11 research outputs found
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
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