Light backscattering by hexagonal ice crystals

Backscattering of light by hexagonal ice columns and plates has been calculated by means of a ray-tracing code. It is shown that backscattering by the hexagonal ice cylinders at their arbitrary orientations is caused by a peculiar corner-reflector effect. A gigantic peak of backscattering is found at the angle of about 32.5° between the principal axis of a particle and the incidence direction for both hexagonal ice columns and plates. This peak is explained by multiple total internal reflections inside the crystals that take place for a part of incident rays. The obtained results on backscattering efficiency allow one to calculate backscattering by an ensemble of the hexagonal ice cylinders of various sizes, shapes and orientations. Slant lidar remote sensing of cirrus clouds for discrimination between aligned columns and plates is suggested as an application of the results obtained.     

Parity-nonconservation effects in the photodisintegration of polarized deuterons

P-odd correlations in deuteron photodisintegration are considered. It is shown that, in the case of unpolarized deuterons, π-meson exchanges do not contribute to these correlations. For polarized deuterons, the contribution of π-meson exchanges to the P-odd correlation is about 0.3×10^?8. The contribution to P-odd effects from weak interactions at short distances substantially exceeds the contribution from π-meson exchanges.     

Asymptotic behavior for the filtration equation in domains with noncompact boundary

We consider the initial value boundary problem with zero Neumann data for an equation modeled after the porous media equation, with variable coefficients. The spatial domain is unbounded and shaped like a (general) paraboloid, and the solution u is integrable in space and nonnegative. We show that the asymptotic profile for large times of u is one dimensional and given by an explicit function, which can be regarded as the fundamental solution of a one-dimensional differential equation with weights. In the case when the domain is a cone or the whole space (Cauchy problem), we obtain a genuine multidimensional profile given by the well-known Barenblatt solution.     

Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators

The majority of first-order methods for large-scale convex–concave saddle point problems and variational inequalities with monotone operators are proximal algorithms. To make such an algorithm practical, the problem’s domain should be proximal-friendly—admit a strongly convex function with easy to minimize linear perturbations. As a by-product, this domain admits a computationally cheap linear minimization oracle (LMO) capable to minimize linear forms. There are, however, important situations where a cheap LMO indeed is available, but the problem domain is not proximal-friendly, which motivates search for algorithms based solely on LMO. For smooth convex minimization, there exists a classical algorithm using LMO—conditional gradient. In contrast, known to us similar techniques for other problems with convex structure (nonsmooth convex minimization, convex–concave saddle point problems, even as simple as bilinear ones, and variational inequalities with monotone operators, even as simple as affine) are quite recent and utilize common approach based on Fenchel-type representations of the associated objectives/vector fields. The goal of this paper was to develop alternative (and seemingly much simpler) decomposition techniques based on LMO for bilinear saddle point problems and for variational inequalities with affine monotone operators.     

Ganglioside partitioning and aggregation in phase-separated monolayers characterized by bodipy GM1 monomer/dimer emission

The distribution of Bodipy GM1 in monolayers of binary and ternary lipid mixtures with coexisting fluid and ordered phases has been examined using a combination of atomic force microscopy and near-field scanning optical microscopy. Monolayers deposited at high (30 mN/m) and low (5 or 10 mN/m) surface pressures were examined and compared to those containing the same concentration of unlabeled ganglioside. Measurements of monomer and dimer Bodipy emission were used to distinguish aggregated from dilute ganglioside levels. For binary DPPC/DOPC monolayers, Bodipy GM1 is distributed throughout both the fluid and ordered phases at low surface pressures, and both labeled and unlabeled gangliosides result in a reduction in the size of ordered DPPC domains at 0.4% and the appearance of small aligned ganglioside-rich domains at 4%. In agreement with earlier studies, GM1 is heterogeneously distributed in small islands in the condensed DPPC domains at high surface pressure. By contrast, Bodipy GM1 causes the disappearance of large DPPC domains at 0.4% and the formation of a new GM1-rich phase at 4%. The addition of both gangliosides leads to a comparable loss of large ordered domains at low surface pressure and the appearance of a new GM1-rich phase at 30 mN/m for ternary lipid mixtures containing cholesterol. The results demonstrate the complexity of GM1 partitioning and illustrate the utility of complementary AFM and high spatial resolution two-color fluorescence experiments for understanding Bodipy GM1 aggregation and distribution.     

Polymerization of propylene by mixed Ziegler–Natta and metallocene catalysts

The polymerization of propylene using a mixture of racemic metallocenes and Ziegler–Natta catalysts was investigated. The polypropylene was obtained as a mixture of a fine powder and beads, with the powder being absorbed partially on the beads. The relative amount of the powder can be controlled by the concentration of the metallocene. The compatibility between the components of the mixed catalytic systems and the effect of the components on the rate of polymerization and on the properties of the new polymers were studied. The metallocene system dramatically affects the melt viscosity, isotacticity and molecular weight of the polymers. The two catalytic systems are able to act jointly, producing different polymers, for which separate melting and crystallization temperatures are obtained. © 1998 John Wiley & Sons, Ltd.     

Polymerization of propylene by metallocene and Ziegler–Natta mixed catalytic systems. Study of polypropylene properties

Propylene was polymerized with metallocene and Ziegler–Natta mixed-catalytic systems to obtain reactor blends of metallocene and Ziegler–Natta-derived propylene homopolymers. The two catalytic systems are able to act jointly, providing individual polymers with different melting and crystallization temperatures. Compatibility between the components of the mixed-catalytic systems and the influence of the components on the polymerization process and on the properties of the reactor blends were studied. Thermal, mechanical, viscoelastic, rheological, and optical properties of the blends were tested and compared with those of conventional polypropylene grades. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 3063–3072, 1998     

Vinyl ether end‐groups in poly(ethylene glycol)s from the Na2CO3‐promoted degradation of 1,3‐dioxolan‐2‐one polymers

The Na₂CO₃‐promoted polymerization of 1,3‐dioxolan‐2‐one (I) to afford poly(ethylene glycol) III was reinvestigated. The reaction appeared to involve a nucleophilic attack against the carbonyl and methylene groups of I to afford poly(carbonate) II with poly(ethylene glycol) linkages and ethylene oxide IV as a side product (10–22%). As the reaction progressed, poly(carbonate) II decreased and poly(ethylene glycol) III increased. Under some conditions, poly(ethylene glycol)s V and VI with vinyl ether terminal groups were formed unexpectedly. The formation of unsaturated products during the polymerization of I/EO (ethylene oxide) has not been reported in the literature. We believe that vinyl ethers were formed from the degradation of poly(carbonate)s and were accompanied by a reduction in molecular weight. The structures of vinyl ethers V and VI were confirmed by hydrogenation of the double bond into the ethyl ether group in VII and VIII, respectively. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 152–160, 2000     

On the Interaction of Turbulent Shear Layers with Harmonic Perturbations

The problem of coherent perturbations in a turbulent shear layer is considered for the purpose of developing a mathematical model based on a triple decomposition that extracts the coherent components of random fluctuations. The governing equations for the mean and the coherent parts of flow are derived, assuming the eddy-viscosity equivalence for the random part of flow, and solved by iterations to provide a coupled solution of the problem as a whole. Calculations agree well with experimental data in the upstream part of the layer where the mean–coherent flow interaction is the most important. In this region, the interaction changes the mean flow velocity distribution in such a manner that the neutral stability curve is shifted upstream relative to its position in the undisturbed layer and the perturbation intensity decreases further downstream. Experiments show that the coherent waves suppress the turbulent Reynolds stress production downstream of this region, but the model fails to predict the layer spreading correctly probably due to an inadequate turbulence closure of the mean flow. For the case of a turbulent mixing layer, we suggest a new closure relation that takes into account this coherent-random interaction.