Topological structure preserving numerical simulations of dynamical models

This paper brings together two methods producing numerical solutions with a statement of their quality — the nonstandard finite difference method and the method of validated computing. It deals with the construction and the analysis of reliable numerical discretizations of dynamical systems by employing these two techniques. An epidemiological model is used as a model example for their combined application.     

Dissipative Time Dependent Density Functional Theory

The simplest density functional theory due to Thomas, Fermi, Dirac and Weizsäcker is employed to describe the non-equilibrium thermodynamic evolution of an electron gas. The temperature effect is introduced via the Fermi-Dirac entropy, while the irreversible dynamics is described by a non-linear diffusion equation. A dissipative Kohn-Sham equation is also proposed, which improves the Thomas-Fermi-Weizsäcker kinetic functional.     

As(III) Determination in the Presence of Pb(II) by Differential Alternative Pulses Voltammetry

Differential Alternative Pulses Voltammetry (DAPV), introduced by the authors earlier, was applied with HMDE for direct As(III) determination in the presence of Pb(II) in natural water without sample pretreatment. Distinguishable peaks of As(III) and Pb(II) were registered in 1 M HCl supporting electrolyte at a concentration ratio as high as 1 : 6, while complete peak overlapping occurs applying DPP at any concentration ratio at the same experimental conditions. In‐situ As(III) determinations in the presence of Pb(II) in contaminated ground waters in Mexico were performed, using especially designed disposable safe mercury drop electrodes.     

EFFECT OF THICKNESS NON-HOMOGENEITY ON THE KINETIC BEHAVIOUR OF MICROSCOPIC FOAM FILM

The effect of thickness non-homogeneity on the drainage of microscopic horizontal foam films was studied experimentally and theoretically. Quasi-static and asymmetrical distribution of thickness irregularities over the film surface was established in the experiment. This type of dimpling was modelled theoretically and employed to derive a new equation for the film thinning. It differs from the theoretical expressions known from the literature and is in better agreement with the experimentally determined functional dependence of thinning rate on film size.     

Snooker: a structure-based pharmacophore generation tool applied to class A GPCRs

G-protein coupled receptors (GPCRs) are important drug targets for various diseases and of major interest to pharmaceutical companies. The function of individual members of this protein family can be modulated by the binding of small molecules at the extracellular side of the structurally conserved transmembrane (TM) domain. Here, we present Snooker, a structure-based approach to generate pharmacophore hypotheses for compounds binding to this extracellular side of the TM domain. Snooker does not require knowledge of ligands, is therefore suitable for apo-proteins, and can be applied to all receptors of the GPCR protein family. The method comprises the construction of a homology model of the TM domains and prioritization of residues on the probability of being ligand binding. Subsequently, protein properties are converted to ligand space, and pharmacophore features are generated at positions where protein ligand interactions are likely. Using this semiautomated knowledge-driven bioinformatics approach we have created pharmacophore hypotheses for 15 different GPCRs from several different subfamilies. For the beta-2-adrenergic receptor we show that ligand poses predicted by Snooker pharmacophore hypotheses reproduce literature supported binding modes for ～75% of compounds fulfilling pharmacophore constraints. All 15 pharmacophore hypotheses represent interactions with essential residues for ligand binding as observed in mutagenesis experiments and compound selections based on these hypotheses are shown to be target specific. For 8 out of 15 targets enrichment factors above 10-fold are observed in the top 0.5% ranked compounds in a virtual screen. Additionally, prospectively predicted ligand binding poses in the human dopamine D3 receptor based on Snooker pharmacophores were ranked among the best models in the community wide GPCR dock 2010.     

Wetting films on chemically patterned surfaces

The behavior of thin wetting films on chemically patterned surfaces was investigated. The patterning was performed by means of imprinting of micro-grid on methylated glass surface with UV-light (λ=184.8 nm). Thus imprinted image of the grid contained hydrophilic cells and hydrophobic bars on the glass surface. For this aim three different patterns of grids were utilized with small, medium and large size of cells. The experiment showed that the drainage of the wetting aqueous films was not affected by the type of surface patterning. However, after film rupturing in the cases of small and medium cells of the patterned grid the liquid from the wetting film underwent fast self-organization in form of regularly ordered droplets covering completely the cells of the grid. The droplets reduced significantly their size upon time due to evaporation. In the cases of the largest cell grid, a wet spot on the place of the imprinted grid was formed after film rupturing. This wet spot disassembled slowly in time. In addition, formation of a periodical zigzag three-phase contact line (TPCL) was observed. This is a first study from the planned series of studies on this topic.     

An experimental test of the fractal model for drainage of foam films

Drainage of foam films with different radii (50-150 μm), stabilized by hexathylene glycol dodecyl ether C(12)E(6) and in a presence of 0.024 M NaCl, were analyzed in the light of a recent dynamic fractal classification of [1]. The latter accounts for the effect of film surface corrugations developed during the film drainage. For simplicity, the film surface mobility is neglected since the presence of surfactants reduces dramatically the film surface velocity. The magnitude of surface non-homogeneities, caused by the film drainage, is accounted via a dynamic fractal dimension parameter α being spanned between zero and two. Depending on the α-value the film drains by different kinetic laws. For example, if the thin film is planar α=2 and it drains according to the Reynolds law; if α=1 the film contains an axisymmetric dimple causing faster drainage; if α=1/2 the film exhibits number of asymmetric dimples and the film drains even faster; finally if α=0 the film contains spatially uncorrelated domains causing the fastest possible drainage. The present analysis of experimental data suggests that the parameter α is inversely proportional to the film radius R and it is independent of the type and concentration of surfactants. A semi-empirical model for α is proposed, thus completing the generic dynamic fractal classification.     

Tribology of thin wetting films between bubble and moving solid surface

This work shows a successful example of coupling of theory and experiment to study the tribology of bubble rubbing on solid surface. Such kind of investigation is reported for the first time in the literature. A theory about wetting film intercalated between bubble and moving solid surface was developed, thus deriving the non-linear evolution differential equation which accounted for the friction slip coefficient at the solid surface. The stationary 3D film thickness profile, which appears to be a solution of the differential equation, for each particular speed of motion of the solid surface was derived by means of special procedure and unique interferometric experimental setup. This allowed us to determine the 3D map of the lift pressure within the wetting film, the friction force per unit area and the friction coefficient of rubbing at different speeds of motion of the solid surface. Thus, we observed interesting tribological details about the rubbing of the bubble on the solid surface like for example:     

Effect of ionic surfactants on drainage and equilibrium thickness of emulsion films

This paper presents new theoretical and experimental results that quantify the role of surfactant adsorption and the related interfacial tension changes and interfacial forces in the emulsion film drainage and equilibrium. The experimental results were obtained with plane-parallel microscopic films from aqueous sodium dodecyl sulphate solutions formed between two toluene droplets using an improved micro-interferometric technique. The comparison between the theory and the experimental data show that the emulsion film drainage and equilibrium are controlled by the DLVO interfacial forces. The effect of interfacial viscosity and interfacial tension gradient (the Marangoni number) on the film drainage is also significant.     

Brownian motion of a classical particle in quantum environment

The Klein–Kramers equation, governing the Brownian motion of a classical particle in a quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.