Class of cooperative stochastic models: Exact and approximate solutions, simulations, and experiments using ionic self-assembly of nanoparticles.

We present exact and approximate results for a class of cooperative sequential adsorption models using matrix theory, mean-field theory, and computer simulations. We validate our models with two customized experiments using ionically self-assembled nanoparticles on glass slides. We also address the limitations of our models and their range of applicability. The exact results obtained using matrix theory can be applied to a variety of two-state systems with cooperative effects.

Cooperative sequential-adsorption model in two dimensions with experimental applications for ionic self-assembly of nanoparticles.

Self-assembly of nanoparticles is an important tool in nanotechnology, with numerous applications, including thin films, electronics, and drug delivery. We study the deposition of ionic nanoparticles on a glass substrate both experimentally and theoretically. Our theoretical model consists of a stochastic cooperative adsorption and evaporation process on a two-dimensional lattice. By exploring the relationship between the initial concentration of nanoparticles in the colloidal solution and the density of particles deposited on the substrate, we relate the deposition rate of our theoretical model to the concentration.

Electronic structure and nesting-driven enhancement of the RKKY interaction at the magnetic ordering propagation vector in Gd2PdSi3 and Tb2PdSi3.

Measurements of the low-energy electronic structure in Gd2PdSi3 and Tb2PdSi3 by means of angle-resolved photoelectron spectroscopy reveal a Fermi surface consisting of an electron barrel at the Gamma point surrounded by spindle-shaped electron pockets originating from the same band. The calculated momentum-dependent RKKY coupling strength is peaked at the 1/2GammaK wave vector, which coincides with the propagation vector of the low-temperature in-plane magnetic order observed by neutron diffraction, thereby demonstrating the decisive role of the Fermi surface geometry in explaining the complex magnetic ground state of ternary rare earth silicides.

Exact energy spectrum of a two-temperature kinetic Ising model.

We develop the exact energy spectrum for a two-temperature kinetic Ising spin chain and its dual reaction-diffusion system with spatially alternating pair annihilation and creation rates. We also discuss the symmetries of the system pseudo-Hamiltonian and their role in developing a general solution. The surprisingly simple form for the eigenvalues leads to interesting physical consequences and to a possible numerical analysis of the dynamical properties of the system.