Reorientation dynamics of nematics encapsulated in microscopic volumes in a strong electric field

We theoretically describe a new regime of reorientation of the director field \(\widehat n\) and velocity v of a nematic liquid crystal (LC) encapsulated in a rectangular cell under the action of strong electric field E directed at angle α (~π/2) to the horizontal surfaces bounding the LC cell. The numerical calculations in the framework of nonlinear generalization of the classical Eriksen–Leslie theory showed that at certain relations between the torques and momenta affecting the unit LC volume and E ? E_th, transition periodic structures can arise during reorientation of \(\widehat n\), if the corresponding distortion mode has the fastest response and, thus, suppresses all the rest of the modes, including uniform ones. The position of sites of these periodic structures is affected by the value of field E, angle α, and the character of anchoring of LC molecules to the bounding surfaces. The calculations performed for the nematic formed by 4-n-penthyl-4’-cyanobiphenyl showed that several vortexes can form in an LC cell under the action of reorientation of the nematic field; the boundaries of these vortexes are determined by the positions of periodic structure sites.     

Interaction of REE ions with organophosphorous compounds microencapsulated in a porous polymer

Microcapsules containing organophosphorous compounds and their mixtures with crown ether are prepared by suspension polymerization. The interaction of microencapsulated substances with metal ions via the contacting of alkaline and acid solutions of the latter with synthesized samples is examined. The process was monitored by means of infrared spectroscopy. From the spectroscopic data, we draw conclusions as to the composition of the formed metal complexes depending on the character of the environment.     

On semidefinite programming relaxations of maximum k-section

We derive a new semidefinite programming bound for the maximum $k$ -section problem. For $k=2$ (i.e. for maximum bisection), the new bound is at least as strong as a well-known bound by Poljak and Rendl (SIAM J Optim 5(3):467?C487, 1995). For $k \ge 3$ the new bound dominates a bound of Karisch and Rendl (Topics in semidefinite and interior-point methods, 1998). The new bound is derived from a recent semidefinite programming bound by De Klerk and Sotirov for the more general quadratic assignment problem, but only requires the solution of a much smaller semidefinite program.     

A chromatographic method for hydrophobicity investigations of sorbents

Summary The energy of interaction (₀) between the methylene group and the surface of a sorbent is proposed for use in the quantitative evaluation of the hydrophobicity of a sorbent. A method was developed to determine the ₀ parameter from chromatographic measurements using the investigated sorbent as the stationary phase and linear methylene-containing homologous series, e.g., alkanols, amino-alkanes, etc., as the test compounds. The effectiveness of this method is demonstrated by using, as examples, a series of bonded stationary phases and a series of cross-linked copolymeric sorbents differing in the concentration of the hydrophobic groups. The proposed method is compared with the Martin rule used extensively in the chromatography of oligomers.     

Reduction of symmetric semidefinite programs using the regular \ast-representation

We consider semidefinite programming problems on which a permutation group is acting. We describe a general technique to reduce the size of such problems, exploiting the symmetry. The technique is based on a low-order matrix $*$ -representation of the commutant (centralizer ring) of the matrix algebra generated by the permutation matrices. We apply it to extending a method of de Klerk et al. that gives a semidefinite programming lower bound to the crossing number of complete bipartite graphs. It implies that cr(K _8,n ) ≥ 2.9299n ² ? 6n, cr(K _9,n ) ≥ 3.8676n ² ? 8n, and (for any m ≥ 9) $$\lim_{n\to\infty}\frac{{\rm cr}(K_{m,n})}{Z(m,n)}\geq 0.8594\frac{m}{m-1},$$ where Z(m,n) is the Zarankiewicz number $\lfloor\frac{1}{4}(m-1)^2\rfloor\lfloor\frac{1}{4}(n-1)^2\rfloor$ , which is the conjectured value of cr(K _m,n ). Here the best factor previously known was 0.8303 instead of 0.8594.     

Coordination of 2-phosphorylalkyl-substituted 1,8-naphthyridines in complexes with lanthanide nitrates

The reaction of 2-phosphorylalkyl-substituted 1,8-naphthyridines, viz., 2-[2-(diphenylphosphoryl)propan-2-yl]-1,8-naphthyridine (L ¹ ) and 2-[2-(diphenylphosphoryl)ethyl]-1,8-naph-thyridine (L ² ), with lanthanide nitrates (Nd, Eu, or Lu) afforded complexes with the metal-to-ligand molar ratio of 1: 1 and 1: 2. Based on the IR and Raman spectroscopic data, it was found that the coordination of the ligands L ¹ and L ² in all complexes occurs through the P=O group and the nitrogen atoms of the naphthyridine moiety.     

On NP-hardness of the clique partition—Independence number gap recognition and related problems

We show that for a graph G it is NP-hard to decide whether its independence number α(G) equals its clique partition number even when some minimum clique partition of G is given. This implies that any α(G)-upper bound provably better than is NP-hard to compute.To establish this result we use a reduction of the quasigroup completion problem (QCP, known to be NP-complete) to the maximum independent set problem. A QCP instance is satisfiable if and only if the independence number α(G) of the graph obtained within the reduction is equal to the number of holes h in the QCP instance. At the same time, the inequality always holds. Thus, QCP is satisfiable if and only if . Computing the Lovász number ?(G) we can detect QCP unsatisfiability at least when . In the other cases QCP reduces to gap recognition, with one minimum clique partition of G known.     

Orientational fluctuations and phase transitions in 8CB confined by cylindrical pores of the PET film

Abstract

Results of optical investigations of the isotropic-nematic and nematic-smectic A phase transitions in porous polyethyleneterephthalate (PET) films filled with octyl-cyanobihenyl (8CB) liquid crystal (LC) are reported. Samples of porous films of thickness 23 µm with normally oriented cylindrical pores of a radius R ranging from 10 nm to 1000 nm were prepared using the track-etched membrane technology. The dynamic light scattering method was used to probe the nematic orientational fluctuations of confined LC samples. The corresponding relaxation time τ was measured as a function of R and temperature T at slow enough cooling rates (0.3–0.6 K/h) to locate the phase transition temperatures. Changes in τ(T) dependencies relatively sensitivity fingerprint the LC phase transformations. Experimental results are analysed using the Landau-de Gennes-Ginzburg phenomenological approach.