Patterns are ubiquitous in the world that surrounds us. They can form via bifurcations, for instance from the spatially uniform state, as a control parameter is varied. Their nature generally is determined by nonlinear terms in the relevant equations of motion, and thus their elucidation is a non-trivial goal in nonlinear physics. In the early 1970's, there… (More)
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton communities, which has been observed to be patchy over a wide range of spatial and temporal scales. Here, we use… (More)
We analyze the mesoscopic dynamics of small-scale systems from the perspective of mesoscopic non-equilibrium thermodynamics. The theory obtains the Fokker–Planck equation as a diffusion equation for the probability density of the mesoscopic variables and the nonlinear relationships between activation rates and affinities proper of activated processes. The… (More)
Some rigorous results concerning the microscopic theory of interfaces and crystal shapes in classical lattice systems are reported. Abstract: Some rigorous results concerning the microscopic theory of interfaces and crystal shapes in classical lattice systems are reported.