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- Juan A. Acebrón, Luis L. Bonilla, Conrad J. Pérez Vicente, Felix Ritort, Renato Spigler
- 2004

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the… (More)

- Ana Carpio, Luis L. Bonilla
- SIAM Journal of Applied Mathematics
- 2003

We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of traveling waves to steady solutions near threshold and give conditions for front pinning (propagation failure). The… (More)

- Luis L. Bonilla
- 2002

Nonlinear charge transport in semiconductor superlattices under strong electric fields parallel to the growth direction results in rich dynamical behaviour including the formation of electric field domains, pinning or propagation of domain walls, self-sustained oscillations of the current and chaos. Theories of these effects use reduced descriptions of… (More)

We propose a self-consistent microscopic model of vertical sequential tunneling through multiple quantum wells. The model includes a detailed description of the contacts, uses the transfer Hamiltonian for expressions of the current and it treats the Coulomb interaction within a mean-field approximation. We analyze the current density through a double well… (More)

- Ana Carpio, Luis L. Bonilla
- Physical review. E, Statistical, nonlinear, and…
- 2003

Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress F: for |F|<F(cd) (dynamic Peierls stress), wave fronts fail to propagate, for F(cd)<|F|<F(cs) stable static and moving wave fronts coexist, and for |F|>F(cs) (static Peierls stress) there are only stable… (More)

- Ana Carpio, Luis L. Bonilla
- Physical review letters
- 2001

Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and controlled by constant external forces. A theory of the depinning transition for… (More)

In weakly coupled, current biased, doped semiconductor superlattices, domain walls may move upstream against the flow of electrons. For appropriate doping values, a domain wall separating two electric-field domains moves downstream below a first critical current, it remains stationary between this value and a second critical current, and then moves upstream… (More)

- Anthony Amann, Andreas Wacker, Luis L. Bonilla, Eckehard Schöll
- Physical review. E, Statistical, nonlinear, and…
- 2001

We analyze the dynamics of charge distributions in weakly coupled, doped, dc voltage biased semiconductor superlattices subject to voltage steps of different sizes. Qualitatively different current responses to voltage switching processes have been observed experimentally. We explain them by invoking distinct scenarios for electric-field domain formation,… (More)

- Luis L. Bonilla, Vincenzo Capasso, M. Alvaro, Manuel Carretero
- Physical review. E, Statistical, nonlinear, and…
- 2014

When modeling of tumor-driven angiogenesis, a major source of analytical and computational complexity is the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the family of interacting underlying fields. To reduce this complexity, we take advantage of the system intrinsic multiscale… (More)

- Filippo Terragni, Manuel Carretero, Vincenzo Capasso, Luis L. Bonilla
- Physical review. E
- 2016

A recent conceptual model of tumor-driven angiogenesis including branching, elongation, and anastomosis of blood vessels captures some of the intrinsic multiscale structures of this complex system, yet allowing one to extract a deterministic integro-partial-differential description of the vessel tip density [Phys. Rev. E 90, 062716 (2014)]. Here we solve… (More)