In this paper, we consider a stochastic SIS epidemic model with vaccination. We prove that the densities of the distributions of the solution can converge in L1 to an invariant density under appropriate conditions. Also we find the support of the invariant density.

Magnetic properties of a biaxial spin-1 system in an applied transverse field are investigated by using the effective-field theory with correlations on the basis of the differential technique. We have studied the effects of the transverse field on the phase diagrams, internal energy, and...

We investigate here self-organised criticality (SOC) in two-dimensional dissipative sandpile models without the local conservation law. Both dissipative cellular automata and dissipative coupled map lattice models with open boundary conditions are considered. There appears to be no evidence for...

We investigate the evolutionary behaviour of a 2-D dry froth with initial ordered/disordered conditions corresponding, respectively, to monodisperse/polydisperse topological networks. Using the direct simulation approach, we discuss the scaling properties of the cell side distribution, f(n), and...

The soap froth provides an idealised example of a cellular structure, which evolves or coarsens over laboratory time-scales and for which topological measures appear to provide an intuitive characterisation. However, froth is an intrinsically non-equilibrium system, and topological measures are...

The scaling properties of 2D froth have been extensively investigated via numerical simulations, theory and experiment. The evolutionary process as a whole, however, consists of two regions involving several distinct stages, which are characterized by the froth structure. In particular,...

Light scattering experiments were performed on several fragile glass-forming materials at temperatures ranging from above the melting temperature Tm to below the calorimetric glass transition temperature Tg in the frequency range 0.2 GHz to 4000 GHz. The experimental susceptibility spectra...

A brief review of the mode coupling theory of the liquid-glass transition is presented. The major experimental techniques that have been used to test its predictions are described. The results of these tests for five glass-forming materials are summarized along with a brief discussion of other...