Synthesis and Characterization of Tris(diethyldithiocarbamato) cobalt(III) as an Undergraduate Inorganic Laboratory

The synthesis of tris(diethyldithiocarbamato) cobalt(III) by the reaction of sodium diethyldithio-carbamate and cobaltous chloride is described. The recovered crystals of the cobalt complex are characterized by magnetic susceptibility, IR and NMR spectroscopy, and cyclic voltammetry.     

Stability and instability of nonlinear defect states in the coupled mode equations—Analytical and numerical study

Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled mode equations (NLCME). This system of PDEs, similar in structure to the Dirac equations, has gap soliton solutions that travel at any speed between 0 and the speed of light. A recently considered strategy for spatial trapping or capture of gap optical soliton light pulses is based on the appropriate design of localized defects in the periodic structure. Localized defects in the periodic structure give rise to defect modes, which persist as nonlinear defect modes as the amplitude is increased. Soliton trapping is the transfer of incoming soliton energy to nonlinear defect modes. To serve as targets for such energy transfer, nonlinear defect modes must be stable. We therefore investigate the stability of nonlinear defect modes. Resonance among discrete localized modes and radiation modes plays a role in the mechanism for stability and instability, in a manner analogous to the nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation. However, the nature of instabilities and how energy is exchanged among modes is considerably more complicated than for NLS/GP due, in part, to a continuous spectrum of radiation modes which is unbounded above and below. In this paper we (a) establish the instability of branches of nonlinear defect states which, for vanishing amplitude, have a linearization with eigenvalues embedded within the continuous spectrum, (b) numerically compute, using Evans function, the linearized spectrum of nonlinear defect states of an interesting multiparameter family of defects, and (c) perform direct time-dependent numerical simulations in which we observe the exchange of energy among discrete and continuum modes.     

The interaction of ultrathin films of Ni and Pd with W(110): an XPS study

The interaction of ultrathin films of Ni and Pd with W(110) has been examined using X-ray photoelectron spectroscopy (XPS) and the effects of annealing temperature and adsorbate coverage (film thickness) are investigated. The XPS data show that the atoms in a monolayer of Pd or Ni supported on W(110) are electronically perturbed with respect to the surface atoms of Pd(100) and Ni(100). The magnitude of the electronic perturbations is larger for Pd than for Ni adatoms. Our results indicate that the difference in Pd(3d_5/2) XPS binding energies between a pseudomorphic monolayer of Pd on W(110) and the surface atoms of Pd(100) correlates with the variations observed for the desorption temperature of CO (i.e., the strength of the Pd---CO bond) on these surfaces. A similar correlation is seen for the Ni(2p_3/2) XPS binding energies of Ni/W(110) and Ni(100) and the CO desorption temperatures from the surfaces. The shifts in XPS binding energies and CO desorption temperatures can be explained in terms of: (1) variations that occur in the Ni---Ni and Pd---Pd interactions when Ni and Pd adopt the lattice parameters of W(110) in a pseudomorphic adlayer; and (2) transfer of electron density from the metal overlayer to the W(110) substrate upon adsorption. Measurements of the Pd(3d_5/2) XP binding energy of Pd/W(110) as a function of film thickness indicate that the Pd---W interaction affects the electronic properties of several layers of Pd atoms.     

Further assessment of forward pressure level for in situ calibration

Quantifying ear-canal sound level in forward pressure has been suggested as a more accurate and practical alternative to sound pressure level (SPL) calibrations used in clinical settings. The mathematical isolation of forward (and reverse) pressure requires defining the The?venin-equivalent impedance and pressure of the sound source and characteristic impedance of the load; however, the extent to which inaccuracies in characterizing the source and/or load impact forward pressure level (FPL) calibrations has not been specifically evaluated. This study examined how commercially available probe tips and estimates of characteristic impedance impact the calculation of forward and reverse pressure in a number of test cavities with dimensions chosen to reflect human ear-canal dimensions. Results demonstrate that FPL calibration, which has already been shown to be more accurate than in situ SPL calibration, can be improved particularly around standing-wave null frequencies by refining estimates of characteristic impedance. Better estimates allow FPL to be accurately calculated at least through 10 kHz using a variety of probe tips in test cavities of different sizes, suggesting that FPL calibration can be performed in ear canals of all sizes. Additionally, FPL calibration appears a reasonable option when quantifying the levels of extended high-frequency (10-18 kHz) stimuli.     

Active to sterile neutrino mixing limits from neutral-current interactions in MINOS

Results are reported from a search for active to sterile neutrino oscillations in the MINOS long-baseline experiment, based on the observation of neutral-current neutrino interactions, from an exposure to the NuMI neutrino beam of 7.07×10(20) protons on target. A total of 802 neutral-current event candidates is observed in the Far Detector, compared to an expected number of 754 ± 28(stat) ± 37(syst) for oscillations among three active flavors. The fraction f(s) of disappearing ν(μ) that may transition to ν(s) is found to be less than 22% at the 90% C.L.     

Measurement of the neutrino mass splitting and flavor mixing by MINOS

Measurements of neutrino oscillations using the disappearance of muon neutrinos from the Fermilab NuMI neutrino beam as observed by the two MINOS detectors are reported. New analysis methods have been applied to an enlarged data sample from an exposure of 7.25×10(20) protons on target. A fit to neutrino oscillations yields values of |Δm(2)|=(2.32(-0.08)(+0.12))×10(-3) eV(2) for the atmospheric mass splitting and sin(2)(2θ)>0.90 (90% C.L.) for the mixing angle. Pure neutrino decay and quantum decoherence hypotheses are excluded at 7 and 9 standard deviations, respectively.     

The 2-D growth of gold on single-layer graphene/Ru(0001): Enhancement of CO adsorption

The growth and morphology of two-dimensional (2-D) gold islands on a single-layer graphene supported on Ru(0001) have been studied by scanning tunneling microscopy (STM). Our findings show that gold exhibits 2-D structures up to a gold dosage of 0.75 equivalent monolayers, and that these 2-D gold islands are thermally stable at room temperature. Parallel polarization modulation infrared reflection absorption spectroscopic (PM-IRAS) and high resolution electron energy loss spectroscopic (HREELS) studies indicate that carbon monoxide (CO) adsorbs on these 2-D gold islands at 85 K, showing a characteristic CO stretching feature at 2095 cm^? 1 for a saturation coverage of CO. The red shift of the CO stretching frequency compared to that on charge neutral gold is consistent with electron transfer from graphene to gold, i.e., an electron-rich gold overlayer. Preliminary data obtained by dosing molecular oxygen onto this CO pre-covered surface suggest that the 2-D gold islands catalyze the oxidation of CO.     

On the limiting profile arising from orthonormalizing shifts of exponentially decaying functions

It is shown that, under certain conditions, orthonormalizingthe positive integer shifts of an exponentially decaying functionon the half line by the Gram-Schmidt process leads to a limitingprofile given by orthonormalizing all their integer shifts onthe whole line. These results derive from properties of Choleskyfactorization of bi-infinite and semi-infinite matrices. Anexample is provided by the negative exponential function andconjectures are given, supported by numerical evidence, forthe Gaussian and Lorentz function.     

On the connected components of the space of line transversals to a family of convex sets

Let ℒ be the space of line transversals to a finite family of pairwise disjoint compact convex sets in ℝ³. We prove that each connected component of ℒ can itself be represented as the space of transversals to some finite family of pairwise disjoint compact convex sets. The research of J. E. Goodman was supported in part by NSF Grant DMS91-22065 and by NSA Grant MDA904-92-H-3069. R. Pollack's research was supported in part by NSF Grant CCR91-22103 and by NSA Grant MDA904-92-H-3075. The research of R. Wenger was supported in part by NSA Grant MDA904-93-H-3026 and by the NSF Regional Geometry Institute (Smith College, July 1993) Grant DMS90-13220.