Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

Effect of Power Density on the Electrochemical Properties of Undoped Amorphous Carbon (a‐C) Thin Films

Undoped a‐C thin films were deposited with varying power density from 10 to 25 W/cm² using unbalanced closed‐field magnetron sputtering (CFUBMS). The effect of power density on the physical and electrochemical properties was investigated by experimental characterization methods and atomistic simulations. XPS indicated that the films were composed mostly of sp²‐bonded carbon (55–58 at.%) with a small amount of oxygen (8–9 at.%) in the surface region. The films appeared completely amorphous in XRD. The I_D/I_G ratio obtained by Raman spectroscopy indicated an increase from 1.76 to 2.34 with power density. The experimental and simulated data suggested a possible ordering and/or clustering of the sp² phase with power density as the cause of the improved electrical properties of the a‐C films. The electrochemical properties of a‐C were between those of glassy carbon and tetrahedral amorphous carbon with potential windows ranging from 2.77 to 2.93 V and double‐layer capacitance values around 0.90 μF cm^?2. Electron transfer for Ru(NH₃)₆^3+/2+ and FcMeOH^+1/0 was reversible whereas that for IrCl₆^2?/3? was quasi‐reversible. Peak potential separation of dopamine and oxidation potential of ascorbic acid decreased with power density, correlating with the structural and electrical changes of the films. The a‐C thin films deposited by CFUBMS are inherently conductive and their physical properties can be adjusted by varying the deposition parameters to a wide range of electrochemical applications.     

Vortices in small Bose or Fermi systems with repulsive interactions

For rotating Bose-Einstein condensates, the occurrence of vortices has been much discussed in the Gross-Pitaevskii approach. Here, we study vortex formation in finite systems with few particles for weak and repulsive two-body interactions, by numerical diagonalization. Vortex formation is surprisingly similar for both (spinless) bosonic and fermionic particles. Breaking the rotational invariance of the Hamiltonian of the system reveals the vortex patterns. A transformation from a many-fermion to a many-boson state is proposed.     

Broken symmetries in the reconstruction of ν=1 quantum Hall edges

Spin-polarized reconstruction of the ν=1 quantum Hall edge is accompanied by a spatial modulation of the charge density along the edge. We find that this is also the case for finite quantum Hall droplets: current spin density functional calculations show that the so-called Chamon–Wen edge forms a ring of apparently localized electrons around the maximum density droplet (MDD). The boundaries of these different phases qualitatively agree with recent experiments. For very soft confinement, Chern–Simons Ginzburg–Landau theory indicates formation of a non-translational invariant edge with vortices (holes) trapped in the edge region.     

Dual cantilever enhanced photoacoustic detector with pulsed broadband IR-source

The cantilever enhanced photoacoustic (CEPA) trace gas detection was combined with an electrically modulated broadband infrared (EMBIR) source. The high sensitivity of the detection method was further improved by using two cantilever sensors on the opposite walls of the photoacoustic cell in order to suppress noise. Methane (CH₄) gas was used to demonstrate the sensitivity of the method yielding a detection limit of 0.5 ppm with 5 s sample integration time employing an optical filter with a center wavenumber 2950 cm⁻¹. The achieved result is very good with a low power infrared source and enables the utilization of the benefits of such a source: low price and power consumption, easily controlled and simple electrical modulation of the radiation intensity and absence of the mechanical chopper and its noise. The structure of the source enables a relatively high pulse rate to be used as the modulating frequency. Optical filters can be used to select the wavenumber region for the selective detection of different gases.     

Comparison of Raman spectra and vibrational density of states between graphene nanoribbons with different edges

Vibrational properties of graphene nanoribbons are examined with density functional based tight-binding method and non-resonant bond polarization theory. We show that the recently discovered reconstructed zigzag edge can be identified from the emergence of high-energy vibrational mode due to strong triple bonds at the edges. This mode is visible also in the Raman spectrum. Total vibrational density of states of the reconstructed zigzag edge is observed to resemble the vibrational density of states of armchair, rather than zigzag, graphene nanoribbon. Edge-related vibrational states increase in energy which corroborates increased rigidity of the reconstructed zigzag edge.