The Complexity of Connectivity Problems in Forbidden-Transition Graphs And Edge-Colored Graphs

The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs of consecutive edges on the walk are permitted. Forbidden-transition graphs and related models have found applications in a variety of fields, such as routing in optical telecommunication networks, road networks, and bio-informatics. We initiate the study of fundamental connectivity problems from the point of view of parameterized complexity, including an in-depth study of tractability with regards to various graph-width parameters. Among several results, we prove that finding a simple compatible path between given endpoints in a forbidden-transition graph is W[1]-hard when parameterized by the vertex-deletion distance to a linear forest (so it is also hard when parameterized by pathwidth or treewidth). On the other hand, we show an algebraic trick that yields tractability when parameterized by treewidth of finding a properly colored Hamiltonian cycle in an edge-colored graph; properly colored walks in edge-colored graphs is one of the most studied special cases of compatible walks in forbidden-transition graphs

Enhancing Optical Up-Conversion Through Electrodynamic Coupling with Ancillary Chromophores

In lanthanide-based optical materials, control over the relevant operating characteristics–for example transmission wavelength, phase and quantum efficiency–is generally achieved through the modification of parameters such as dopant/host combination, chromophore concentration and lattice structure. An alternative avenue for the control of optical response is through the introduction of secondary, codoped chromophores. Here, such secondary centers act as mediators, commonly bridging the transfer of energy between primary absorbers of externally sourced optical input and other sites of frequency-converted emission. Utilizing theoretical models based on experimentally feasible, three-dimensional crystal lattice structures; a fully quantized theoretical framework provides insights into the locally modified mechanisms that can be implemented within such systems. This leads to a discussion of how such effects might be deployed to either enhance, or potentially diminish, the efficiency of frequency up-conversion

A study of defects in single crystal CVD diamond

EPR measurements have been carried out on a range of differently doped samples, and amongst the many systems observed, two previously unreported defects have been identified. They both incorporate hydrogen and are the first defects to be positively identified to contain hydrogen in the diamond lattice. The two defects have been identified as the negatively charged nitrogen-vacancy-hydrogen centre (NVH-), and the negatively charged vacancy-hydrogen centre (VH-). The NVH- centre has been identified as having trigonal (C3v) symmetry and an overall electron spin of S = ½ . The spin Hamiltonian parameters have been determined and explained in terms of the proposed model of the defect. The hydrogen atom of the defect is located in the vacancy of the nearest-neighbour nitrogen-vacancy defect and appears to be bonded to the nitrogen atom, thus maintaining the observed C3v symmetry. The VH- centre has also been identified as having C3v symmetry, but has an overall electron spin of S = 1. The hydrogen atom is bonded to one of the four carbon atoms surrounding the vacancy and produces a very small hyperfine interaction. This is explained with the aid of the model and by performing an extended dipole calculation between the hydrogen atom and the unpaired electron probability density localised on the three equivalent carbon neighbours. No reasonable predictions on this defect could be made from studying the same defect found in silicon. The well-documented NV- defect has also been studied and modified spin Hamiltonian parameters have been determined. They vary significantly from the previously accepted ones and for the first time can explain the accepted model of the defect

Some magnetic effects of clustering in iron doped magnesium oxide

The growth of a magnesioferrite precipitate in iron doped (˜lOOOOppm wt.) magnesium oxide crystals, heat treated at 973K in oxygen, is studied with torque, magnetisation and magnetic resonance measurements. The torque and magnetisation results are in agreement with a model which assumes that the precipitate grows by diffusion limited Ostwald ripening.The effects of the particle size distribution and cubic magnetocrystalline anisotropy of the orientated octahedral precipitate particles on the magnetisation and torque curves are calculated. A magnetometrie demagnetisation tensor is defined for assemblies of orientated dipoles, its variation with the assembly size is investigated and used to calculate the longitudinal demagnetisation factors of octahedra. The ferromagnetic resonance spectra obtained were not in agreement with the generally used theory of de Biasi and Devezas (J. Appl. Phys. (1978)49, 2466). A new theory, based on a spin Hamiltonian, of the FMR response of an anisotropic superparamagnet is proposed and compared with some of the experimental spectra

Separating codes and traffic monitoring

International audienceThis paper studies the problem of traffic monitoring which consists of differentiating a set of walks on a directed graph by placing sensors on as few arcs as possible. The problem of characterising a set of individuals by testing as few attributes as possible is already well-known, but traffic monitoring presents new challenges that the previous models of separation fall short from modelling such as taking into account the multiplicity and order of the arcs in a walk. We introduce a new and stronger model of separation based on languages that generalises the traffic monitoring problem. We study three subproblems with practical applications and develop methods to solve them by combining integer linear programming, separating codes and language theory

Synchrotron radiation-based characterization of GaN- based MQW structures and strongly correlated materials

The following dissertation applies synchrotron radiation-based characterization techniques to the fields of gallium nitrides, multiferroic manganites, and self-assembled nano-domain oxide films. These material systems were chosen due to their unusual properties and potential device applications, which have made them very attractive to the scientific community. Synchrotron-based High Resolution X-ray Diffraction (HRXRD) was used to characterize the structural properties of GaN-based multiple quantum well (MQW) structures grown on trapezoidal shaped GaN ridges. Results where interpreted within the framework of vapor-phase diffusion and surface-migration effects during the metalorganic vapor phase epitaxial growth. The relatively short diffusion length of group- III precursors and growth enhancement, due to facet migration was found to have significant effects on the MQW formation. The use of synchrotron based HRXRD and in particular cross-sectional reciprocal space mapping (RSM) was then extended to studying the intriguing structural properties of a ZnMnGaO4 film epitaxially grown on MgO (001) substrate. The results of this study helped in identifying the ZnMnGaO4 film, as consisting of a self-assembled nano- checkerboard structure of highly aligned and regularly spaced vertical nanorods. The results demonstrated the importance of lattice distortion symmetry at the phase boundaries as a means for the coherent coexistence of two domain types within the film volume. Synchrotron-based far-infrared spectroscopy was performed at low temperatures on the single crystal multiferroic manganite HoMn2O5. A number of the infrared-active excitations were attributed to electric-dipole transitions between ligand-field split states of Ho3+ ions. It is proposed that the proximity in energy between magnons and Ho3+ ligand fields (LF) might connect the magnetism and dielectric properties of this compound through coupling with the Mn spin structure

Spectrographic studies of the aurora polaris and their airglow

Fifty years ago very little was known about conditions in the earth's atmosphere above a height of a few kms. and such ideas as did exist were mainly speculative. Since then, however, much work has been done, powerful new techniques developed, and a store of information accumulated about the inaccessible region above the maximum height of balloon ascent where no direct measurement has been possible until the recent development of high altitude rockets. Indirect methods have been used and one of the most successful of these has been the spectrographic study of the light emitted by these regions. The most intense source of this is the "northern lights" or aurora polaris. Although this phenomenon has been observed and classified for many years - Seneca, in the first century A.D. gives a description of it.- it was not until iTegard and his collaborators in the second decade of the present century analysed its light spectrographically that it was used to provide qualitative information about the condition of the upper atmosphere. The aurora occurs irregularly and is most frequent in a region known as the Auroral zone centred 23.5° from the poles. In addition to this transient phenomenon .Rayleigh found that there was emitted from the earth's lines of the spectrum. This was not a very satisfactory state of affairs as it would have been of great interest to have examined and compared spectra obtained from different phases of a display. However, it was found that if the size of these prism instruments was increased, very little gain in sensitivity was achieved as the absorption of the large prisms involved and the reflections from the many optical surfaces required effectively reduced the theoretical gain to negligible proportions. Thus the desire to have simultaneously high resolution and high light power was found impossible with prism instruments using traditional optics. Vegard4overcame this in his later work by using low dispersion instruments of maximum power to investigate the variations in intensity of the more prominent lines of the spectrum and larger dispersion instruments over long periods to obtain details of the spectrum.Those who were investigating the airglow were in an even less fortunate position as the intensity of the source they were dealing with was much less than that of the aurora. When using low dispersion instruments with optics of speeds of nearly f /I, which is at the limit of convention4 design, exposure times for useful plates were of the order of 30 to 60 hours. As with the aurora this meant that all spectra obtained were the integrated effects over these long exposure times. This was not very satisfactory but a practical limit seemed to have been reached in the development of the instruments.With the invention by Schmidt of a camera system which can have speeds considerably faster that f.I. a new tool was available for further progress. Memel in America. designed a special auroral spectrograph using Schmidt's principle. As the dispersive medium he chose a reflecting grating so as to reduce the loss of light and to give nearly uniform dispersion throughout the range. He kept the optical components down to a minimum, used reflecting surfaces wherever possible, and in- corporated a Schmidt camera of f /0,7. This type of instrument has tw ice the range of a prism instrument and can be used from ultra-violet to infra -red with a combination of very high light power and a uniform dispersion of convenient size. Also using modern "blazed" gratings a high percentage of the light can be concentrated into a single order so increasing the efficiency still further.A few instruments have been built to this pattern. One of these - the instrument used in this investigation - has been lent to St, Andrews Observatory by the Cambridge Air Force Research Centre, Massachusetts, U.S.A. for use over the International Geophysical Year period 1957 -58.It was planned that in the first instance the following problems should be examined: (1) Measurement of the wavelengths of the lines and bands in the auroral and night airglow spectra over as wide a range of wavelengths and intensities as possible. (2) Estimation of upper atuosphere temperatures from the profiles of suitable nitrogen bands. (3) Investigation of the enhancement of the sodium D lines at twilight