Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schr?dinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves.     

Modeling of ion processes in atmospheric pressure matrix-assisted laser desorption/ionisation

Atmospheric pressure matrix-assisted laser desorption/ionization (AP-MALDI) has proven a convenient and rapid method for ion production in the mass spectrometric analysis of biomolecules. This technique, like other atmospheric pressure ionization methods, suffers from ion loss during ion transmission from the atmosphere into the vacuum of the mass spectrometer. In this work, a simple model describing ion formation and ion motion towards the inlet capillary of the mass spectrometer is described. Both the gas flow and electric field near the MALDI plate were numerically calculated using the boundary element method (BEM). The ions were moving along with the gas flow and drifting in the electric field in accordance with their ion mobility properties. The ion signal dependence on an electric field strength obtained in the proposed model correlates well with experimental results.     

Thermal stability of surface freezing films in Ga-based alloys: an x-ray photoelectron spectroscopy and scanning tunneling microscopy study

We have investigated the thickness and surface structure of surface freezing films in Ga-Bi and Ga-Pb alloys over a wide temperature range between room temperature and the respective surface freezing transitions by x-ray photoelectron spectroscopy (XPS) and scanning tunnelling microscopy (STM). For the example of a Ga-Bi alloy dilute in Bi, XPS measurements show that the surface freezing film has a nearly constant value of approximately 25 A between the surface freezing temperature of 130 degrees C and room temperature if the sample is cooled slowly (5 Kh). On heating to 130 degrees C the film thickness exhibits a clear hysteresis on melting. On quenching the alloy sample (>100 Kh) the film thickness increases by almost a factor of 10. These observations indicate that the surface freezing films are metastable. The surface structure of the surface freezing films of various Ga-rich Ga-Bi and Ga-Pb alloys has been probed for the first time by STM at different temperatures below and above the bulk eutectic point. Atomically resolved STM images show the surface structures of pure Bi (0001) and Pb (111), respectively, at room temperature. On heating above the eutectic temperature the surface structure of the films does not change significantly as judged from the size and thickness of Pb or Bi terraces. These observations together with the film thickness variation with temperature indicate that the surface freezing films behave like a metastable independent surface phase. These results together with the wetting characteristics of these alloys suggest that surface freezing in these systems is a first order surface phase transition between wetting and metastable surface freezing films. The energy barrier for nucleation is strongly reduced due to a lowering of the interfacial energy if the nucleus is completely immersed in the respective wetting layer.     

Control of sp2/sp3 carbon ratio and surface chemistry of nanodiamond powders by selective oxidation in air

The presence of large amounts of nondiamond carbon in detonation-synthesized nanodiamond (ND) severely limits applications of this exciting nanomaterial. We report on a simple and environmentally friendly route involving oxidation in air to selectively remove sp(2)-bonded carbon from ND. Thermogravimetric analysis and in situ Raman spectroscopy shows that sp(2) and sp(3) carbon species oxidize with different rates at 375-450 degrees C and reveals a narrow temperature range of 400-430 degrees C in which the oxidation of sp(2)-bonded carbon occurs with no or minimal loss of diamond. X-ray absorption near-edge structure spectroscopy detects an increase of up to 2 orders of magnitude in the sp(3)/sp(2) ratio after oxidation. The content of up to 96% of sp(3)-bonded carbon in the oxidized samples is comparable to that found in microcrystalline diamond and is unprecedented for ND powders. Transmission electron microscopy and Fourier transform infrared spectroscopy studies show high purity 5-nm ND particles covered by oxygen-containing surface functional groups. The surface functionalization can be controlled by subsequent treatments (e.g., hydrogenization). In contrast to current purification techniques, the air oxidation process does not require the use of toxic or aggressive chemicals, catalysts, or inhibitors and opens avenues for numerous new applications of nanodiamond.     

Heat equation with a general stochastic measure on nested fractals

A stochastic heat equation on an unbounded nested fractal driven by a general stochastic measure is investigated. Existence, uniqueness and continuity of the mild solution are proved provided that the spectral dimension of the fractal is less than 4/3.     

Water-Soluble Non-Classical Benzene Mimetics

A new generation of saturated benzene mimetics, 2-oxabicyclo[2.1.1]hexanes, was developed. These compounds were designed as analogues of bicyclo[1.1.1]pentane with an improved water solubility. Crystallographic analysis of 2-oxabicyclo[2.1.1]hexanes revealed that they occupy a novel chemical space, but, at the same time, resemble the motif of meta-disubstituted benzenes.     

Double photoexcitation of helium in a strong dc electric field

We report the first experimental measurements of the effect of an applied field on the photoexcitation and autoionization of doubly excited states of helium. Ground-state photoionization spectra have been measured in the region below the He+(N=2) threshold with static electric fields of up to 84.4 kV/cm across the interaction region. The results are compared to the theoretical calculations of Chung et al. [J. Phys. B 34, 165 (2001)]], which are the only calculations available in this regime. Transitions to several states in the N=2, n=6 manifold are assigned, and a wealth of new structure is observed. Our data show that many more series are mixed in by the field than those predicted by theory.