Effects of Polymer Bridging and Electrostatics on the Rheological Behavior of Aqueous Colloidal Dispersions†

Effects of a low molecular weight physically adsorbed polyethylene oxide (PEO) and the range of the electrostatic repulsion on the rheological behavior of silica dispersions (as a model system) has been investigated. Particular attention is given to the evolution of the rheological behavior with increasing the polymer concentration in the system and also effectiveness of the polymer as a dispersant under extreme conditions (high ionic strength). Results indicate that at small separation distances and low polymer coverage, the polymer chains are long enough to adsorb on the surface of two particles simultaneously causing bridging flocculation in the system and hence increasing the viscosity and linear viscoelastic functions of the dispersion. A significant increase was observed in the viscosity of the dispersion at salt concentrations high enough to eliminate electrostatics between the particles. Under these conditions,the viscosity of the system increased significantly when PEO was added to the dispersion showing that at high electrolyte concentrations, a neutral polymer such as PEO is not able to stabilize the system.     

On p-Extensions of Fields of Characteristic p

It is proved that a Galois extension of a field of characteristic p is completely determined by its Galois group and the endomorphism of the additive group of the group algebra that corresponds to the raising to the power p.     

Generalized Artin–Hasse and Iwasawa Formulas for the Hilbert Symbol in a High-Dimensional Local Field

The generalized Hilbert symbol in a cyclotomic extension of an absolutely unramified higher local field of characteristic 0 with a perfect last residue field of characteristic p > 2 is considered. Generalized Artin–Hasse and Iwasawa formulas are derived from an explicit Kummer Type Vostokov formula. Bibliography: 13 titles.     

A Kinematic Formula for Affine Diameters and Affine Medians of a Convex Set

For a planar convex set K with C ²-smooth boundary, the area of the set of the points lying on a given number of affine diameters of K is estimated. As a corollary, it is proved that the area of K is at most pM² /4\pi M^2 /4 , where M is the largest length of a chord of K halving the area of K. Bibliography: 2 titles.     

Projective varieties with projectively equivalent singular 0-dimensional sections

Fix integers m, n such that 1 ≤ m ≤ n ? 3. Let X ? Pⁿ be an integral non-degenerate m-dimensional variety. Assume either char(K) = 0 or char(K) > deg(X). Here we prove that all general 0-dimensional sections of X containing a tangent vector to a smooth point of X are protectively equivalent if and only if n ? m + 1 ≤ deg(X) ≤ n ? m + 2.     

Multipulse regimes of excitation of optical superradiance due to a two-photon transition

Multimode triggered optical superradiance due to a two-photon transition is theoretically studied. Kinetic equations are derived for the dynamics of cooperative development of coherence and population inversion of optical centers interacting with each other through a common field of emitted photons. Various regimes of triggering of optical superradiance due to a two-photon transition are considered. The possibility of creating a quantum photomultiplier on the basis of the triggered optical superradiance is discussed.     

Focusing of singular beams

The process of focusing of an inhomogeneously polarized beam passed through a system consisting of a uniaxial crystal and a polarization filter is considered. It is shown that the action of this system is equivalent to the action of a phase transparency with a complex relief of the refractive index. In particular, if the angle between the axes of the quarter-wave plate and the polarizer is equal to 45°, this transparency has a helicoidal relief. Simultaneously, two singular beams with different curvatures of their wavefronts arise in the transparency. The action of the lens consists in formation of a combined singular beam having three focal waists. The boundary wave arising upon focusing is able not only to form a new spectrum of toroidal vortices, but also to straighten the focusing region, forming a fairly extended range with a weak divergence.     

Decrease in the group velocity of a light pulse in the Bose-Einstein condensate of a dilute gas

A semiclassical theory of electromagnetically induced transparency in a Bose-Einstein condensate is considered. A nonlinear Schrödinger equation that describes the interaction of the Bose-Einstein condensate with an electromagnetic field is derived. An analysis of the obtained solutions to this equation demonstrates a decrease in the group velocity of the light pulse.