Disentangling phase transitions and critical points in the proton-neutron interacting boson model by catastrophe theory

We introduce the basic concepts of catastrophe theory needed to derive analytically the phase diagram of the proton-neutron interacting boson model (IBM-2). Previous studies [1,2,3] were based on numerical solutions. We here explain the whole IBM-2 phase diagram including the precise order of the phase transitions in terms of the cusp catastrophe.Comment: To be published in Physics Letters

Macroscopic approximation to relativistic kinetic theory from a nonlinear closure

We use a macroscopic description of a system of relativistic particles based on adding a nonequilibrium tensor to the usual hydrodynamic variables. The nonequilibrium tensor is linked to relativistic kinetic theory through a nonlinear closure suggested by the Entropy Production Principle; the evolution equation is obtained by the method of moments, and together with energy-momentum conservation closes the system. Transport coefficients are chosen to reproduce second order fluid dynamics if gradients are small. We compare the resulting formalism to exact solutions of Boltzmann's equation in 0+1 dimensions and show that it tracks kinetic theory better than second order fluid dynamics.Comment: v2: 6 two-column pages, 2 figures. Corrected typos and a numerical error, and added reference

Irreducible complexity of iterated symmetric bimodal maps

We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a $\ast$-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the *-product induced on the associated Markov shifts

European lessons for Green and Blue Services in The Netherlands

Green and Blue Services were developed in The Netherlands to reward farmers for the environmental services they provide to society. Especially the first initiatives were area specific, developed together with farmers and different from the national Agri-environmental scheme. In the PLUREL case study region Haaglanden, Green and Blue Services are seen as a strategy to strengthen agriculture in the urban fringe