SPATIAL PATTERNING IN EPIDEMIOLOGY AND IN MACROMOLECULAR SELF-ASSEMBLY

Jaroslav Ilnytskyi(Personal webpage)

Spatial patterning is in the focus of both academic and practical needs: from intricate tiling ornaments in household interiors and image recognition in digital media to clustering of nanoparticles and geography-based population or disease spread. I will be providing some examples from two particular fields: epidemiology and macromolecular physical chemistry.

The simplest epidemiology model, the SIS model, provides direct link to the Ising model but with the “spin” updates governed by medically-inspired rules. For the purpose of the epidemiology, both a stationary state and the system evolution towards it are literally vital. I will be considering spatial patterns of the disease spread for the classic SIS model as well as for its generalisations for the case of (i) the coexistence of the ordinary and multi-drug-resistant carriers, (ii) competing carriers with various interaction rules for their interaction, and (iii) self-adapting model with dynamically adjusted curability.

The example from the macromolecular chemistry is focused on the aggregation of surface modified gold nanoparticles. These represent a perspective new class of soft matter objects that coined the name of “patchy colloids”, the Janus particles being one particular example. I will discuss the merits of their aggregation in selective solvent and in bulk including the case of a photo-controllable aggregation for the azobenzene-modified nanoparticles. Resulting spatial patterns, intrinsic networks and percolation between two adsorbing walls will be considered. Practical applications will be given in relation to the plasmon resonance phenomena and photo-controllable electro-conductivity.