A Reality Proof in PT-Symmetric Quantum Mechanics

We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral equivalences inspired by the correspondence are also discussed.     

Tabu search applied to the general fixed charge problem

Recent successes in applying tabu search to a wide variety of classical optimization problems have motivated the investigation of applying tabu search to the well-known general fixed charge problem (GFCP). In this paper, an adaptation of tabu search to GFCP is described and computational results are given. In addition, the computational results are compared with those obtained from SWIFT-2, the most well-known and frequently used heuristic method for GFCP. As will be shown, the results are very encouraging.     

Near-infrared laser photoacoustic detection of methane: the impact of molecular relaxation

A photoacoustic sensor has been developed for trace-gas monitoring using a near-infrared semiconductor laser emitting in the 2ν₃ band of methane at 1.65 μm. The apparatus was designed for on-line process control in the manufacturing of the novel low-water-peak fibres developed for optical telecommunications. The importance of collisional relaxation processes in the generation of the photoacoustic signal is reported in the particular case of CH₄ detection in dry O₂ and O₂–N₂ mixtures. The negative influence of these effects results in a strongly reduced and phase-shifted photoacoustic signal, induced by a fast resonant coupling between the vibrational states of methane and oxygen, associated with the slow relaxation of the excited oxygen molecules. An unusual parabolic response of the sensor with respect to the methane concentration has been observed and is discussed. Finally, the beneficial effect of several species, including water vapour and helium, acting as a catalyst to hasten the relaxation of the CH₄–O₂ system, is demonstrated. PACS 42.62.Fi; 33.20.Ea; 34.50.Ez     

P-N junctions in semiconducting TiO2 studied through computer modelling

The dependence of the formation of a p-n or p-p⁺ junction in semiconducting TiO₂ as a function of various parameters is investigated through a computer model. The effect of the polarizing conditions on the I–V characteristics is also discussed and related to experimental results. Paper presented at the 3rd Euroconference on Solid State Ionics, Teulada, Sardinia, Sept. 15–22, 1996     

Effect of stoichiometry on liquid crystalline supramolecular polymers formed with complementary nucleobase pair interactions

We report herein studies on the liquid crystalline behavior of a series of supramolecular materials that contain different ratios of two complementary symmetrically-substituted alkoxy-bis(phenylethynyl)benzene AA- and BB-type monomers. One monomer has thymine units placed at either end of the rigid mesogenic core, while the other has N⁶-(4-methoxybenzoyl)-adenine units placed on the ends. Differential scanning calorimetric and polarized optical microscopy studies have been carried out on these systems. These studies show that the material's behavior is strongly dependent on its thermal history. As a result, the materials can exhibit, on heating, either a liquid crystalline phase, a crystalline phase, or the coexistence of crystalline and liquid crystalline regions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5049–5059, 2006     

Bounds on Codes Derived by Counting Components in Varshamov Graphs

We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10]     

Optimal node disjoint paths on partial 2-trees: A linear algorithm and polyhedral results

We present anO(p · n) algorithm for the problem of finding disjoint simple paths of minimum total length betweenp given pairs of terminals on oriented partial 2-trees withn nodes and positive or negative arc lengths. The algorithm is inO(n) if all terminals are distinct nodes. We characterize the convex hull of the feasible solution set for the casep=2.We gratefully acknowledge the referee's many helpful suggestions to improve the presentation of this paper.     

Proximity effect in superconductor/ferromagnet layered system: Influence of superconductivity on magnetic properties of Nb/Fe epitaxial bilayers

Magnetic and superconducting properties of Fe/Nb epitaxial bilayers have been studied. Single crystal Fe/Nb (110) bilayers with a Nb thicknessd _Nb in the range from 250 to 650 Å and with a Fe thicknessd _Fe in the range from 7 to 27 Å were prepared using molecular beam epitaxy techniques. Magnetization measurements showed the existence of a magnetically “dead” Fe-interface layer with a thicknessd _NM varying strongly with minor modifications of the growth conditions. For bilayers with a small magnetic layer thicknessd _M and a smalld _NM the FMR measurements revealed an anomalous decrease of the effective magnetization 4πM _eff of the ferromagnetic Fe layer below the superconducting transition temperatureT _c. The absolute change of 4πM _eff belowT _c depends strongly on the actual values ofd _M andd _NM: upon decreasing bothd _M andd _NM the effect increases considerably. As a possible mechanism for the anomalous temperature dependence of 4πM _eff belowT _c we discuss a spatial modulation of ferromagnetic order due to a modification of the RKKY inter-action in the superconducting state.     

Spin wave spectrum and exchange interactions in the antiferromagnetic garnet Ca3Cr2Ge3O12 by inelastic neutron scattering

We have measured the spin wave spectrum for the garnet Ca₃Cr₂Ge₃O₁₂ by means of inelastic neutron scattering. The data can be well described in the framework of linear spin wave theory if we assume a Heisenberg model with two exchange parameters up to the next nearest neighbours (J ₁ andJ ₂) and a staggered anisotropy field (A). A least squares fit to the observed dispersion relations yield the following values for these parameters: J ₁=–0.582(8)K,J ₂=0.416(4)K,A=0.25(8)K. Although symmetry requires that two nearest neighbour exchange constantsJ ₁ andJ ₁ ^' must be distinguished, only the average J ₁=(J ₁+3J ₁ ^' )/4 and the condition –0.35 K <J ₁=J ₁-J ₁ ^' <0.50 K could be deduced from the experiment. The most striking result is the positive value ofJ ₂. We discuss the implications for an understanding of superexchange mediated by more than one oxygen atom. In an extension of the conventional analysis we have calculated the integrated intensities in order to check the eigenvectors directly. Good agreement between observed and calculated intensities was obtained.