Iron nanoparticles in the coupling of alkyl halides with aryl Grignard reagents

Iron nanoparticles, either formed in situ stabilized by 1,6-bis(diphenylphosphino)hexane or polyethylene glycol (PEG), or preformed stabilized by PEG, are excellent catalysts for the cross-coupling of aryl Grignard reagents with primary and secondary alkyl halides bearing beta-hydrogens and they also prove effective in a tandem cyclization/cross-coupling reaction.     

Fluorinated liquid crystals formed by halogen bonding

New, halogen-bonded fluorinated mesogens are reported; the expected microphase separation associated with perfluoroalkyl chains is surprisingly absent in the mesophase.     

Thermo-optically tunable silicon photonic crystal light modulator

We designed, fabricated, and characterized a thermo-optically tunable compact (10 μm × 10 μm) silicon photonic crystal (PhC) light modulator that operates at around 1.55 μm for TE polarization. The operational principle of the device is the modulation of the cutoff frequency in a silicon-based line defect PhC. The cutoff frequency is shifted because of the thermo-optic tuning of the silicon refractive index, which is realized by localized heating on the PhC. The modulator is formed by a triangular lattice array of cylindrical air holes on a silicon-on-insulator wafer. Optical characterization was carried out, and the result clearly showed thermo-optic tuning of the cutoff frequency at around 1.55 μm.     

Aggregation kinetics and the nature of phase separation in two-dimensional dipolar fluids

The kinetics of aggregation in a monolayer of dipolar particles are studied using stochastic dynamics computer simulations. Transient concentrations of end defects (at low density) and Y-shaped defects (at high density) clearly exceed those at equilibrium. Although very large dipole moments are expected to disfavor such defects at equilibrium, it is found that the transient defect concentrations increase with increasing dipole moment. The results suggest that the conditions for defect-driven condensation--as proposed by Tlusty and Safran [T. Tlusty and S. A. Safran, Science 290, 1328 (2000)]--could be met by kinetic trapping, giving rise to a metastable phase transition between isotropic fluid phases.     

Surface Chemistry of Polyacetylene: Adhesion to Silica,Derivatization With Nickel And Catalytic Activity

Adhesion of (CH)_x film prepared by the Luttinger method to glass can be improved by silylation in order to more closely match dispersive surface energies. Treatment of n-type (CH) films with NiBr₂/HMPA/THF affords (CH)_x -supported N° which shows selectivity in hydrogenation of phenyl acetylene.     

Temporal breakdown and Borel resummation in the complex Langevin method

We reexamine the Parisi–Klauder conjecture for complex e^iθ/2?⁴$e^{i\theta /2}{?}^4$ measures with a Wick rotation angle 0≤θ/2≤π/2$0\le \theta /2\le \pi /2$ interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t$t$ encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t→0$t\to 0$ asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t$t$, including their t→∞$t\to \infty$ equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the ‘correct’ result for t$t$ larger than a finite t_c$t_c$. The breakdown time t_c$t_c$ increases powerlike for decreasing strength of the noise’s imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure.     

White matter maturation in the brains of Long Evans shaker myelin mutant rats by ex-vivo QSI and DTI

The brains of Long Evans shaker (les) rats, a model of dysmyelination, and their age- matched controls were studied by ex-vivo q-space diffusion imaging (QSI) and diffusion tensor imaging (DTI). The QSI and DTI indices were computed from the same acquisition. The les and the control brains were studied at different stages of maturation and disease progression. The mean displacement, the probability for zero displacement and kurtosis were computed from QSI data while the fractional anisotropy (FA) and the eigenvalues were computed from DTI. It was found that all QSI indices detect the les pathology, at all stages of maturation, while only some of the DTI indices could detect the les pathology. The QSI mean displacement was larger in the les group as compared with their age-matched controls while the probability for zero displacement and the kurtosis were both lower all indicating higher degree of restriction in the control brains. Since all the DTI eigenvalues were higher in the les brains as compared to controls, the less efficient DTI measure for discerning the les pathology was found to be the FA. Clearly, the most sensitive DTI parameter to the les pathology is λ₃, i.e. the minimal diffusivity. Since the QSI and DTI data were obtained from the same acquisition, despite the somewhat higher SNR of the QSI data compared to the DTI data, it seems that the higher diagnostic capacity of the QSI data in this experimental model of dysmyelination, originates mainly from the higher diffusing weighting of the QSI data.     

Coupled spring equations

Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described. For the linear model using Hooke's Law, the motion of each weight is described by a fourth-order linear differential equation. A nonlinear model is also described and damping and external forcing are considered. The model has many features that permit the meaningful introduction of many concepts including: accuracy of numerical algorithms, dependence on parameters and initial conditions, phase and synchronization, periodicity, beats, linear and nonlinear resonance, limit cycles, harmonic and subharmonic solutions. These solutions produce a wide variety of interesting motions and the model is suitable for study as a computer laboratory project in a beginning course on differential equations or as an individual or a small-group undergraduate research project.     

Direct Form I Realization of Active Photonic Filters

Abstract

An integrated photonic architecture is introduced and used to realize an optical filter with direct form I realization. The architecture offers gain from semiconductor optical amplifiers, and this gain results in an active optical filter whose filter response depends on the individual gains. The presence of gain provides advantages in filter performance, and tunable and adaptive functionality. The optical filter is modeled as a discrete time system and the z-transform is used in its analysis and design. A low-pass filter design example is presented and the filter coefficients are derived in terms of gains and coupler splitting ratios. The region of stable operations is derived by applying the Schur-Cohn stability test.