On strongly stable normal operators in Krein spaces

For bounded normal operators in Krein spaces we give a necessary and sufficient condition for strong stability. The same result for unitary operators was obtained by M.G.Krein [1] (see also [2]). For selfadjoint operators we refer to the papers of P.Jonas, H.Langer [3] and H.Langer [4].     

Non-integrability of some Painlevé VI-equations and dilogarithms

The paper studies the Painlevé VI^e equations from the point of view of Hamiltonian nonintegrability. For certain infinite number of points in the parameter space we prove that the equations are not integrable. Our approach uses recent advance in Hamiltonian integrability reducing the problem to higher differential Galois groups as well as the monodromy of dilogarithic functions.      

Dynamics of foams of ethoxylated ionic surfactant in the presence of micelles and multivalent ions

Foams produced from surfactant solutions containing micelles of the anionic surfactant sodium polyoxyethylene-2 sulfate and counterions of different valence (aluminium, calcium or sodium) are investigated. For this purpose an experimental setup consisting of a glass column and units for detection of pressure, flow and frequency is constructed. Blowing gas bubbles in the surfactant solution at a constant gas pressure produces the foam. Simultaneous monitoring of the bubble volume and frequency relates the foam growth rate to the dynamic surface tension of the surfactant solution. The foam growth rate plotted versus the gas flow rate exhibits a break point at about 80 mL/min, attributed to the transition from regime of bubbles (at lower flow rates - monodisperse foam) to jet regime (at higher flow rates - polydisperse foam). Due to the high surfactant concentration, the foam is stable and its height is linearly increasing with the time. Two types of experiments are carried out. (i) At a constant counterion concentration and variable surfactant concentration, the rate of foam growth increases initially with increasing of the surfactant concentration reaching a plateau at higher concentrations. The foams of pure surfactant grow always slower than the foams with added aluminium ions. (ii) At a constant surfactant concentration and variable counterion concentration, the rate of foam growth exhibits a maximum. It corresponds to number of aggregated surfactant monomers nearly equal to the number of charges provided by the counterions, for example when one aluminium ion binds three surfactant monomers in a micelle. The point of maximum coincides with the transition from small spherical micelles to large cylindrical ones. This transition affects also the micelle lifetime, which is related to the ability of releasing monomers by a micelle in order to supply the bubble surface with surfactant. In support to this hypothesis, the maximum foam growth is found corresponding to lower dynamic surface tension allowing the generation of a large number smaller in size bubbles. The results for the foam growth agree in some extent with the data from independent measurements on the liquid drainage from wet foams.     

Adsorption Kinetics of Some Polyethylene Glycol Octylphenyl Ethers Studied by the Fast Formed Drop Technique

The adsorption kinetics of Triton X-100 and Triton X-405 at solution/air and solution/hexane interfaces is studied by the recently developed fast formed drop technique. The dynamic interfacial tension of Triton X-100 and Triton X-405 solutions against hexane has been measured without preequilibration of the water and oil phases. It is found that the dynamic interfacial tension of Triton X-100 solutions passes through a minimum. This strange behavior is attributed to partial solubility of the surfactant in hexane. Such minima of the dynamic interfacial tension of Triton X-405 solutions have not been observed, which correlates well with the solubilities of both surfactants in hexane reported in the literature. The dynamic surface tension of solutions of both surfactants and the dynamic interfacial tension of Triton X-405 solutions are interpreted by the Ward and Tordai model for diffusion controlled adsorption. It is shown that proper interpretation of the experimental data depends on the type of isotherm used. More consistent results are obtained when the Temkin isotherm is used instead of the Langmuir isotherm. The results obtained with Triton X-100 at the solution/air interface confirm that the adsorption of this surfactant occurs under diffusion control. The adsorption of Triton X-405 at solution/air and at solution/hexane interfaces seems to occur under diffusion control at short periods of time, but under mixed (diffusion-kinetic) control at long periods of time. A hypothesis is drawn to explain this phenomenon by changes in the shape of the large hydrophilic heads of Triton X-405 molecules. Copyright 2000 Academic Press.     

Particle zips: vertical emulsion films with particle monolayers at their surfaces

Vertical emulsion films with particle monolayers at their surfaces have been studied by direct microscope observations. The effects of particle wettability and surface coverage on the structure and stability of water films in octane and octane films in water have been investigated. Monodisperse silica particles (3 microm in diameter) hydrophobized to different extents have been used. It is found that the structure and stability of emulsion films strongly depend on the film type (water-in-oil or oil-in-water), the particle contact angle, the interactions between particles from the same and the opposite monolayer, and the monolayer density. Stable films are observed only when the particle wettability fulfills the condition for stable particle bridges--in agreement with the concept that hydrophilic particles can give stable oil-in-water emulsions, whereas hydrophobic ones give water-in-oil emulsions. In the case of water films with dilute disordered monolayers at their surfaces, the hydrophilic particles are expelled from the film center toward its periphery, giving a dimple surrounded by a ring of particles bridging the film surfaces. In contrast, the thinning of octane films with dilute ordered monolayers at their surfaces finally leads to the spontaneous formation of a dense crystalline monolayer of hydrophobic particles bridging both surfaces at the center of the film. The behaviors of water and octane films with dense close-packed particle monolayers at their surfaces are very similar. In both cases, a transition from bilayer to bridging monolayer is observed at rather low capillary pressures. The implications of the above finding for particle stabilized emulsions are discussed.     

Bispectral Operators of Prime Order

 The aim of this paper is to solve the bispectral problem for bispectral operators whose order is a prime number. More precisely we give a complete list of such bispectral operators. We use systematically the operator approach and in particular – Dixmier ideas on the first Weyl algebra. When the order is 2 the main theorem is exactly the result of Duistermaat-Grünbaum. On the other hand our proofs seem to be simpler. Received: 14 February 2002 / Accepted: 10 June 2002 Published online: 21 October 2002     

Adsorption of sterically stabilized latex particles at liquid surfaces: effects of steric stabilizer surface coverage, particle size, and chain length on particle wettability

A series of five near-monodisperse sterically stabilized polystyrene (PS) latexes were synthesized using three well-defined poly(glycerol monomethacrylate) (PGMA) macromonomers with mean degrees of polymerization (DP) of 30, 50, or 70. The surface coverage and grafting density of the PGMA chains on the particle surface were determined using XPS and (1)H NMR spectroscopy, respectively. The wettability of individual latex particles adsorbed at the air-water and n-dodecane-water interfaces was studied using both the gel trapping technique and the film calliper method. The particle equilibrium contact angle at both interfaces is relatively insensitive to the mean DP of the PGMA stabilizer chains. For a fixed stabilizer DP of 30, particle contact angles were only weakly dependent on the particle size. The results are consistent with a model of compact hydrated layers of PGMA stabilizer chains at the particle surface over a wide range of grafting densities. Our approach could be utilized for studying the adsorption behavior of a broader range of sterically stabilized inorganic and polymeric particles of practical importance.     

Ultraheavy Yukawa-bound states of fourth-generation at Large Hadron Collider

A study of bound states of the fourth-generation quarks in the range of 500?C700 GeV is presented, where the binding energies are expected to be mainly of Yukawa origin, with QCD subdominant. Near degeneracy of their masses exhibits a new ??isospin??. The production of a colour-octet, isosinglet vector meson via $q\bar q \to \omega_8$ is the most interesting. Its leading decay modes are $\pi_8^\pm W^\mp$ , $\pi_8^0Z^0$ , and constituent quark decay, with $q\bar q$ and $t\bar t'$ and $b\bar b'$ subdominant. The colour octet, isovector pseudoscalar ?? ₈ meson decays via constituent quark decay, or to Wg. This work calls for more detailed study of fourth-generation phenomena at LHC.     

Wetting phenomena at the CO2/water/glass interface

A novel high-pressure apparatus and technique were developed to measure CO2/water/solid contact angles (theta) in situ for pressures up to 204 bar. For two glass substrates with different hydrophilicities, theta increased significantly with CO2 pressure. As the pressure was increased, an increase in the cohesive energy density of CO2 caused the substrate/CO2 and water/CO2 interfacial tensions (gamma) to decrease, whereas the water/substrate gamma value increased. theta for the more hydrophobic substrate was predicted accurately from the experimental water/CO2 gamma value and an interfacial model that included only long-range forces. However, for the more hydrophilic substrate, short-range specific interactions due to capping of the silanol groups by physisorbed CO2 resulted in an unusually large increase in the water/substrate gamma value, which led to a much larger increase in theta than predicted by the model. A novel type of theta hysteresis was discovered in which larger theta values were observed during depressurization than during pressurization, even down to ambient pressure. Effective receding angles were observed upon pressurization, and effective advancing angles were observed upon depressurization on the basis of movement of the three-phase contact line. The greater degree of hysteresis for the more hydrophilic silica can be attributed in part to the capping of silanol groups with CO2. The large effects of CO2 on the various interfacial energies play a key role in the enhanced ability of CO2, relative to many organic solvents, to dry silica surfaces as reported previously on the basis of FTIR spectroscopy (Tripp, C. P.; Combes, J. R. Langmuir 1998, 14, 7348-7352).     

Stability of suspensions, emulsions, and foams studied by a novel automated analyzer

The stability of dilute and concentrated dispersions (suspensions, emulsions, and foams) has been studied by a newly developed automated dispersion stability analyzer, DiStA 24. The analyzer operates by taking consecutive images of the samples studied and analyzing them by a personal computer (PC). As a result, the vertical profile of light scattered from each sample is obtained, recorded, and analyzed at time intervals preset by the computer software. In this way, the destructive processes in dispersions (sedimentation, creaming, and coalescence) can be detected well before it is possible by the naked eye and monitored automatically in the temperature range 0-50 degrees C. The new analyzer differs from the existing instruments by its simplicity and high productivity, allowing 24 samples to be measured simultaneously.