The effect of structural variation of alcohols on water solubilization in nonionic microemulsions 1. From linear to branched amphiphiles--general considerations

This article is the first part of a two-part study that exemplifies how to treat the solubilization of water in multicomponent surfactant-based systems. In particular, it aims at clarifying the role of cosurfactants in water solubilization in these systems. The judicious selection of the components in such systems to maximize water solubilization is occasionally thought to be dictated by the chain length compatibility principle, which may be expressed quantitatively by the BSO (Bansal, Shah, O'Connell) equation. Here we demonstrate some limitations of the equation. For example, in our best model system, C12(EO)8/dodecane+pentanol=1:1 (by weight)/water at 27+/-0.2 degrees C, the BSO equation predicts that no alcohol is needed for maximum water solubilization, contrary to our experimental findings. We discuss how to optimize the alcohol/oil weight ratio needed for stabilizing four-component microemulsions. In our model systems C12(EO)8 or C(18:1)(EO)10/pentanol/dodecane/water, this optimal weight ratio is 1:1. We also highlight the difference between the effect of normal alcohols on water solubilization-which passes via a maximum-and their effect on percolation processes and structured changes of proteins, which depends solely upon the alcohol hydrophobicity. For the investigation of the effect of branching on phase behavior the utilization of an extended form of the geometrical branching factor F(b) is suggested. The meaning of this factor is elucidated by comparing it with topological indices.     

Direct measurement of the flow field around swimming microorganisms

Swimming microorganisms create flows that influence their mutual interactions and modify the rheology of their suspensions. While extensively studied theoretically, these flows have not been measured in detail around any freely-swimming microorganism. We report such measurements for the microphytes Volvox carteri and Chlamydomonas reinhardtii. The minute (～0.3%) density excess of V. carteri over water leads to a strongly dominant Stokeslet contribution, with the widely-assumed stresslet flow only a correction to the subleading source dipole term. This implies that suspensions of V. carteri have features similar to suspensions of sedimenting particles. The flow in the region around C. reinhardtii where significant hydrodynamic interaction is likely to occur differs qualitatively from a puller stresslet, and can be described by a simple three-Stokeslet model.     

A Note On Subloop Lattices

Pálfy and Pudlák (Algebra Universalis 11, 22–27, 1980) posed the question: is every finite lattice isomorphic to an interval sublattice of the lattice of subgroups of a finite group? in this paper we will look at examples of lattices that can be realized as subloop lattices but not as subgroup lattices. This is a first step in answering a new question: is every finite lattice isomorphic to an interval sublattice of the subloop lattice of a finite loop?     

Almost Hamiltonian Groups

In this paper we investigate the following problem in Group Theory: which properties $cal P$ transfer (or do not transfer) from all cyclic subgroups, or all abelian subgroups to all arbitrary subgroups? We solve this problem completely when $cal P$ is the property of having finite index in its normal closure, proving that $cal P$ carries from abelian, but not from cyclic to arbitrary subgroups. We use primarily some results of B.H. Neumann.     

Nature's microfluidic transporter: rotational cytoplasmic streaming at high Péclet numbers

Cytoplasmic streaming circulates the contents of large eukaryotic cells, often with complex flow geometries. A largely unanswered question is the significance of these flows for molecular transport and mixing. Motivated by "rotational streaming" in Characean algae, we solve the advection-diffusion dynamics of flow in a cylinder with bidirectional helical forcing at the wall. A circulatory flow transverse to the cylinder's long axis, akin to Dean vortices at finite Reynolds numbers, arises from the chiral geometry. Strongly enhanced lateral transport and longitudinal homogenization occur if the transverse Péclet number is sufficiently large, with scaling laws arising from boundary layers.     

The effect of structural variation of alcohols on water solubilization in nonionic microemulsions 2. Branched alcohols as solubilization modifiers: results and interpretation

In this second part of a paper dealing with the effect of branched alcohols on solubilization, an attempt has been made to provide explanations of experimental data related mostly to the system Brij 97/branched alcohol + dodecane = 1:1 (by weight)/water at 27+/-0.2 degrees C. Applying the Hou-Shah mechanism it was shown that for many C4-C6 branched alcohol isomers having one methyl branch, solubilization behavior is readily interpreted by assuming control of the critical radius, R(c). Two parameters, both included in the definition of the branching factor, F(b) (which was treated in the first part of the paper), were also used to analyze solubilization data. The first, l(i), is defined as the distance from the free end of the alcohol molecule to the methyl branch. The second, d, is virtually N(A), the chain length of the alcohol. When l(i)>3, the solubilization becomes dominated by the natural radius of curvature, R0. Also, we have suggested that for R(c)-control, solubilization will be enhanced in direct proportion to the distance d-l(i), whereas for R0-control, solubilization will increase with decreasing d-l(i). The validity of our assumptions was demonstrated in many cases. Some examples of the more complicated case of double branching (two methyl groups along the alcohol chain) were also analyzed.     

Resolving sets and integer programs for recommender systems

Recommender systems make use of different sources of information for providing users with recommendations of items. Such systems are often based on either collaborative filtering methods which make automatic predictions about the interests of a user, using preferences of similar users, or content based filtering that matches the user’s personal preferences with item characteristics. We adopt the content-based approach and propose to use the concept of resolving set that allows to determine the preferences of the users with a very limited number of ratings. We also show how to make recommendations when user ratings are imprecise or inconsistent, and we indicate how to take into account situations where users possibly don’t care about the attribute values of some items. All recommendations are obtained in a few seconds by solving integer programs.

     

Chiral symmetry breaking during crystallization: an advection-mediated nonlinear autocatalytic process

When a chiral chemical compound crystallizes from solution or from its melt, stirring often results in the formation of crystals of just one of the two possible enantiomers, while without fluid advection both enantiomers are formed. We demonstrate with simulations of the dynamics of the system that secondary nucleation is a nonlinear autocatalytic phenomenon that can explain these observations. Furthermore, we present theoretical arguments and experimental results that suggest that at the microscale the mechanism of secondary nucleation is whisker crystal growth and dispersion in the fluid flow.     

Polar Decomposition of Locally Finite Groups

The study of loops as transversals in groups dates back to the works of Reinhold Baer. In the past few years there have been several papers using polar decomposition in linear algebra in order to construct Bruck loops. In this paper we generalize the notion of polar decomposition to any arbitrary group, and we show that in any polar decomposition the binary operation “inherited” from the group leads to the construction of a Bruck loop.