31,714 research outputs found
Dynamics and bifurcations in a simple quasispecies model of tumorigenesis
Cancer is a complex disease and thus is complicated to model. However, simple
models that describe the main processes involved in tumoral dynamics, e.g.,
competition and mutation, can give us clues about cancer behaviour, at least
qualitatively, also allowing us to make predictions. Here we analyze a
simplified quasispecies mathematical model given by differential equations
describing the time behaviour of tumor cells populations with different levels
of genomic instability. We find the equilibrium points, also characterizing
their stability and bifurcations focusing on replication and mutation rates. We
identify a transcritical bifurcation at increasing mutation rates of the tumor
cells population. Such a bifurcation involves an scenario with dominance of
healthy cells and impairment of tumor populations. Finally, we characterize the
transient times for this scenario, showing that a slight increase beyond the
critical mutation rate may be enough to have a fast response towards the
desired state (i.e., low tumor populations) during directed mutagenic
therapies
Magnetic field evolution and equilibrium configurations in neutron star cores: the effect of ambipolar diffusion
As another step towards understanding the long-term evolution of the magnetic
field in neutron stars, we provide the first simulations of ambipolar diffusion
in a spherical star. Restricting ourselves to axial symmetry, we consider a
charged-particle fluid of protons and electrons carrying the magnetic flux
through a motionless, uniform background of neutrons that exerts a collisional
drag force on the former. We also ignore the possible impact of beta decays,
proton superconductivity, and neutron superfluidity. All initial magnetic field
configurations considered are found to evolve on the analytically expected
time-scales towards "barotropic equilibria" satisfying the "Grad-Shafranov
equation", in which the magnetic force is balanced by the degeneracy pressure
gradient, so ambipolar diffusion is choked. These equilibria are so-called
"twisted torus" configurations, which include poloidal and toroidal components,
the latter restricted to the toroidal volumes in which the poloidal field lines
close inside the star. In axial symmetry, they appear to be stable, although
they are likely to undergo non-axially symmetric instabilities.Comment: MNRAS, accepte
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