Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth

In this work we consider the discretization of a recently formulated (Collis et al., [22]) multiscale model for drug- and nutrient-limited tumour growth. The key contribution of this work is the proposal of a discontinuous Galerkin finite element scheme which incorporates a non-standard coupling across a singular surface, and the presentation of full details of a suitable discretization for the coupled flow and transport systems, such as that arising in Collis et al. [22] and other similar works. We demonstrate the application of the proposed discretizations via representative numerical experiments; furthermore, we present a short numerical study of convergence for the proposed microscale scheme, in which we observe optimal rates of convergence for sufficiently smooth data

Empirical Phi-Discrepancies and Quasi-Empirical Likelihood: Exponential Bounds

We review some recent extensions of the so-called generalized empirical likelihood method, when the Kullback distance is replaced by some general convex divergence. We propose to use, instead of empirical likelihood, some regularized form or quasi-empirical likelihood method, corresponding to a convex combination of Kullback and χ2 discrepancies. We show that for some adequate choice of the weight in this combination, the corresponding quasi-empirical likelihood is Bartlett-correctable. We also establish some non-asymptotic exponential bounds for the confidence regions obtained by using this method. These bounds are derived via bounds for self-normalized sums in the multivariate case obtained in a previous work by the authors. We also show that this kind of results may be extended to process valued infinite dimensional parameters. In this case some known results about self-normalized processes may be used to control the behavior of generalized empirical likelihood

Dilatonic global strings

We examine the field equations of a self-gravitating global string in low energy superstring gravity, allowing for an arbitrary coupling of the global string to the dilaton. Massive and massless dilatons are considered. For the massive dilaton the spacetime is similar to the recently discovered non-singular time-dependent Einstein self-gravitating global string, but the massless dilaton generically gives a singular spacetime, even allowing for time-dependence. We also demonstrate a time-dependent non-singular string/anti-string configuration, in which the string pair causes a compactification of two of the spatial dimensions, albeit on a very large scale.Comment: 18 pages RevTeX, 3 figures, references amende

Comparison of s- and d-wave gap symmetry in nonequilibrium superconductivity

Recent application of ultrafast pump/probe optical techniques to superconductors has renewed interest in nonequilibrium superconductivity and the predictions that would be available for novel superconductors, such as the high-Tc cuprates. We have reexamined two of the classical models which have been used in the past to interpret nonequilibrium experiments with some success: the mu* model of Owen and Scalapino and the T* model of Parker. Predictions depend on pairing symmetry. For instance, the gap suppression due to excess quasiparticle density n in the mu* model, varies as n^{3/2} in d-wave as opposed to n for s-wave. Finally, we consider these models in the context of S-I-N tunneling and optical excitation experiments. While we confirm that recent pump/probe experiments in YBCO, as presently interpreted, are in conflict with d-wave pairing, we refute the further claim that they agree with s-wave.Comment: 14 pages, 11 figure

Anomalous Effects of "Guest" Charges Immersed in Electrolyte: Exact 2D Results

We study physical situations when one or two "guest" arbitrarily-charged particles are immersed in the bulk of a classical electrolyte modelled by a Coulomb gas of positive/negative unit point-like charges, the whole system being in thermal equilibrium. The models are treated as two-dimensional with logarithmic pairwise interactions among charged constituents; the (dimensionless) inverse temperature $\beta$ is considered to be smaller than 2 in order to ensure the stability of the electrolyte against the collapse of positive-negative pairs of charges. Based on recent progress in the integrable (1+1)-dimensional sine-Gordon theory, exact formulas are derived for the chemical potential of one guest charge and for the asymptotic large-distance behavior of the effective interaction between two guest charges. The exact results imply, under certain circumstances, anomalous effects such as an effective attraction (repulsion) between like-charged (oppositely-charged) guest particles and the charge inversion in the electrolyte vicinity of a highly-charged guest particle. The adequacy of the concept of renormalized charge is confirmed in the whole stability region of inverse temperatures and the related saturation phenomenon is revised.Comment: 21 pages, 1 figur

The Physics of Cluster Mergers

Clusters of galaxies generally form by the gravitational merger of smaller clusters and groups. Major cluster mergers are the most energetic events in the Universe since the Big Bang. Some of the basic physical properties of mergers will be discussed, with an emphasis on simple analytic arguments rather than numerical simulations. Semi-analytic estimates of merger rates are reviewed, and a simple treatment of the kinematics of binary mergers is given. Mergers drive shocks into the intracluster medium, and these shocks heat the gas and should also accelerate nonthermal relativistic particles. X-ray observations of shocks can be used to determine the geometry and kinematics of the merger. Many clusters contain cooling flow cores; the hydrodynamical interactions of these cores with the hotter, less dense gas during mergers are discussed. As a result of particle acceleration in shocks, clusters of galaxies should contain very large populations of relativistic electrons and ions. Electrons with Lorentz factors gamma~300 (energies E = gamma m_e c^2 ~ 150 MeV) are expected to be particularly common. Observations and models for the radio, extreme ultraviolet, hard X-ray, and gamma-ray emission from nonthermal particles accelerated in these mergers are described.Comment: 38 pages with 9 embedded Postscript figures. To appear in Merging Processes in Clusters of Galaxies, edited by L. Feretti, I. M. Gioia, and G. Giovannini (Dordrecht: Kluwer), in press (2001

The Self Model and the Conception of Biological Identity in Immunology

The self/non-self model, first proposed by F.M. Burnet, has dominated immunology for sixty years now. According to this model, any foreign element will trigger an immune reaction in an organism, whereas endogenous elements will not, in normal circumstances, induce an immune reaction. In this paper we show that the self/non-self model is no longer an appropriate explanation of experimental data in immunology, and that this inadequacy may be rooted in an excessively strong metaphysical conception of biological identity. We suggest that another hypothesis, one based on the notion of continuity, gives a better account of immune phenomena. Finally, we underscore the mapping between this metaphysical deflation from self to continuity in immunology and the philosophical debate between substantialism and empiricism about identity

Active Galactic Nuclei at the Crossroads of Astrophysics

Over the last five decades, AGN studies have produced a number of spectacular examples of synergies and multifaceted approaches in astrophysics. The field of AGN research now spans the entire spectral range and covers more than twelve orders of magnitude in the spatial and temporal domains. The next generation of astrophysical facilities will open up new possibilities for AGN studies, especially in the areas of high-resolution and high-fidelity imaging and spectroscopy of nuclear regions in the X-ray, optical, and radio bands. These studies will address in detail a number of critical issues in AGN research such as processes in the immediate vicinity of supermassive black holes, physical conditions of broad-line and narrow-line regions, formation and evolution of accretion disks and relativistic outflows, and the connection between nuclear activity and galaxy evolution.Comment: 16 pages, 5 figures; review contribution; "Exploring the Cosmic Frontier: Astrophysical Instruments for the 21st Century", ESO Astrophysical Symposia Serie

Metal enrichment processes

There are many processes that can transport gas from the galaxies to their environment and enrich the environment in this way with metals. These metal enrichment processes have a large influence on the evolution of both the galaxies and their environment. Various processes can contribute to the gas transfer: ram-pressure stripping, galactic winds, AGN outflows, galaxy-galaxy interactions and others. We review their observational evidence, corresponding simulations, their efficiencies, and their time scales as far as they are known to date. It seems that all processes can contribute to the enrichment. There is not a single process that always dominates the enrichment, because the efficiencies of the processes vary strongly with galaxy and environmental properties.Comment: 18 pages, 8 figures, accepted for publication in Space Science Reviews, special issue "Clusters of galaxies: beyond the thermal view", Editor J.S. Kaastra, Chapter 17; work done by an international team at the International Space Science Institute (ISSI), Bern, organised by J.S. Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke

Measurement of the Proton Spin Structure Function g1p with a Pure Hydrogen Target

A measurement of the proton spin structure function g1p(x,Q^2) in deep-inelastic scattering is presented. The data were taken with the 27.6 GeV longitudinally polarised positron beam at HERA incident on a longitudinally polarised pure hydrogen gas target internal to the storage ring. The kinematic range is 0.021<x<0.85 and 0.8 GeV^2<Q^2<20 GeV^2. The integral Int_{0.021}^{0.85} g1p(x)dx evaluated at Q0^2 of 2.5 GeV^2 is 0.122+/-0.003(stat.)+/-0.010(syst.).Comment: 7 pages, 3 figures, 1 table, RevTeX late