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

Comparison of toughened composite laminates using NASA standard damage tolerance tests

The proposed application of composite materials to transport wing and fuselage structures prompted the search for tougher materials having improved resistance to impact damage and delamination. Several resin/graphite fiber composite materials were subjected to standard damage tolerance tests and the results were compared to ascertain which materials have superior toughness. In addition, test results from various company and NASA laboratories were compared for repeatability

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

Real-Time Cavity QED with Single Atoms

The combination of cold atoms and large coherent coupling enables investigations in a new regime in cavity QED with single-atom trajectories monitored in real time with high signal-to-noise ratio. The underlying “vacuum-Rabi” splitting is clearly reflected in the frequency dependence of atomic transit signals recorded atom by atom, with evidence for mechanical light forces for intracavity photon number <1. The nonlinear optical response of one atom in a cavity is observed to be in accord with the one-atom quantum theory but at variance with semiclassical predictions

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