Self-gravitating Newtonian disks revisited

Recent analytic results concerning stationary, self-gravitating fluids in Newtonian theory are discussed. We give a theorem that forbids infinitely extended fluids, depending on the assumed equation of state and the rotation law. This part extends previous results that have been obtained for static configurations. The second part discusses a Sobolev bound on the mass of the fluid and a rigorous Jeans-type inequality that is valid in the stationary case.Comment: A talk given at the Spanish Relativity Meeting in Portugal 2012. To appear in Progress in Mathematical Relativity, Gravitation and Cosmology, Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimaraes, Portugal, 3-7 September 2012, Springer Proceedings in Mathematics & Statistics, Vol. 6

(In)finite extent of stationary perfect fluids in Newtonian theory

For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the corresponding stationary Newton-Euler system). Under more restrictive conditions, we can also exclude the presence of "hollow" configurations. Our main result, which does not assume axial symmetry, uses the virial theorem as the key ingredient and generalises a known result in the static case. In the axially symmetric case stronger results are obtained and examples are discussed.Comment: Corrections according to the version accepted by Ann. Henri Poincar

Bifurcation analysis of nonlinear reaction-diffusion equations: I. Evolution equations and the steady state solutions

info:eu-repo/semantics/publishe

Bifurcation analysis of reaction-diffusion equations: III. Chemical oscillations

SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Dissipative structures, catastrophes and pattern formation

info:eu-repo/semantics/publishe

Characteristic Analysis of Response Threshold Model and Its Application for Self-organizing Network Control

International audienceThere is an emerging research area to adopt bio-inspired algorithms to self-organize an information network system. Despite strong interests on their benefits, i.e. high robustness, adaptability, and scalability, the behavior of bio-inspired algorithms under non-negligible perturbation such as loss of information and failure of nodes observed in the realistic environment is not well investigated. Because of lack of knowledge, none can clearly identify the range of application of a bio-inspired algorithm to challenging issues of information networks. Therefore, to tackle the problem and accelerate researches in this area, we need to understand characteristics of bio-inspired algorithms from the perspective of network control. In this paper, taking a response threshold model as an example, we discuss the robustness and adaptability of bio-inspired model and its application to network control. Through simulation experiments and mathematical analysis, we show an existence condition of the equilibrium state in the lossy environment. We also clarify the influence of the environmental condition and control parameters on the transient behavior and the recovery time

Periodic travelling waves in cyclic populations: field studies and reaction–diffusion models

Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction–diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur. We also discuss wave stability, including recent computational developments. Although we focus on oscillatory reaction–diffusion equations, a brief discussion of other types of model in which periodic travelling waves have been demonstrated is also included. We end by proposing 10 research challenges in this area, five mathematical and five empirical