Replication and differentiation of spots in a class of reaction–diffusion equations are studied by extending the Gray–Scott model with self-replicating spots so that it includes many chemical species. By examining many possible reaction networks, the behavior of this model is categorized into three types: replication of homogeneous fixed spots, replication of oscillatory spots, and differentiat...

The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in complex systems. However, it is unclear whether the Fisher-Rao metric does indeed detect these more general transitions, especially in the absence of a statistical...

In this second paper, we develop a geometrical method to systematically study the singular perturbed problem associated to slowly modulated two-pulse solutions. It enables one to see that the characteristics of these solutions are strongly determined by the flow on a slow manifold and, hence, also to identify the saddle-node bifurcations and bifurcations to classical traveling waves in which th...

Some 40 years ago, Dana Scott proved that every countable Scott set is the standard system of a model of PA. Two decades later, Knight and Nadel extended his result to Scott sets of size ω1. Here, I show that assuming the Proper Forcing Axiom (PFA), every proper Scott set is the standard system of a model of PA. I define that a Scott set X is proper if it is arithmetically closed and the quotie...

SCOTT (Semantically Constrained Otter) is a resolution-based automatic theorem prover for first order logic. It is based on the high performance prover OTTER by W. McCune and also incorporates a model generator. This finds finite models which SCOTT is able to use in a variety of ways to direct its proof search. Clauses generated by the prover are in turn used as axioms of theories to be modelle...

The Peaceman–Rachford scheme is a commonly used splitting method for discretizing semilinear evolution equations, where the vector fields are given by the sum of one linear and one nonlinear dissipative operator. Typical examples of such equations are reaction-diffusion systems and the damped wave equation. In this paper we conduct a convergence analysis for the Peaceman– Rachford scheme in the...