Continuous and discontinuous transitions in geophysical turbulence

Geophysical Turbulence Geophysical Turbulence

Continuous and discontinuous phase transitions in hypergraph processes

Let V denote a set of N vertices. To construct a hypergraph process, create a new hyperedge at each event time of a Poisson process; the cardinality K of this hyperedge is random, with generating function ρ(x) def = ∑ ρkx , where P (K = k) = ρk; given K = k, the k vertices appearing in the new hyperedge are selected uniformly at random from V . Assume ρ1 + ρ2 > 0. Hyperedges of cardinality 1 ar...

From Continuous to Discontinuous Transitions in Social Diffusion

Models of social diffusion reflect processes of how new products, ideas, or behaviors are adopted in a population. These models typically lead to a continuous or a discontinuous phase transition of the number of adopters as a function of a control parameter. We explore a simple model of social adoption where the agents can be in two states, either adopters or non-adopters, and can switch betwee...

Predictability in a Model of Geophysical Turbulence

The nature of predictability is examined in a numerical model relevant to the midlatitude atmosphere and oceans. The approach followed is novel and uses new theoretical tools from information theory, namely entropy functionals, as measures of information content and their application to finite ensembles. Particular attention is paid here to the practical application of these methods to the prob...

Instabilities, Transitions and Turbulence

This article provides our perspective on the problem of active control of combustion instability. It makes no claim to complete or historically accurate survey, but attempts to put our past work in the context of existing literature. Starting with an equation for the energy of a general type of infinitesimal disturbance, we argue that the perturbation energy can be mitigated (or enhanced) by su...