Local structure of multiferroic RMn2O5: Important role of the R site

The temperature and magnetic field dependent local structure of RMn₂O₅ systems was examined. While no significant displacements of the Mn ions are observed, it is found that the R-O distribution exhibits changes at low temperature which are possibly related to the changes in the electric polarization. Density functional computations are used to explore the system dynamics and to link the local structural measurements with anomalous changes in the infrared absorption spectra. The anomalous R-O distribution and observed coupling to magnetic fields point to the need to properly treat the 4f electrons on the R sites in these systems.     

Synchronization of eukaryotic cells by periodic forcing

We study a cell population described by a minimal mathematical model of the eukaryotic cell cycle subject to periodic forcing that simultaneously perturbs the dynamics of the cell cycle engine and cell growth, and we show that the population can be synchronized in a mode-locked regime. By simplifying the model to two variables, for the phase of cell cycle progression and the mass of the cell, we calculate the Lyapunov exponents to obtain the parameter window for synchronization. We also discuss the effects of intrinsic mitotic fluctuations, asymmetric division, and weak mutual coupling on the pace of synchronization.     

Modulus and Poincaré Inequalities on Non-Self-Similar Sierpiński Carpets

A carpet is a metric space homeomorphic to the Sierpiński carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincaré inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincaré inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.     

Growth, new growth, and amplification of carbon nanotubes as a function of catalyst composition

Carbon nanotubes (CNTs) have been grown using Fe, Co, Ni, and Co/Fe spin-on-catalyst (SOC) systems, involving the metal salt dispersed with a spin-on-glass precursor. During initial growth runs (CH4/H2/900 degrees C), the CNT yield followed the order Co-SOC > Fe-SOC > Ni-SOC. The Fe catalysts produced the longest nanotubes at the expense of a larger average CNT diameter and broader diameter distribution than the Co-SOC system. A series of Co/Fe-SOCs were prepared where as the atomic percentage of Co is increased nucleation of CNT increases but the CNT length decreases. The linear relationship between the diameter and length of CNTs grown from the Co/Fe-SOC suggests that slow growth is beneficial with respect to control over CNT diameter. After initial CNT growth, the original samples were subjected to additional growth runs. Four individual reactions were observed in the Fe-SOC and binary Co/Fe-SOC: regrowth (amplification), double growth (a second CNT growing from a previously active catalyst), CNT etching, and nucleation from initially inactive catalysts (new growth). CNT etching was observed for the mixed catalyst systems (Co/Fe-SOC) but not for either Fe-SOC or Co-SOC. During the regrowth experiments, CNTs were observed that were not present after the initial growth run (and were not as a result of amplification or double growth). Thus, catalysts, which were initially inactive toward nucleation of CNTs in the original growth run, are capable of becoming activated when placed back into the furnace and submitted to regrowth under identical conditions.     

Removable sets for homogeneous linear partial differential equations in Carnot groups

Let L be a homogeneous left-invariant differential operator on a Carnot group. Assume that both L and L^t are hypoelliptic. We study the removable sets for L-solutions. We give precise conditions in terms of the Carnot- Caratheodory Hausdorff dimension for the removability for L-solutions under several auxiliary integrability or regularity hypotheses. In some cases, our criteria are sharp on the level of the relevant Hausdorff measure. One of the main ingredients in our proof is the use of novel local self-similar tilings in Carnot groups.     

Determination of silicon by an indirect atomic-absorption method using carbon-rod electrothermal atomization

An indirect procedure has been developed for the determination of trace amounts of silicon by atomic-absorption with carbon-rod electrothermal atomization. After dissolution, the silicon is extracted as silicomolybdic acid into a mixture of diethyl ether and pentan-1-ol (5 + 1). The co-extraction of excess of molybdate reagent is prevented by the addition of citrate, which also destroys phosphomolybdic and arsenomolybdic acids. The organic layer is washed with hydrochloric acid, mul quantities are transferred to the electrothermal atomizer and the molybdenum is measured. The method has been applied to analysis of several steels.     

Peptides—XXXV: Synthesis of the 17–26 fragment of a lysozyme analogue

The fully protected 17–26 fragment of a lysozyme analogue has been synthesised. A fragment condensation approach has been employed using the protected subfragments 17–19, 20–22 and 23–26. In the synthesis of the subfragments the use of the diphenylphosphinyl mixed anhydride method has been demonstrated.