Emergent biaxiality in nematic microflows illuminated by a laser beam

Anisotropic fluids (e.g. liquid crystals) offer a remarkable promise as optofluidic materials owing to the directional, tunable, and coupled interactions between the material, flow, and the optical fields. Here we present a comprehensive in silico treatment of this anisotropic interaction by performing nonequilibrium molecular dynamics simulations. We quantify the response of a nematic liquid crystal (NLC) undergoing a Poiseuille flow in the Stokes regime, while being illuminated by a laser beam incident perpendicular to the flow direction. We adopt a minimalistic model to capture the interactions, accounting for two features: first, the laser heats up the NLC locally; and second, the laser polarises the NLC and exerts an optical torque that tends to reorient molecules of the nematic phase. Because of this reorientation the liquid crystal exhibits small regions of biaxiality, where the nematic director is one symmetry axis and the axis of rotation for the reorientation of the molecules is the other one. We find that the relative strength of the viscous and the optical torques mediates the flow-induced response of the biaxial regions, thereby tuning the emergence, shape and location of the regions of enhanced biaxiality. The mechanistic framework presented here promises experimentally tractable routes toward novel optofluidic applications based on material-flow-light interactions.     

Tris(oxalato)phosphorus acid and its lithium salt

The conversion of three equivalents of anhydrous oxalic acid with phosphorus pentachloride yields tris(oxalato)phosphorus acid 1, which crystallizes from diethyl ether solutions as protonated diethyl ether complex [(Et2O)2H](+)[P(C2O3)3)]-. The superacidic compound can be used as catalyst for Friedel-Crafts-type reactions. Upon neutralization with lithium hydride, the lithium salt Li[P(C2O3)3] 2 is obtained, which is highly soluble in aprotic solvents and which exhibits a wide voltage window. Thus, the lithium compound is a promising candidate as electrolyte for high performance non-aqueous batteries.     

On a new construction in group theory

This paper continues the investigation of the groups RF(G)\mathcal{RF}(G) introduced and studied in [I.M. Chiswell and T.W. Müller, A class of groups with canonical ℝ-tree action, Springer LNM, to appear]. Two new concepts, that of a test function, and that of a pair of locally incompatible (test) functions are introduced, and their theory is developed. As application, we obtain a number of new quantitative as well as structural results concerning RF(G)\mathcal{RF}(G) and its quotient RF(G)/E(G)\mathcal{RF}(G)/E(G) modulo the subgroup E(G) generated by the elliptic elements. Among other things, the cardinality of RF(G)\mathcal{RF}(G) is determined, and it is shown that both RF(G)\mathcal{RF}(G) and RF(G)/E(G)\mathcal{RF}(G)/E(G) contain large free subgroups, and that their abelianizations both contain a large ℚ-vector space as direct summand.     

Normal growth of large groups, II

We show that a large class of groups has normal subgroup growth of type n^{log n}, which is the same as the growth type of a free group of rank 2.Received: 21 June 2004     

Weakly multiplicative arithmetic functions and the normal growth of groups

Archiv der Mathematik - We show that an arithmetic function which satisfies some weak multiplicativity properties and in addition has a non-decreasing or $$\log $$ -uniformly continuous normal...     

The order of elements in Sylow p-subgroups of the symmetric group

Define a random variable ξ_n by choosing a conjugacy class C of the Sylow p-subgroup of S_pn by random, and let ξ_n be the logarithm of the order of an element in C. We show that ξ_n has bounded variance and mean order log n /log p +O(1), which differs greatly from the average order of elements chosen with equal probability. This revised version was published online in June 2006 with corrections to the Cover Date.     

Leaching of the Anthraquinone Dye Solvent Blue 59 Incorporated into Organically Modified Silica Xerogels

The effects of preparation method and precursor composition on the leaching behavior of the anthraquinone dye Solvent Blue 59 incorporated into silica based xerogels have been studied. Xerogels were prepared under acidic conditions from mixtures of 20 mol% of organically modified silicon alkoxides, R–Si(OR)3, in Si(OR)4 (R = methyl or ethyl, R = methyl, vinyl, phenyl). The dye was added at the beginning of the sol-gel reaction. The reaction was carried out by either hydrolysis under acidic conditions or acidolysis by formic acid. The dye incorporated was leached with refluxing ethanol using a Soxhlet extraction procedure to simulate the long-term stability of the samples prepared. With increasing size of organic substituent (methyl < vinyl < phenyl), the amount of dye leached decreases. Results from nitrogen adsorption experiments show that all samples characterized have about the same average pore diameter, but they differ in total pore volume and BET surface area. With increasing size of the organic residue, the pore volume decreases by an order of magnitude. Therefore, it is concluded that the microstructure of the xerogels prepared determines the retention behavior of dyes incorporated during the sol-gel reaction.     

Sets with more differences than sums

We show that a random set of integers with density 0 has almost always more differences than sums.      

Interference-free coulometric titration of water in lithium bis(oxalato)borate using Karl Fischer reagents based on N-methylformamide

A non-alcoholic coulometric reagent based on N-methylformamide (NMF) was shown to eliminate the severe interference effect caused by the alcohol component of the conventional Karl Fischer (KF) reagent on the battery electrolyte lithium bis(oxalato)borate (LiBOB). For sample amounts up to 240 μg of water, the stoichiometry of the KF reaction deviated only slightly from the ideal 1:1 ratio for the best reagent composition. Both solid and dissolved (in acetonitrile, tetrahydrofuran (THF), and ethylene carbonate/ethyl methyl carbonate) LiBOB were titrated successfully using a Metrohm 756 KF Coulometer with a diaphragm cell. The detection limit was estimated to be 0.5-1 μg of water using 100 ml of reagent in this system.