On duality between observation and control for implicit linear discrete-time systems

Some results concerning the problem of duality between observationand control for implicit linear discrete-time systems are presented.It is not assumed that the considered systems are regular. Inthis case, some new concepts of observability and controllabilityturn out to be necessary for studying the problem of duality.     

Demixing of a binary mixture in slit-like pores at high temperatures

We investigate the fluid—fluid demixing transitions in the case of adsorption of so-called symmetric binary mixtures in slit-like pores at temperatures higher than the bulk gas—liquid critical temperature. The aim of the study is to determine how the demixing of such mixtures in the pores depends on the bulk phase composition and on the parameters characterizing the pore. The calculations have been carried out by means of a density functional theory. In the case of an equimolar bulk mixture, the demixing transition inside the pore occurs only when the adsorption potentials of both species are identical. The occurrence of this transition is manifested by a cusp in the adsorption isotherm. For nonequimolar bulk phase compositions, the transition can also take place if the adsorption energies of both components are different. However, the difference in the adsorption energies should be small enough, otherwise a continuous demixing takes place. For non-equimolar compositions two branches of the grand canonical potential intersect, whereas for equimolar bulk composition they meet tangentially. We have determined phase behaviour for several model systems.     

Insights into enzyme catalysis from QM/MM modelling: transition state stabilization in chorismate mutase

Chorismate mutase provides an important test of theories of enzyme catalysis, and of modelling methods. The Claisen rearrangement of chorismate to prephenate in the enzyme has been modelled here by a combined quantum mechanics/molecular mechanics (QM/MM) method. Several pathways have been calculated. The sensitivity of the results to details of model preparation and pathway calculation is tested, and the results are compared in detail to previous similar studies and experiments. The potential energy barrier for the enzyme reaction is estimated at 24.5—31.6 kcal mol^?1 (AMl/CHARMM), and 2.7—11.9 kcal mol^?1 with corrections (e.g. B3LYP/6-31 + G(d)). In agreement with previous studies, the present analysis of the calculated paths provides unequivocal evidence of significant transition state stabilization by the enzyme, indicating that this is central to catalysis by the enzyme. The active site is exquisitely complementary to the transition state, stabilizing it more than the substrate, so reducing the barrier to reaction. A number of similar pathways for reaction exist in the protein, as expected. Small structural differences give rise to differences in energetic contributions. Major electrostatic contributions to transition state stabilization come in all cases from Arg90, Arg7, one or two water molecules, and Glu78 (Glu78 destabilizes the transition state less than the substrate), while Arg63 contributes significantly in one model.     

Periodic Motion of Atoms Near a Charged Wire

We study the classical motion of an atom in the vicinity of an infinite straight wire which carries an oscillating uniform charge. This system has been proposed as a mechanism for trapping cold neutral atoms. The parameters of the problem are the magnitude Q and frequency of oscillation of the charge, the mass M and polarizability of the atom, and the angular momentum L of the atom about the wire. For 0 and 2MQ ² greater than, but close to, L ², we prove that the atom's radial motion is periodic (with period 2/), and that the atom moves in a helical path around the wire. For 2MQ ² L ² we prove that the atom must either collide with the wire or else escape to infinity in the radial direction.     

New applications of the good old wavelength-dispersive X-ray fluorescence

Wavelength-dispersive X-ray fluorescence can be characterized by its advantages and drawbacks. Unbeaten spectral resolution in a range below 5 keV, good operational stability, excellent ability of making averaged analysis, and good presentation of peak shape which gives the basis for the chemical speciation are the advantages. Among the drawbacks, the following are important: system with sequential analysis of particular elements, low output of energy supplied to the device, and great cost of instrument which can be amortized only in routine operations. In routine geological and environmental analyses, the WD-XRF performs better than other simpler instrumental or wet techniques. WD-XRF is continuously improved, by applying new multilayer interference mirrors (MIM) for detection and quantification of very light elements. Bad spectral resolution of MIM noted earlier is now improved by tailoring their shape to the shape of gratings. The progress in the long wavelength spectral region joined with efficient and precise wavelength resolution systems enables the application of WD-XRF for speciation analysis. In another effort, XRF spectrometry is treated as a tool for obtaining quantitative basis for the judgement on Linnaean systematic classification of plants and opens the field to a new discipline – quantitative biology.     

The chemical potential of Lennard-Jones associating fluids from osmotic Monte Carlo simulations

The chemical potential for a two-component Lennard-Jones fluid with associative interaction between opposite species promoting the formation of dimers is calculated using osmotic Monte Carlo (OMC) canonical ensemble simulations. Grand canonical Monte Carlo simulations also are performed to verify the accuracy of the OMC approach. The data from both methods agree very well for thermodynamic states with different degrees of dimerization. It follows that the OMC is a promising approach for the determination of the thermodynamics of and equilibria between associating and non-associating fluids and associating fluid mixtures.     

Phase coexistence and interface structure of a two-component Lennard-Jones fluid in porous media: application of Born—Green—Yvon equation

The Born-Green-Yvon equation with smoothed density approximation is used to calculate the liquid-liquid density profiles of a symmetric Lennard-Jones fluid in a hard sphere disordered matrix. The phase diagrams are evaluated for model systems characterized by different matrix densities and compared with the results of theoretical predictions and the Monte Carlo simulations of Gordon, P. A., and Glandt, E. D., 1996, J. chem. Phys., 105, 4257. It was found that increasing the matrix packing fraction reduces the magnitude of the miscibility gap and smooths the density profiles between two coexisting phases.     

Molecular dynamics study of the formation of small crystallites of Lennard-Jones particles in slit-like pores with (100) fcc walls

Canonical ensemble molecular dynamics is used to investigate the formation of small crystallites in slit-like pores with crystalline walls of (100) fcc symmetry. We study the influence of the pore width and the energetic parameters of the fluid particle-pore wall potential on the structure of the frozen droplets. We analyse the density profiles, in-plane radial distribution functions, in-plane diffusion coefficients, the distributions of Voronoi polygons, as well as the snapshots of consecutive configurations.     

Liquid—liquid interface in a binary mixture of associating fluids exhibiting a closed-loop immiscibility

We investigate the structure and thermodynamic properties of the liquid-liquid interface for a two-component mixture of associating fluids, exhibiting the closed-loop liquid-liquid immiscibility. In the study we apply the density functional approach and evaluate the density profiles, the ratio of unbound particles and the surface tension in order to investigate how those properties depend on the association energy.     

Polydisperse fluid in contact with a semipermeable membrane

Using density functional theory developed by Rosefeld, a model polydisperse fluid has been studied in contact with a membrane permeable to some components of the fluid. Calculations were carried out for three kinds of polydisperse fluid, each characterized by a different distribution of particle sizes. The structure of fluid has been evaluated on both sides of the membrane, plus the distribution of the particles in bulk fluid and in the surface layers. The adsorption and osmotic pressure in the system have been calculated.