Dynamic boundary conditions as limit of singularly perturbed parabolic problems
Ángela Jiménez-Casas Aníbal Rodríguez-Bernal
We obtain dynamic boundary conditions as a limit of parabolic problems with null flux where the time derivative concentrates near the boundary.
keywords: flux null Dynamic boundary conditions parabolic problems concentrating integrals
Linear model of traffic flow in an isolated network
Ángela Jiménez-Casas Aníbal Rodríguez-Bernal
We obtain a mathematical linear model which describes automatic operation of the traffic of material objects in a network. Existence and global solutions is obtained for such model. A related model which used outdated information is shown to collapse in finite time.
keywords: traffic flow Networks delay integral systems.
Stabilizing interplay between thermodiffusion and viscoelasticity in a closed-loop thermosyphon
Justine Yasappan Ángela Jiménez-Casas Mario Castro
Viscoelastic fluids represent a major challenge both from an engineering and from a mathematical point of view. Recently, we have shown that viscoelasticity induces chaos in closed-loop thermosyphons. This induced behavior might interfere with the engineering choice of using a specific fluid. In this work we show that the addition of a solute to the fluid can, under some conditions, stabilize the system due to thermodiffusion (also known as the Soret effect). Unexpectedly, the role of viscoelasticity is opposite to the case of single-element fluids, where it (generically) induces chaos. Our results are derived by combining analytical results based on the projection of the dynamics on an inertial manifold as well as numerical simulations characterized by the calculation of Lyapunov exponents.
keywords: viscoelastic fluid Thermosyphon thermodiffusion non-newtonian fluids heat flux soret effect asymptotic behavior. numerical analysis

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