Multi-type branching processes (MBPs) are stochastic processes modeling populations in which the individuals of a generation produce a random number of children of different types or species in the next generation. Individuals can be elementary particles, genes, animals, or program threads [1,2]. MBPs are classified into subcritical, critical, and supercritical, depending on the spectral radius...

where {Fn, n ∈ N}, is the natural filtration associated to (Xn). We assume that X0 ∈ R d + and that random vectors ξn are such that for all n, Xn ∈ R d + almost surely. The Perron-Frobenius Theorem [10, pp. 3-4] states that M has a positive Perron root ρ. We call Xn “subcritical” if ρ < 1, “supercritical” if ρ > 1 and “critical” if ρ = 1. In the “subcritical” case, one has P(‖Xn‖ → ∞) = 0 becau...

We prove a local version of a (global) result of Merle and Zaag about ODE behavior of solutions near blowup points for subcritical nonlinear heat equations. As an application, for the equation ut = ∆u+V (x)f(u), we rule out the possibility of blowup at zero points of the potential V for monotone in time solutions when f(u) ∼ u for large u, both in the Sobolev subcritical case and in the radial ...

We use the Percus-Yevick approximation to study indirect correlation functions in the sticky hard-sphere model introduced by Baxter. The model has a critical point below which there is a liquid gas transition. We illustrate the changes in the structure of the correlation function as the density increases on the critical isotherm and on supercritical and subcritical isotherms. We also examine th...

We study the inhomogeneous random graphs in the subcritical case. We derive an exact formula for the size of the largest connected component scaled to log n where n is the size of the graph. This generalizes the recent result for the ”rank 1 case”. Here we discover that the same well-known equation for the survival probability, whose positive solution determines the asymptotics of the size of t...

In this study, subcritical water was used for the extraction and fractionation of organic atmospheric particulate. Two types of carbonaceous aerosol, diesel exhaust particulate (a relatively nonpolar matrix) and wood smoke particulate (a polar matrix), were sequentially extracted using subcritical water at temperatures ranging from 25°C to 300°C. The importance of each fraction was evaluated us...

The classical random graph model G(n, λ/n) satisfies a ‘duality principle’, in that removing the giant component from a supercritical instance of the model leaves (essentially) a subcritical instance. Such principles have been proved for various models; they are useful since it is often much easier to study the subcritical model than to directly study small components in the supercritical model...

Relative to the first two long-term goals our specific objective for FY07 was to document both the results from the Sediment Acoustics Experiment in 2004 (SAX04) and the associated analysis and modeling techniques that were developed. Those results include (1) measurement of backscattering levels from buried objects at subcritical grazing angles using synthetic aperture sonar (SAS) measurements...

The distance-resolved effective interaction between two colloidal particles in a subcritical solvent is explored both by an explicit and implicit modeling. An implicit solvent approach based on a simple thermodynamic interface model is tested against grand-canonical Monte Carlo computer simulations using explicit Lennard-Jones solvent molecules. Close to liquid-gas coexistence, a joint gas bubb...

We consider the delayed feedback control of a torsion-free unstable periodic orbit originated in a dynamical system at a subcritical Hopf bifurcation. Close to the bifurcation point the problem is treated analytically using the method of averaging. We discuss the necessity of employing an unstable degree of freedom in the feedback loop as well as a nonlinear coupling between the controlled syst...