Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Analysis of a stochastic chemical system close to a sniper bifurcation of its mean field model

A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs for example in the modelling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) is studied. Our approach is based on the chemical Fokker Planck equation. To get some insights into advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, before the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size

Radio emission from the massive stars in the Galactic Super Star Cluster Westerlund 1

Current mass-loss rate estimates imply that main sequence winds are not sufficient to strip away the H-rich envelope to yield Wolf-Rayet (WR) stars. The rich transitional population of Westerlund 1 (Wd 1) provides an ideal laboratory to observe mass-loss processes throughout the transitional phase of stellar evolution. An analysis of deep radio continuum observations of Wd 1 is presented. We detect 18 cluster members. The radio properties of the sample are diverse, with thermal, non-thermal and composite thermal/non-thermal sources present. Mass-loss rates are ~10^{-5} solar mass/year across all spectral types, insufficient to form WRs during a massive star lifetime, and the stars must undergo a period of enhanced mass loss. The sgB[e] star W9 may provide an example, with a mass-loss rate an order of magnitude higher than the other cluster members, and an extended nebula of density ~3 times the current wind. This structure is reminiscent of luminous blue variables, and one with evidence of two eras of high, possibly eruptive, mass loss. Three OB supergiants are detected, implying unusually dense winds. They also may have composite spectra, suggesting binarity. Spatially resolved nebulae are associated with three of the four RSGs and three of the six YHGs in the cluster, which are due to quiescent mass loss rather than outbursts. For some of the cool star winds, the ionizing source may be a companion star though the cluster radiation density is sufficiently high to provide the necessary ionizing radiation. Five WR stars are detected with composite spectra, interpreted as arising in colliding-wind binaries.Comment: 15 pages, 6 figures. Accepted for publication in Astronomy and Astrophysic

Bose-Einstein Correlations for Three-Dimensionally Expanding, Cylindrically Symmetric, Finite Systems

The parameters of the Bose-Einstein correlation function may obey an {\it $M_t$-scaling}, as observed in $S + Pb$ and $Pb + Pb$ reactions at CERN SPS. This $M_t$-scaling implies that the Bose-Einstein correlation functions view only a small part of the big and expanding system. The full sizes of the expanding system at the last interaction are shown to be measurable with the help the invariant momentum distribution of the emitted particles. A vanishing duration parameter can also be generated in the considered model-class with a specific $M_t$ dependence.Comment: 35 pages, ReVTeX, LaTeX, no figures, discussion extende

Many--Particle Correlations in Relativistic Nuclear Collisions

Many--particle correlations due to Bose-Einstein interference are studied in ultrarelativistic heavy--ion collisions. We calculate the higher order correlation functions from the 2--particle correlation function by assuming that the source is emitting particles incoherently. In particular parametrizations of and relations between longitudinal, sidewards, outwards and invariant radii and corresponding momenta are discussed. The results are especially useful in low statistics measurements of higher order correlation functions. We evaluate the three--pion correlation function recently measured by NA44 and predict the 2--pion--2--kaon correlation function. Finally, many particle Coulomb corrections are discussed.Comment: 5 corrected misprints, 14 pages, revtex, epsfig, 6 figures included, manuscript also available at http://www.nbi.dk/~vischer/publications.htm

Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity

The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and $\kappa$, the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of $(\kappa,d)$ for which it is close to the primary bifurcation from the normal state. These values of $(\kappa,d)$ form a curve in the $\kappa d$-plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232]

Analytical and experimental investigations of low level acceleration measurement techniques

Construction techniques for accelerometer with low level threshold sensitivit

Radio emission from the massive stars in Westerlund 1

The diverse massive stellar population in the young massive clusterWesterlund 1 (Wd 1) provides an ideal laboratory to observe and constrain mass-loss processes throughout the transitional phase of massive star evolution. A set of high sensitivity radio observations of Wd 1 leads to the detection of 18 cluster members, a sample dominated by cool hypergiants, but with detections among hotter OB supergiants and WR stars. Here the diverse radio properties of the detected sample are briefly described. The mass-loss rates of the detected objects are surprisingly similar across the whole transitional phase of massive star evolution, at ~ 10-5 Mo yr−1. Such a rate is insufficient to strip away the H-rich mantle in a massive star lifetime, unless the stars go through a period of enhanced mass-loss. The radio luminous star W9 provides an example of such an object, with evidence for two eras of mass-loss with rates of ~ 10−4 Mo yr−1