Broadening compensation for ultrashort pulses in photonic crystals

Extremely large group velocity dispersion of both signs can be achieved at the band edges of guided modes in photonic crystal waveguides. The selection of a proper value and sign of this parameter allows the design of short-length waveguides to compensate for pulse broadening. This pulse broadening can be caused, for instance, when a photonic crystal delay line is introduced. We present a theoretical study of the possibilities of using photonic crystal waveguides as intra-circuital dispersion compensation elements for ultrashort pulses, so the width of a transmitted pulse can be reduced. However, we also demonstrate that recovering the original pulse shape is not possible for these large-bandwidth pulses due to higher-order dispersion terms.     

Nonmonotone travelling waves in a single species reaction-diffusion equation with delay

We prove the existence of a continuous family of positive and generally nonmonotone travelling fronts for delayed reaction-diffusion equations , when g∈C²(R₊,R₊) has exactly two fixed points: x₁=0 and x₂=K>0. Recently, nonmonotonic waves were observed in numerical simulations by various authors. Here, for a wide range of parameters, we explain why such waves appear naturally as the delay h increases. For the case of g with negative Schwarzian, our conditions are rather optimal; we observe that the well known Mackey-Glass-type equations with diffusion fall within this subclass of (∗). As an example, we consider the diffusive Nicholson's blowflies equation.     

Upper bound for the magnetic force gradient in graphite

In this work we investigate possible ferromagnetic order on the graphite surface by using magnetic force microscopy (MFM). Our data show that the tip-sample interaction along the steps is independent of an external magnetic field. Moreover, by combining kelvin probe force microscopy and MFM, we are able to separate the electrostatic and magnetic interactions along the steps obtaining an upper bound for the magnetic force gradient of 16 μN/m. Our experiments suggest the absence of ferromagnetic signal in graphite at room temperature.     

Relation between asymmetrical orbital angular momentum and irradiance-profile rotation for partially coherent beams

On the basis of the irradiance-moment formalism for describing general partially coherent beams, we investigate the relation between the spatial orientation of the transverse beam profile upon propagation and the asymmetrical part of its orbital angular momentum (OAM). More specifically, a necessary and sufficient condition (one-to-one correspondence) is shown between freely propagating non-rotating beams and vanishing asymmetrical OAM. As a corollary, it is obtained that any beam emerging from optical systems that transform a rotating field into a non-rotating beam exhibits vortex OAM only.     

Motzkin predecomposable sets

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family.     

Heuristic solution approaches for the maximum minsum dispersion problem

The Maximum Minsum Dispersion Problem (Max-Minsum DP) is a strongly NP-Hard problem that belongs to the family of equitable dispersion problems. When dealing with dispersion, the operations research literature has focused on optimizing efficiency-based objectives while neglecting, for the most part, measures of equity. The most common efficiency-based functions are the sum of the inter-element distances or the minimum inter-element distance. Equitable dispersion problems, on the other hand, attempt to address the balance between efficiency and equity when selecting a subset of elements from a larger set. The objective of the Max-Minsum DP is to maximize the minimum aggregate dispersion among the chosen elements. We develop tabu search and GRASP solution procedures for this problem and compare them against the best in the literature. We also apply LocalSolver, a commercially available black-box optimizer, to compare our results. Our computational experiments show that we are able to establish new benchmarks in the solution of the Max-Minsum DP.     

Mechanically Interlocked Single‐Wall Carbon Nanotubes

Extensive research has been devoted to the chemical manipulation of carbon nanotubes. The attachment of molecular fragments through covalent‐bond formation produces kinetically stable products, but implies the saturation of some of the C? C double bonds of the nanotubes. Supramolecular modification maintains the structure of the SWNTs but yields labile species. Herein, we present a strategy for the synthesis of mechanically interlocked derivatives of SWNTs (MINTs). In the key rotaxane‐forming step, we employed macrocycle precursors equipped with two π‐extended tetrathiafulvalene SWNT recognition units and terminated with bisalkenes that were closed around the nanotubes through ring‐closing metathesis (RCM). The mechanically interlocked nature of the derivatives was probed by analytical, spectroscopic, and microscopic techniques, as well as by appropriate control experiments. Individual macrocycles were observed by HR STEM to circumscribe the nanotubes.     

Microemulsion electrokinetic chromatography as a suitable tool for lipophilicity determination of acidic,neutral, and basic compounds

In the present work, several MEEKC systems are studied to assess their suitability for lipophilicity determination of acidic, neutral, and basic compounds. Thus, several microemulsion compositions over a wide range of pH values (from 2.0 to 12.0), containing heptane, 1?butanol and different types and amounts of surfactant (SDS or sodium cholate: from 1.3 to 3.3%) are characterized using Abraham's solvation model. The addition of acetonitrile (up to 10%) is also studied, since it increases the resolution of the technique for the most lipophilic compounds. The system coefficients obtained are very similar to those of the 1?octanol/water, used as the reference lipophilicity index, allowing simple and linear correlations between the 1?octanol/water partition values (log P_o/w) and MEEKC mass distribution ratios (log k_MEEKC). Variations in the microemulsion composition (aqueous buffer, surfactant, concentration of ACN) did not significantly affect the similarity of the MEEKC systems to log P_o/w partition.     

Dinuclear azolato-bridged complexes of the nickel group metals with haloaryl ligands: a reinvestigation of their behavior in solution

A reinvestigation of the NMR spectra of the complexes (NBu4)2[M2(mu-LL)2R4] (M = Pd, Ni, Pt, LL = pyrazolate (pz), 3,5-dimethylpyrazolate (dmpz), 3-methylpyrazolate (mpz), indazolate (indz), R = C6F5; M = Pd, LL = pz, dmpz, mpz, indz, R = 2,4,6-C6F3H2) shows that the boat-shaped dimeric structures of their anions are quite stable in solution, and the previously proposed fast equilibria or dissociations to give species such as [R2M(N-N)(acetone)]-, [R2M(acetone)2] + 2dmpz-, or [R2M(N1-N2)(acetone)]- + [R2M(N2-N1)(acetone)]- in no case occur. A mixture of the two diastereoisomers (head-to-head, HH, and head-to-tail, HT) is present for the asymmetrically substituted azolates (mpz and indz), in a ratio ranging from 1:7 to 1:30 for the different complexes. Strong through-space coupling between the endo ortho fluorine nuclei of different MR2 fragments is observed in the 19F NMR spectra of these diastereoisomers whose boatlike structures place these atoms at short distances.