Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

We consider a possibly degenerate porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution

Dynamics of semi-flexible polymer solutions in the highly entangled regime

We present experimental evidence that the effective medium approximation (EMA), developed by D.C. Morse [Phys. Rev. E {\bf 63}, 031502, (2001)], provides the correct scaling law of the macroscopic plateau modulus $G^{0}\propto\rho^{4/3}L^{-1/3}_{p}$ (where $\rho$ is the contour length per unit volume and $L_{p}$ is the persistence length) of semi-flexible polymer solutions, in the highly entangled concentration regime. Competing theories, including a self-consistent binary collision approximation (BCA), have instead predicted $G^{0}\propto\rho^{7/5}L^{-1/5}_{p}$. We have tested both the EMA and BCA scaling predictions using actin filament (F-actin) solutions which permit experimental control of $L_p$ independently of other parameters. A combination of passive video particle tracking microrheology and dynamic light scattering yields independent measurements of the elastic modulus $G$ and $L_{p}$ respectively. Thus we can distinguish between the two proposed laws, in contrast to previous experimental studies, which focus on the (less discriminating) concentration functionality of $G$.Comment: 4 pages, 6 figures, Phys. Rev. Lett. (accepted

Event-based control of basic wastewater treatment plant control loops

[Abstract] This paper addresses the problem of basic control loops in wastewater treatment plants. By basic control loops we are referring to the traditional dissolved oxygen and nitrates. They are the basic controls more sophisticated control solutions can be based upon. Therefore it is important that these loops perform in an efficient way. The problem is addressed here within the framework provided by the Benchmark Simulation Model Number 1 (BSM1) and by the use of an event-based solution. It will be verified that the solution can slightly improve the performance of the already exiting controllers both at loop level as well as at plant operation level.[Resumen] Este documento aborda el problema de los bucles de control básicos en las plantas de tratamiento de aguas residuales. Por bucles de control básicos nos referimos a los tradicionales disueltos de oxígeno y nitratos. Son los controles básicos en los que se pueden basar las soluciones de control más sofisticadas. Por lo tanto, es importante que estos bucles funcionen de manera eficiente. El problema se aborda aquí dentro del marco provisto por el Número de modelo de simulación de referencia (BSM1) y por el uso de una solución basada en eventos. Se verificará que la solución puede mejorar ligeramente el rendimiento de los controladores que ya existen, tanto a nivel de bucle como a nivel de operación de la planta