Branching processes exhibit a particularly rich longtime behaviour when evolving in a random environment. Then the transition from subcriticality to supercriticality proceeds in several steps, and there occurs a second ‘transition’ in the subcritical phase (besides the phase-transition from (sub)criticality to supercriticality). Here we present and discuss limit laws for branching processes in ...

The problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via Volterra series approach is addressed. The related aeroelastic governing equations are based upon the inclusion of structural nonlinearities, of the linear unsteady aerodynamics and consideration of an arbitrary time-d...

Analytical estimates of the rate at which energy is extracted from the barotropic tide at topography and converted into internal gravity waves are given. The ocean is idealized as an inviscid, vertically unbounded fluid on the f plane. The gravity waves are treated by linear theory and freely escape to z 5 `. Several topographies are investigated: a sinusoidal ripple, a set of Gaussian bumps, a...

Consider a Galton-Watson process with immigration. The limiting distributions of the non-sequential estimators of the offspring mean have been proved to be drastically different for the critical case and subcritical and supercritical cases. A sequential estimator, proposed by Sriram, Basawa and Huggins (1991), was shown to be asymptotically normal for both the subcritical and critical cases. Ba...

We describe a finite-dimensional reduction method to find solutions for a class of slightly supercritical elliptic problems. A suitable truncation argument allows us to work in the usual Sobolev space even in the presence of supercritical nonlinearities: we modify the supercritical term in such a way to have subcritical approximating problems; for these problems, the finite-dimensional reductio...

We analyze the rate of convergence towards self-similarity for the subcritical KellerSegel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a...

Robust heteroclinic cycles between equilibria lose stability either through local bifurcations of their equilibria or through global bifurcations. This paper considers a global loss of stability termed a ‘resonant’ bifurcation. This bifurcation is usually associated with the birth or death of a nearby periodic orbit, and generically occurs in either a supercritical or subcritical manner. For a ...

We analyse the one-dimensional pressureless Euler-Poisson equations with a linear damping and non-local interaction forces. These equations are relevant for modelling collective behavior in mathematical biology. We provide a sharp threshold between the supercritical region with finite-time breakdown and the subcritical region with global-in-time existence of the classical solution. We derive an...

The statistical behavior of the size (or mass) of the largest cluster in subcritical percolation on a finite lattice of size N is investigated (below the upper critical dimension, presumably d(c)=6). It is argued that as N-->infinity the cumulative distribution function converges to the Fisher-Tippett (or Gumbel) distribution e(-e(-z)) in a certain weak sense (when suitably normalized). The mea...