The discrete Hamiltonian of Su, Schrieffer and Heeger (SSH) is a well-known one-dimensional translation-invariant model in condensed matter physics. consists two atoms per unit cell describes in-cell out-of-cell electron-hopping between sub-lattices. It among the simplest models exhibiting non-trivial topological phase; to SSH one can associate winding number, Zak phase, which depends on ratio ...

A multi-wavelength study of radio and IR emission from the nearby galaxy M33 is presented. We focus on three main topics: 1) energy sources of IR emission and its correlation with radio continuum emission at different spatial scales, 2) separation of thermal and nonthermal components of the radio continuum emission without assuming a constant nonthermal spectral index, and 3) distribution of th...

Any renewal processes on [Formula: see text] with a polynomial tail, with exponent [Formula: see text], has a non-trivial scaling limit, known as the [Formula: see text]-stable regenerative set. In this paper we consider Gibbs transformations of such renewal processes in an i.i.d. random environment, called disordered pinning models. We show that for [Formula: see text] these models have a univ...

The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to abstraction and piracy of the smaller tributaries as the evolution proceeds. An algebraic distribution of the average basin areas and a power law relationship ...