arXiv subjects
Publications and source records attributed to Carlos Escudero.
We study a reaction model that presents stochastic resonance purely due to internal noise. This means that the only source of fluctuations comes from the discrete character of the reactants, and no more noises enter into the system. Our analysis reveals that the phenomenon is highly complex, and that is generated by the interplay of different stochasticity at the three fixed points of a bistable system.
To date it has not been possible to prove whether or not the three-dimensional incompressible Euler equations develop singular behaviour in finite time. Some possible singular scenarios, as for instance shock-waves, are very important from a physical point of view, since they imply the connection among the macroscopic and the microscopic scale. Therefore, the appearence of this type of singularity or a similar one might be interpreted as a possible explanation of the transition to turbulence. In order to clarify the question, some one-dimensional models for ideal incompressible hydrodynamics have been introduced and analyzed, and it was proven that shock-waves appear in finite time within this type of flow. In this work we question the validity of these models and analyze the physical meaning that the occurrence of a singularity in an incompressible flow, if it happens, may have.
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion of cells at the growing edge. Tumor growth is thus conceived as a competition for space between the tumor and the host, and cell diffusion at the tumor border is an optimal strategy adopted for minimizing the pressure and helping tumor development. Two stochastic partial differential equations are introduced in this work in order to correctly model the physical properties of tumoral growth in (1+1) and (2+1) dimensions. The advantages of these models is that they reproduce the correct geometry of the tumor and are defined in terms of polar variables. Analysis of these models allow us to quantitatively estimate the response of the tumor to an unfavorable perturbation during the growth.
We study a master equation system modelling a population dynamics problem in a lattice. The problem is the calculation of the minimum size of a refuge that can protect a population from hostile external conditions, the so called critical patch size problem. We analize both cases in which the particles are considered fermions and bosons and show using exact analitical methods that, while the Fermi-Dirac statistics leads to certain extinction for any refuge size, the Bose-Eistein statistics allows survival even for the minimal refuge.
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at the results already confirmed by numerical simulations.
We study the extended hydrodynamics proposed by Philip Rosenau [Phys. Rev. A 40, 7193 (1989)] in the context of a regularization of the Chapman-Enskog expansion. We are able to prove that shock waves appear in finite time in Rosenau's extended Burgers' equation, and we discuss the physical implications of this fact and its connection with a possible extension of hydrodynamics to the short wavelength domain.
We study the effect of chemotactic signaling among mesenchymal cells. We show that the particular physiology of the mesenchymal cells allows one-dimensional collapse in contrast to the case of bacteria, and that the mesenchymal morphogenesis represents thus a more complex type of pattern formation than those found in bacterial colonies. We finally compare our theoretical predictions with recent in vitro experiments.