Theory of emission from an active photonic lattice

The emission from a radiating source embedded in a photonic lattice is calculated. The analysis considers the photonic lattice and free space as a combined system. Furthermore, the radiating source and electromagnetic field are quantized. Results show the deviation of the photonic lattice spectrum from the blackbody distribution, with intracavity emission suppressed at certain frequencies and enhanced at others. In the presence of rapid population relaxation, where the photonic lattice and blackbody populations are described by the same equilibrium distribution, it is found that the enhancement does not result in output intensity exceeding that of the blackbody at the same frequency. However, for slow population relaxation, the photonic lattice population has a greater tendency to deviate from thermal equilibrium, resulting in output intensities exceeding those of the blackbody, even for identically pumped structures.Comment: 19 pages, 11 figure

Robust Dropping Criteria for F-norm Minimization Based Sparse Approximate Inverse Preconditioning

Dropping tolerance criteria play a central role in Sparse Approximate Inverse preconditioning. Such criteria have received, however, little attention and have been treated heuristically in the following manner: If the size of an entry is below some empirically small positive quantity, then it is set to zero. The meaning of "small" is vague and has not been considered rigorously. It has not been clear how dropping tolerances affect the quality and effectiveness of a preconditioner $M$. In this paper, we focus on the adaptive Power Sparse Approximate Inverse algorithm and establish a mathematical theory on robust selection criteria for dropping tolerances. Using the theory, we derive an adaptive dropping criterion that is used to drop entries of small magnitude dynamically during the setup process of $M$. The proposed criterion enables us to make $M$ both as sparse as possible as well as to be of comparable quality to the potentially denser matrix which is obtained without dropping. As a byproduct, the theory applies to static F-norm minimization based preconditioning procedures, and a similar dropping criterion is given that can be used to sparsify a matrix after it has been computed by a static sparse approximate inverse procedure. In contrast to the adaptive procedure, dropping in the static procedure does not reduce the setup time of the matrix but makes the application of the sparser $M$ for Krylov iterations cheaper. Numerical experiments reported confirm the theory and illustrate the robustness and effectiveness of the dropping criteria.Comment: 27 pages, 2 figure

Non-uniqueness in conformal formulations of the Einstein constraints

Standard methods in non-linear analysis are used to show that there exists a parabolic branching of solutions of the Lichnerowicz-York equation with an unscaled source. We also apply these methods to the extended conformal thin sandwich formulation and show that if the linearised system develops a kernel solution for sufficiently large initial data then we obtain parabolic solution curves for the conformal factor, lapse and shift identical to those found numerically by Pfeiffer and York. The implications of these results for constrained evolutions are discussed.Comment: Arguments clarified and typos corrected. Matches published versio

Killing Vector Fields in Three Dimensions: A Method to Solve Massive Gravity Field Equations

Killing vector fields in three dimensions play important role in the construction of the related spacetime geometry. In this work we show that when a three dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the ricci tensor. Using this property we give ways of solving the field equations of Topologically Massive Gravity (TMG) and New Massive Gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three dimensional symmetric tensors of the geometry, the ricci and einstein tensors, their covariant derivatives at all orders, their products of all orders are completely determined by the Killing vector field and the metric. Hence the corresponding three dimensional metrics are strong candidates of solving all higher derivative gravitational field equations in three dimensions.Comment: 25 pages, some changes made and some references added, to be published in Classical and Quantum Gravit

Gradient flows and instantons at a Lifshitz point

I provide a broad framework to embed gradient flow equations in non-relativistic field theory models that exhibit anisotropic scaling. The prime example is the heat equation arising from a Lifshitz scalar field theory; other examples include the Allen-Cahn equation that models the evolution of phase boundaries. Then, I review recent results reported in arXiv:1002.0062 describing instantons of Horava-Lifshitz gravity as eternal solutions of certain geometric flow equations on 3-manifolds. These instanton solutions are in general chiral when the anisotropic scaling exponent is z=3. Some general connections with the Onsager-Machlup theory of non-equilibrium processes are also briefly discussed in this context. Thus, theories of Lifshitz type in d+1 dimensions can be used as off-shell toy models for dynamical vacuum selection of relativistic field theories in d dimensions.Comment: 19 pages, 1 figure, contribution to conference proceedings (NEB14); minor typos corrected in v

Front Stability in Mean Field Models of Diffusion Limited Growth

We present calculations of the stability of planar fronts in two mean field models of diffusion limited growth. The steady state solution for the front can exist for a continuous family of velocities, we show that the selected velocity is given by marginal stability theory. We find that naive mean field theory has no instability to transverse perturbations, while a threshold mean field theory has such a Mullins-Sekerka instability. These results place on firm theoretical ground the observed lack of the dendritic morphology in naive mean field theory and its presence in threshold models. The existence of a Mullins-Sekerka instability is related to the behavior of the mean field theories in the zero-undercooling limit.Comment: 26 pp. revtex, 7 uuencoded ps figures. submitted to PR

Hydraulic resistance to overland flow on surfaces with partially submerged vegetation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96239/1/wrcr13661.pd

The Importance of Audit Firm Characteristics and the Drivers of Auditor Change in UK Listed Companies

This paper explores the importance of audit firm characteristics and the factors motivating auditor change based on questionnaire responses from 210 listed UK companies (a response rate of 70%). Twenty-nine potentially desirable auditor characteristics are identified from the extant literature and their importance elicited. Exploratory factor analysis reduces these variables to eight uncorrelated underlying dimensions: reputation/quality; acceptability to third parties; value for money; ability to provide non-audit services; small audit firm; specialist industry knowledge; non-Big Six large audit firm; and geographical proximity. Insights into the nature of 'the Big Six factor' emerge. Two thirds of companies had recently considered changing auditors; the main reasons cited being audit fee level, dissatisfaction with audit quality and changes in top management. Of those companies that considered change, 73% did not actually do so, the main reasons cited being fee reduction by the incumbent and avoidance of disruption. Thus audit fee levels are both a key precipitator of change and a key factor in retaining the status quo

Low-Energy Charge-Density Excitations in MgB2_{2}: Striking Interplay between Single-Particle and Collective Behavior for Large Momenta

A sharp feature in the charge-density excitation spectra of single-crystal MgB$_{2}$, displaying a remarkable cosine-like, periodic energy dispersion with momentum transfer ($q$) along the $c^{*}$-axis, has been observed for the first time by high-resolution non-resonant inelastic x-ray scattering (NIXS). Time-dependent density-functional theory calculations show that the physics underlying the NIXS data is strong coupling between single-particle and collective degrees of freedom, mediated by large crystal local-field effects. As a result, the small-$q$ collective mode residing in the single-particle excitation gap of the B $\pi$ bands reappears periodically in higher Brillouin zones. The NIXS data thus embody a novel signature of the layered electronic structure of MgB$_{2}$.Comment: 5 pages, 4 figures, submitted to PR

The Sagnac Phase Shift suggested by the Aharonov-Bohm effect for relativistic matter beams

The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a a formal analogy with the the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.Comment: 18 pages, LaTeX, 2 EPS figures. To appear in General Relativity and Gravitatio