of leaching has been verified and used for numerical simulations. Unlike the commonly used “simple” non-porous shrinking particle model (S NSPM), the G NSPM assumes n−th order chemical reaction, the influence of the L/S ratio and non-ideal behaviour of the leach solution. The leaching of dead-burned magnesite with hydrochloric acid has been chosen to verify the proposed mathematical model, as the (apparent) reaction order for HCl, n, may be both positive and negative, depending on the HCl concentration. Comparison of the simulations with experiments revealed that the S NSPM does not reflect the qualitatively different leaching behaviour at positive and negative n, especially at near-to-stoichiometric HCl/MgO ratio. The G NSPM reflects the effect of n not only qualitatively, but also with acceptable accuracy. At the stoichiometric HCl/MgO ratio, the mean squared error of the predictions obtained using the S NSPM was 100–130 rel. % as compared to those provided by the G NSPM. The common effect of the reaction order, n, L/S ratio (represented by the reduced HCl/MgO molar ratio, ϕ) and non-ideal behaviour of the acid were studied in detail by means of numerical simulations. The values of parameters n and ϕ can alter the leaching behaviour qualitatively. In contrast, the activity coefficient of HCl only slightly modifies the shape of the kinetic curves, but does not change the overall picture. The error of the time for complete conversion of MgO calculated using the S NSPM can reach more than 100 rel. % for n = − 0.5 and even up to several hundred rel. % for n = 1, because the conversion vs. time curves predicted by the G NSPM are markedly skewed towards longer leaching times.

A generalized non-porous shrinking particle model (NSPM) of leaching is proposed, which - unlike commonly used “simplified” mathematical models - takes into account the influence of the L/S ratio (by means of the so-called reduced A/B molar ratio, ϕ, which indicates how many times the leaching agent (A)-to-valuable substance (B) molar ratio actually used exceeds its stoichiometric value) and non-ideal behaviour of concentrated lixiviants. Moreover, n-th order chemical reaction with power-law kinetics is considered, which makes determination of the rate-determining step of the overall process more reliable. Correlation between the proposed model and experiment was tested using the hydrochloric acid leaching of dead-burned magnesite, which provides the opportunity to experimentally verify how the mathematical model fits the leaching data for both the positive and negative reaction order. Calculated values of the reaction order for HCl, n, different from unity (n = 0.28 and n = −0.23 obtained for low (0.20–1.03 M) and high HCl concentrations (2.06–3.83 M), respectively), together with relatively high values of the activation energy (57.5 J mol−1 and 56.6 J mol−1) indicate that the leaching rate is controlled by the intrinsic chemical reaction under the conditions considered in the present work. Simulations made using the calculated values of the parameters have shown that the proposed generalized NSPM model clearly reflects two most important experimental facts: (a) L/S ratio affects the leaching process; and (b) qualitatively different leaching behaviour has been observed for the positive and negative reaction order. Unlike the simplified NSPM model, the generalized model describes the leaching process quantitatively in the whole range of the parameter ϕ, for both n > 0 and n

This paper deals with the laws of information in decentralized control systems. In the case of decentralized control of complex systems, often referred to hierarchical systems, theoretically analyze the possibility of using an n-dimensional information theory to deal with such systems. N-dimensional information theory is an interesting tool to deal with these systems. On the basis of information theory the partition laws of information rates are listed. These laws are fundamental requirements for complex systems that must be met and by their quantification one can be able to compare these complex control systems and track how different parts of the system communicate and collaborate with others, etc. In the final section the deterministic partition law of information rates and its possibility of use for dynamical systems are presented.

The article deals with modeling of a system with hybrid dynamics and with two tools for modeling of such systems. For purpose of modeling we chose the system of coupled tanks. The tanks are situated in different heights and dynamics of the system changes in the moment when the liquid level in the second tank runs over the height of bottom of the first tank. That represents hybrid nature of this system. We chose two tools for simulation of hybrid systems – MPT toolbox and HYSDEL and we specifically aim on modeling of the system of coupled tanks by both these tools and on comparison of these tools. The tools are free however they do not work independently but as a part of the simulation language Matlab.