A weak instability in an expanding universe?

We use higher derivative classical gravity to study the nonlinear coupling between the cosmological expansion of the universe and metric oscillations of Planck frequency and very small amplitude. We derive field equations at high orders in the derivative expansion and find that the nature of the new dynamics is extremely restricted. For the equation of state parameter $w>0$ the relative importance of the oscillations grows logarithmically. Their effect on the cosmological expansion resembles that of dark energy.Comment: 14 pages, 4 figures, minor changes to conform to published versio

Polarization Properties of the "Photon Pistol"

The deterministic single-photon emission by means of STIRAP through the atoms with degenerate levels is studied. The expression for the polarization matrix of the emitted photon is obtained and its dependence on the polarization of the driving laser field and on the initial atomic state is examined.Comment: 13 pages, 3 figure

Lattice isomorphisms of bisimple monogenic orthodox semigroups

Using the classification and description of the structure of bisimple monogenic orthodox semigroups obtained in \cite{key10}, we prove that every bisimple orthodox semigroup generated by a pair of mutually inverse elements of infinite order is strongly determined by the lattice of its subsemigroups in the class of all semigroups. This theorem substantially extends an earlier result of \cite{key25} stating that the bicyclic semigroup is strongly lattice determined.Comment: Semigroup Forum (published online: 15 April 2011

Two-pathogen model with competition on clustered networks

Networks provide a mathematically rich framework to represent social contacts sufficient for the transmission of disease. Social networks are often highly clustered and fail to be locally tree-like. In this paper, we study the effects of clustering on the spread of sequential strains of a pathogen using the generating function formulation under a complete cross-immunity coupling, deriving conditions for the threshold of coexistence of the second strain. We show that clustering reduces the coexistence threshold of the second strain and its outbreak size in Poisson networks, whilst exhibiting the opposite effects on uniform-degree models. We conclude that clustering within a population must increase the ability of the second wave of an epidemic to spread over a network. We apply our model to the study of multilayer clustered networks and observe the fracturing of the residual graph at two distinct transmissibilities.Publisher PDFPeer reviewe

Degree correlations in graphs with clique clustering

Funding: This work was partially supported by the UK Engineering and Physical Sciences Research Council under grant number EP/N007565/1 (Science of Sensor Systems Software).Correlations among the degrees of nodes in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for nodes in the giant component of clustered configuration model networks which are comprised of higher-order subgraphs. We use this model to investigate, in detail, the organisation among nearest-neighbour subgraphs for random graphs as a function of subgraph topology as well as clustering. We find an expression for the average joint degree of a neighbour in the giant component at the critical point for these networks. Finally, we introduce a novel edge-disjoint clique decomposition algorithm and investigate the correlations between the subgraphs of empirical networks.PostprintPeer reviewe

Electron-Phonon Dynamics in an Ensemble of Nearly Isolated Nanoparticles

We investigate the electron population dynamics in an ensemble of nearly isolated insulating nanoparticles, each nanoparticle modeled as an electronic two-level system coupled to a single vibrational mode. We find that at short times the ensemble-averaged excited-state population oscillates but has a decaying envelope. At long times, the oscillations become purely sinusoidal about a ``plateau'' population, with a frequency determined by the electron-phonon interaction strength, and with an envelope that decays algebraically as t^-{1/2} We use this theory to predict electron-phonon dynamics in an ensemble of Y_2 O_3 nanoparticles.Comment: 11 pages, 3 figure

Exact formula for bond percolation on cliques

The authors would like to thank the School of Computer Science, the School of Chemistry, and the School of Biology of the University of St Andrews for funding this work.We present exact solutions for the size of the giant connected component of complex networks composed of cliques following bond percolation. We use our theoretical result to find the location of the percolation threshold of the model, providing analytical solutions where possible. We expect the results derived here to be useful to a wide variety of applications including graph theory, epidemiology, percolation, and lattice gas models, as well as fragmentation theory. We also examine the Erdős-Gallai theorem as a necessary condition on the graphicality of configuration model networks comprising clique subgraphs.Publisher PDFPeer reviewe

Theory of the Magnetic Catalysis of Chiral Symmetry Breaking in QED

The theory of the magnetic catalysis of chiral symmetry breaking in QED is developed. An approximation for the Schwinger-Dyson equations describing reliably this phenomenon is established, i.e., it is shown that there exists a consistent truncation of those equations in this problem. The equations are solved both analytically and numerically, and the dynamical mass of fermions is determined.Comment: 22 pages, 5 figures, REVTe

Schrödinger operators with δ and δ′-potentials supported on hypersurfaces

Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity

The challenges and benefits of analyzing feedback comments in surveys: Lessons from a cross-national online survey of small-scale cannabis growers

It is common practice in survey questionnaires to include a general open and non-directive feedback question at the end, but the analysis of this type of data is rarely discussed in the methodological literature. While these open-ended comments can be useful, most researchers fail to report on this issue. The aim of this article is to illustrate and reflect upon the benefits and challenges of analyzing responses to open-ended feedback questions. The article describes the experiences of coding and analyzing data generated through a feedback question at the end of an international online survey with small-scale cannabis cultivators carried out by the Global Cannabis Cultivation Research Consortium. After describing the design and dataset of the web survey, the analytical approach and coding frame are presented. The analytical strategies chosen in this study illustrate the diversity and complexity of feedback comments which pose methodological challenges to researchers wishing to use them for data analyses. In this article, three types of feedback comments (political/policy comments, general comments of positive and negative appreciation, and methodological comments) are used to illustrate the difficulties and advantages of analyzing this type of data. The advantages of analyzing feedback comments are well known, but they seem to be rarely exploited. General feedback questions at the end of surveys are typically non-directive. If researchers want to use these data for research and analyses, they need a clear strategy. They ought to give enough thought to why they are including this type of question, and develop an analytical strategy at the design stage of the study