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We consider a cell growth model involving a nonlinear system of partial differential equations which describes the growth of two types of cell populations with contact inhibition. Numerical experiments show that there is a parameter regime where, for a large class of initial data, the large time behaviour of the solutions is described by a segregated travelling wave solution with positive wave speed c. Here, the word segregated expresses the fact that the different types of cells are spatially segregated, and that the single densities are discontinuous at the moving interface which separates the two populations. In this paper, we show that, for each wave speed c > c, there exists an overlapping travelling wave solution, whose profile is continuous and no longer segregated. We also show that, for a large class of initial functions, the overlapping travelling wave solutions cannot represent the large time profile of the solutions of the system of partial differential equations. The structure of the travelling wave solutions strongly resembles that of the scalar Fisher-KPP equation, for which the special role played by the travelling wave solution with minimal speed has been extensively studied.
A new approach is proposed for the description of thin viscous flows near the edges of a solid surface. For a steady flow, the lubrication approximation and the no-slip condition are assumed to be valid on most of the surface, except for relatively small neighbourhoods of the edges, where a universality principle is postulated: the behaviour of the liquid in these regions is universally determined by flux, external conditions and material properties. The resulting mathematical model is formulated as an ordinary differential equation involving the height of the liquid film and the flux as unknowns, and analytical results are outlined. The form of the universal functions which describe the behaviour in the edge regions is also discussed, obtaining conditions of compatibility with lubrication theory for small fluxes. Finally, an ordinary differential equation is introduced for the description of intermediate asymptotic profiles of a liquid film which flows off a bounded solid surface.
Generic guidance on the withdrawal of sheltering, withdrawal of evacuation and evacuation
of sheltered populations (displacement) has been developed based on previously unpublished
work in the UK and France and on input from stakeholder panels in Germany, Belgium, France
and the UK. The guidance is a living document that can be developed further in the future,
both in its generic form and also as customised versions in some Member States. The
guidance outlines the many factors which influence the withdrawal of emergency
countermeasures: official confirmation that any release has stopped; adequacy of
monitoring data; radiological criteria; radiological protection advice; availability of
resources; social and psychological needs; stakeholder dialogue; and communication
strategy. The relative importance placed by decision makers on each of these criteria
would vary according to the nature and scale of the accident and also on socio-political,
economic and cultural perspectives. In the event of a radiological incident, decision
makers will need to be in a position to construct a strategy for managing the withdrawal
of emergency countermeasures. For larger scale, longer duration releases involving several
nuclides, a management strategy is likely to be complex. The guidance therefore includes a
series of checklists which have been developed in conjunction with stakeholders to take
into account the main criteria and factors which should be considered.
In nuclear and radiological emergency and post-accident management decisions on
countermeasures and remediation strategies have to be made. Whereas in the early phase
decisions on emergency actions must be made in a very short time, according to emergency
plans and dose thresholds, in the recovery phase complexity is higher. But there is also
more time for evaluating alternative countermeasures and remediation strategies with
respect to several goals. In this paper evaluation strategies supporting the decision
makers throughout all phases are presented. The applied decision support techniques range
from graphical presentations of decision relevant information about the alternatives for
action to multi-criteria decision making (MCDM) methods. In particular methods to cope
with several types of uncertainties inherent in the different phases are presented. By the
integration of these techniques, the decision support system RODOS is able to provide
support for more conscious, transparent and coherent decision making.
The crystal chemistry of a number of Fe-Si systems (Si/Fe 0-4, pH 3-10) was investigated by combining local scale spectroscopic methods (EXAFS, FTIR and NMR) and at the semi local scale (SAXS). The Fe clusters within the precipitates have two growth regimes depending on the Si/Fe ratio: the growth is three and two dimensional for Si/Fe fl and Si/Fe ≤ 1 respectively. The presence of Fe-O-Si bonds within the precipitated phases has been demonstrated. Their formation and relative proportion was found to be very dependent on the pH and Si concentration The size of silica domains within the precipitates was shown to increase with increasing Si/Fe and/or decreasing pH. The high fractal dimension (Df) of the aggregates is attributed to the presence of the SiO4 ligands, but the evolution of Df linearly depends on the polymerization state of iron.
In the full paper in the companion volume, we introduce a new
subclass of the context
free languages, the meta-deterministic languages, which includes the deterministic
languages, but also the languages that result if deterministic languages
are combined via regular expressions.
Gamma Ray Bursts (GRBs) have puzzled astronomers since their discovery more than 20 years ago. As no counterparts at wavelengths other than X- and γ-rays have yet been found the identification of the sources is still missing. Theoretical explanations range from colliding comets (1993) and merging neutron stars (1982) to more exotic objects, such as superconducting cosmic strings (1988). Data accumulated until now still do not discriminate between these models, although results from the BATSE (Burst and Transient Source Experiment) instrument aboard the Compton Gamma Ray Observatory (CGRO) strongly favor extragalactic models.
The Energetic Gamma Ray Experiment Telescope (EGRET) aboard CGRO has s ofar detected photons from 5 GRBs with its spark chamber. These are the highest energy γ-rays associated with GRBs to date. In this work we review previously published data and summarize the properties of these events. Elsewhere we present possible constraints from the data on the models proposed to explain GRBs.
We study the semi-empirical b—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy density b and the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.
It is commonly assumed that heat flux and temperature diffusivity coefficients obtained in steady-state measurements can be used in the derivation of the heat conduction equation for fluid flows. Meanwhile it is also known that the steady-state heat flux as a function of temperature gradient in stably stratified turbulent shear flow is not monotone: at small values of temperature gradient the flux is increasing, whereas it is decreasing after a certain critical value of the temperature gradient. Therefore the problem of heat conduction for large values of temperature gradient becomes mathematically ill-posed, so that its solution (if it exists) is unstable.
In the present paper it is shown that a well-posed mathematical model is obtained if the finiteness of the adjustment time of the turbulence field to the variations of temperature gradient is taken into account. An evolution-type equation is obtained for the temperature distribution (a similar equation can be derived for the concentration if the stratification is due to salinity or suspended particles). The characteristic property which is obtained from a rigorous mathematical investigation is the formation of stepwise distributions of temperature and/or concentration from continuous initial distributions.
In this paper we consider a one-dimensional Stefan problem with a source term. Under the assumption that the initial profile is monotone, we obtain continuity of the free boundaries between the solid, the mushy and the liquid region.