25,840 research outputs found
Large time behavior for vortex evolution in the half-plane
In this article we study the long-time behavior of incompressible ideal flow
in a half plane from the point of view of vortex scattering. Our main result is
that certain asymptotic states for half-plane vortex dynamics decompose
naturally into a nonlinear superposition of soliton-like states. Our approach
is to combine techniques developed in the study of vortex confinement with weak
convergence tools in order to study the asymptotic behavior of a self-similar
rescaling of a solution of the incompressible 2D Euler equations on a half
plane with compactly supported, nonnegative initial vorticity.Comment: 30 pages, no figure
A Monte Carlo Approach to Measure the Robustness of Boolean Networks
Emergence of robustness in biological networks is a paramount feature of
evolving organisms, but a study of this property in vivo, for any level of
representation such as Genetic, Metabolic, or Neuronal Networks, is a very hard
challenge. In the case of Genetic Networks, mathematical models have been used
in this context to provide insights on their robustness, but even in relatively
simple formulations, such as Boolean Networks (BN), it might not be feasible to
compute some measures for large system sizes. We describe in this work a Monte
Carlo approach to calculate the size of the largest basin of attraction of a
BN, which is intrinsically associated with its robustness, that can be used
regardless the network size. We show the stability of our method through
finite-size analysis and validate it with a full search on small networks.Comment: on 1st International Workshop on Robustness and Stability of
Biological Systems and Computational Solutions (WRSBS
- …