6 research outputs found
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Diffusion, Absorbing States, and Nonequilibrium Phase Transitions in Range Expansions and Evolution
The spatial organization of a population plays a key role in its evolutionary dynamics and growth. In this thesis, we study the dynamics of range expansions, in which populations expand into new territory. Focussing on microbes, we first consider how nutrients diffuse and are absorbed in a population, allowing it to grow. These nutrients may be absorbed before reaching the population interior, and this "nutrient shielding" can confine the growth to a thin region on the population periphery. A thin population front implies a small local effective population size and enhanced number fluctuations (or genetic drift). We then study evolutionary dynamics under these growth conditions. In particular, we calculate the survival probability of mutations with a selective advantage occurring at the population front for two-dimensional expansions (e.g., along the surface of an agar plate), and three-dimensional expansions (e.g., an avascular tumor). We also consider the effects of irreversible, deleterious mutations which can lead to the loss of the advantageous mutation in the population via a "mutational meltdown," or non-equilibrium phase transition. We examine the effects of an inflating population frontier on the phase transition. Finally, we discuss how spatial dimension and frontier roughness influence range expansions of mutualistic, cross-feeding variants. We find here universal features of the phase diagram describing the onset of a mutualistic phase in which the variants remain mixed at long times.Physic
Linear and nonlinear stability in nuclear reactors with delayed effects
The research of a nuclear reactor model has been observed, where the system consists of two differential equations with one delay. A linear analysis has been performed, the asymptotic stability model of the area D0 and D2 has been defined, in which a stable periodic solution of one frequency appears. In the nonlinear analysis the analytical expression of the solution is presented with the help of bifurcation theories. In the numerical experiment using the scientific simulation program “Model Maker” numerical Runge–Kutta IV series method asymptotically stable solution and a stable periodic solution has been received and compared to the stable periodic solution received in nonlinear analysis with the help of bifurcation theories
Front propagation into unstable states
This paper is an introductory review of the problem of front propagation into
unstable states. Our presentation is centered around the concept of the
asymptotic linear spreading velocity v*, the asymptotic rate with which
initially localized perturbations spread into an unstable state according to
the linear dynamical equations obtained by linearizing the fully nonlinear
equations about the unstable state. This allows us to give a precise definition
of pulled fronts, nonlinear fronts whose asymptotic propagation speed equals
v*, and pushed fronts, nonlinear fronts whose asymptotic speed v^dagger is
larger than v*. In addition, this approach allows us to clarify many aspects of
the front selection problem, the question whether for a given dynamical
equation the front is pulled or pushed. It also is the basis for the universal
expressions for the power law rate of approach of the transient velocity v(t)
of a pulled front as it converges toward its asymptotic value v*. Almost half
of the paper is devoted to reviewing many experimental and theoretical examples
of front propagation into unstable states from this unified perspective. The
paper also includes short sections on the derivation of the universal power law
relaxation behavior of v(t), on the absence of a moving boundary approximation
for pulled fronts, on the relation between so-called global modes and front
propagation, and on stochastic fronts.Comment: final version with some added references; a single pdf file of the
published version is available at http://www.lorentz.leidenuniv.nl/~saarloo