State models and asymptotic behaviour of 2D positive systems

Homogeneous 2D positive systems are 2D state-space models whosevariables are alwalys nonnegative and, consequently, are describedby a pair of nonnegative square matrices (A, B). In the paper,the properties of these pairs are discussed both in the generalcase and under particular assumptions like finite memory, separability,and property L. Various aspects of the positive asymptotic dynamic are considered;in particular, sufficient conditions are provided guaranteeingthat the local states are eventually strictly positive. Finally,some results on the convergence of the states towards a constantasymptotic distribution are presented.     

Regeneration of the Oxidation Catalysts Based on the Aqueous Solutions of Non‐Keggin Mo‐V‐P Heteropoly Acids by Molecular Oxygen

Kinetic peculiarities of regeneration of the aqueous solutions of non‐Keggin‐type Mo‐V‐P heteropoly acids H_aP_zMo_yV_x′O_b (HPA‐x′) and their acidic salts by O₂ are studied. The HPA‐x′ solutions have heightened thermal stability that permits to consider them as highly efficient catalysts for different oxidation processes. In the HPA‐x′ and their salts solutions, these peculiarities prove to be similar. The studied reaction is of the first order with respect to O₂ and V(IV), if [V(IV)] is higher than 0.8 M. As [V(IV)] decreases during the reaction, its order with respect to V(IV) increases to the third. The apparent activation energy of the reaction at temperatures 150–170°С is 37.5 kJ mol^?1. The obtained kinetic equation was used to calculate a new effective air reactor for the regeneration of the homogeneous HPA‐x′ catalyst in a pilot process of methylethylketone synthesis.     

Linear dynamical systems with integer constraints

We study properties of dynamic discrete-time linear systemswith the input or the state constrained to have integer components.The reachability of input-constrained systems is investigated,and consistency conditions for state-constrained systems aregiven.     

Molecular dynamics computation of solvent contribution to work of ion solvation

Clusters of water with various (charged and neutral) solute particles were simulated by molecular dynamics, and the radial profiles of local density, energy, electric potential, normal pressure, and polarization were obtained. The work of cluster formation was calculated. On the basis of an estimate of the surface potential for the vacuum-liquid and liquid-solid interfaces, the linear contribution of the ion charge to the chemical work of solvation was determined. In the case of the K⁺ ion, the linear contribution to the total work of solvation proved to be practically negligible.     

Mobility of water in NaCl and brain heart infusion (BHI) solutions as studied by 17O NMR

The molecular dynamic behaviour of water molecules in aqueous solution has been determined by oxygen-17 NMR according to the anisotropic reorientation, two-correlation-time model for bound water. Solutions of brain heart infusion (BHI), NaCl and their 1:1 mixture have been analysed. The anisotropic water population was distinguished into a slow (τ^s _bw) and a fast (τ^f _bw) relaxing component. The slow relaxing component was affected by the nature of the solute, while the fast relaxing component was not. NaCl was found to bind water molecules more strongly (higher τ^s _bw) than BHI. Water was more bound in the 1:1 mixture than in the solution containing only BHI. The population of bound water (P _bw) was concentration dependent and increased with increasing solids content. BHI, at the suspension point, bound ～50% of the total water, while NaCl at saturation bound only ～10%. The 1:1 mixture bound water in a synergistic manner that resulted in a slightly higher P_bw, than in BHI at each solid concentration. The P_bw correlated well with the amount of unfreezable water (as measured by DSC) present in the BHI samples.     

Solid-liquid phase transition in small water clusters: a molecular dynamics simulation study

Water clusters, (H₂O) _n , of varying sizes (n = 8, 12, 16, 20, 24, 28, 32, 36, and 40) have been studied at different temperatures from 0 to 200 K using molecular dynamics simulations. Transitions between solid and liquid phases were investigated to estimate the melting temperature of the clusters. Although the melting temperatures showed non-monotonic behaviour as a function of cluster size, their general tendency follows the classical relationship T _m ∝ n ^?1/3 to the cluster size n. Moreover, it was observed that the liquid-solid surface tension decreased with the cluster size in a similar way to the liquid-vapour surface tension in bulk water. Upon cooling, ice-like crystals were formed from the smaller clusters with n up to 20, while the larger clusters were transformed to glassy structures. The decrease in the glass transition temperature with the cluster size was observed to be much less than the corresponding melting temperature. The mutual order of the melting and glass-transition temperatures were found to be reversed compared with that observed for bulk water.     

Molecular dynamics computation of the work of ion solvation: comparison of two models of water

Clusters of the TIP4P water model with 125 and 256 molecules and with the K⁺ or K^? ions were simulated by the molecular dynamics method. The radial profiles of local density, energy, normal pressure and molecular orientation were obtained. The work of cluster formation was calculated from the normal pressure profile. The results for the TIP4P and SPC/E model of water are discussed in comparison with each other. A divergence in behaviour of water molecules in the two models was discovered.