ar X iv : n lin / 0 50 50 44 v 1 [ nl in . C G ] 1 7 M ay 2 00 5 Spatial correlations in SIR epidemic models

ar X iv : n lin / 0 50 50 44 v 2 [ nl in . C G ] 1 7 M ay 2 00 5 Spatial correlations in SIR epidemic models

We investigate the role of global mixing in epidemic processes. We first construct a simplified model of the SIR epidemic using a realistic population distribution. Using this model, we examine possible mechanisms for destruction of spatial correlations, in an attempt to produce correlation curves similar to those reported recently for real epidemiological data. We find that introduction of a l...

ar X iv : n lin / 0 50 50 19 v 1 [ nl in . S I ] 7 M ay 2 00 5 Bazhanov - Stroganov model from 3 D approach

We apply a 3-dimensional approach to describe a new parametrization of the L-operators for the 2-dimensional Bazhanov-Stroganov (BS) integrable spin model related to the chiral Potts model. This parametrization is based on the solution of the associated classical discrete integrable system. Using a 3-dimensional vertex satisfying a modified tetrahedron equation, we construct an operator which g...

ar X iv : n lin / 0 30 50 05 v 1 [ nl in . C D ] 5 M ay 2 00 3 Asymptotic behaviour of multiple scattering on infinite number of parallel demi - planes

The exact solution for the scattering of electromagnetic waves on an infinite number of parallel demi-planes has been obtained by J.F. Carlson and A.E. Heins in 1947 using the Wiener-Hopf method [7]. We analyze their solution in the semiclassical limit of small wavelength and find the asymptotic behaviour of the reflection and transmission coefficients. The results are compared with the ones ob...

ar X iv : n uc l - th / 0 50 50 24 v 1 9 M ay 2 00 5 Structure of isomeric states in 66 As and 67 As

ar X iv : n lin / 0 30 50 20 v 1 [ nl in . C D ] 1 2 M ay 2 00 3 Nodal domains on quantum graphs 8 February 2008

We consider the real eigenfunctions of the Schrödinger operator on graphs, and count their nodal domains. The number of nodal domains fluctuates within an interval whose size equals the number of bonds B. For well connected graphs, with incommensurate bond lengths, the distribution of the number of nodal domains in the interval mentioned above approaches a Gaussian distribution in the limit whe...