Papers by Miguel Hoyuelos
Physical Review E, 2009
We study evolution equations for electric and magnetic field amplitudes in a ring cavity with pla... more We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative-refraction-index material with third-order effective electric and magnetic nonlinearities. Two coupled nonlinear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato-Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.
Physical Review E, 2003
The consequences of introducing the polarization degree of freedom of the light are studied for t... more The consequences of introducing the polarization degree of freedom of the light are studied for the transverse patterns of a laser with detuning equal to zero. We deduce the vectorial Swift-Hohenberg amplitude equation from the corresponding Maxwell-Bloch equations. The vectorial character of the equation introduces modifications in the stability of traveling waves and new types of localized structures.
European Physical Journal B, 2008
Order parameter equations, such as the complex Swift-Hohenberg (CSH) equation, offer a simplified... more Order parameter equations, such as the complex Swift-Hohenberg (CSH) equation, offer a simplified and universal description that hold close to an instability threshold. The universality of the description refers to the fact that the same kind of instability produces the same order parameter equation. In the case of lasers, the instability usually corresponds to the emitting threshold, and the CSH equation can be obtained from the Maxwell-Bloch (MB) equations for a class C laser with small detuning. In this paper we numerically check the validity of the CSH equation as an approximation of the MB equations, taking into account that its terms are of different asymptotic order, and that, despite of having been systematically overlooked in the literature, this fact is essential in order to correctly capture the weakly nonlinear dynamics of the MB. The approximate distance to threshold range for which the CSH equation holds is also estimated.
Journal of Physics A-mathematical and General, 1997
We introduce a contact model with evaporation and deposition of particles at rates p and (1-p), r... more We introduce a contact model with evaporation and deposition of particles at rates p and (1-p), respectively, per occupied lattice site; while the deposition probability on empty sites depends on the number of occupied nearest-neighbour sites. At large times t this model has three different phases, separated by two critical points (0305-4470/30/2/011/img6 and 0305-4470/30/2/011/img7). Such phases are: (i) The growth phase 0305-4470/30/2/011/img8. Here the mean value of particles per lattice site n and its fluctuations w always increase as time increases. However, two different regimes can be observed, that is 0305-4470/30/2/011/img9 and 0305-4470/30/2/011/img10, for 0305-4470/30/2/011/img11; while just at 0305-4470/30/2/011/img12 one has 0305-4470/30/2/011/img13. (ii) The steady-state phase 0305-4470/30/2/011/img14, in which n and w reach finite non trivial (n > 0 and w > 0) values, but both quantities diverge for 0305-4470/30/2/011/img15 as 0305-4470/30/2/011/img16. (iii) The inactive (or vacuum) state 0305-4470/30/2/011/img17, for which n=0. At 0305-4470/30/2/011/img18 the system exhibits an irreversible phase transition which belongs to the universality class of directed percolation model, so for 0305-4470/30/2/011/img19, 0305-4470/30/2/011/img20 and 0305-4470/30/2/011/img21, with 0305-4470/30/2/011/img22. Transitions between phases are continuous, however, the transition at 0305-4470/30/2/011/img12 0305-4470/30/2/011/img24 is reversible (irreversible), respectively.
Journal of Computational Physics, 2011
We analyze the different degrees of accuracy of two Monte Carlo methods for the simulation of one... more We analyze the different degrees of accuracy of two Monte Carlo methods for the simulation of one-dimensional diffusion processes with homogeneous or spatial dependent diffusion coefficient that we assume correctly described by a differential equation. The methods analyzed correspond to fixed and Gaussian steplengths. For a homogeneous diffusion coefficient it is known that the Gaussian steplength generates exact results at fixed time steps Dt. For spatial dependent diffusion coefficients the symmetric character of the Gaussian distribution introduces an error that increases with time. As an example, we consider a diffusion coefficient with constant gradient and show that the error is not present for fixed steplength with appropriate asymmetric jump probabilities.
Journal of Computational Physics, 2009
We consider biased diffusion in a one-dimensional lattice and compare results obtained with fixed... more We consider biased diffusion in a one-dimensional lattice and compare results obtained with fixed time step and kinetic Monte Carlo methods. Spurious dispersion and particle position correlation appear with the fixed time step Monte Carlo approach. The mentioned correlation increases with time. We demonstrate that the correct results, that correspond to a time step that tends to zero, are obtained using the kinetic Monte Carlo method. The conclusions also apply to biased diffusion in two or more dimensions and to random deposition.
Journal of Computational Physics, 2011
We analyze the different degrees of accuracy of two Monte Carlo methods for the simulation of one... more We analyze the different degrees of accuracy of two Monte Carlo methods for the simulation of one-dimensional diffusion processes with homogeneous or spatial dependent diffusion coefficient that we assume correctly described by a differential equation. The methods analyzed correspond to fixed and Gaussian steplengths. For a homogeneous diffusion coefficient it is known that the Gaussian steplength generates exact results at fixed time steps Δ t. For spatial dependent diffusion coefficients the symmetric character of the Gaussian distribution introduces an error that increases with time. As an example, we consider a diffusion coefficient with constant gradient and show that the error is not present for fixed steplength with appropriate asymmetric jump probabilities.
Journal of Computational Physics, 2009
We consider biased diffusion in a one-dimensional lattice and compare results obtained with fixed... more We consider biased diffusion in a one-dimensional lattice and compare results obtained with fixed time step and kinetic Monte Carlo methods. Spurious dispersion and particle position correlation appear with the fixed time step Monte Carlo approach. The mentioned correlation increases with time. We demonstrate that the correct results, that correspond to a time step that tends to zero, are obtained using the kinetic Monte Carlo method. The conclusions also apply to biased diffusion in two or more dimensions and to random deposition.
Physica A-statistical Mechanics and Its Applications, 1997
We introduce a branching annihilating random walker process with two species, particles A and B, ... more We introduce a branching annihilating random walker process with two species, particles A and B, which diffuse creating new particles and annihilating instantaneously (A + B --, 0) when they meet. Each kind of particle branches stochastically having offsprings of the same or different type. The model is defined and studied by means of epidemic simulations in a one-dimensional discrete lattice. The phase diagram of the model exhibits two states, the vacuum and the active one, separated by a critical line. Along that line the system undergoes irreversible second order phase transitions. Monte Carlo results show that the transitions belong to the same universality class as directed percolation. In the limiting case when the generation of offsprings is forbidden, the model is mapped into the standard diffusion-limited reaction A + B --~ 0 which asymptotically evolves towards the vacuum state. The transition between the stationary regime and such vacuum states is also studied.
Journal of Physics A-mathematical and General, 1995
We study the coagulation (A+A -, A) and annihilation (A+A -+ 0) reactions with input probability ... more We study the coagulation (A+A -, A) and annihilation (A+A -+ 0) reactions with input probability B and reaction probability p in a omdimensional latlice. In the steady state we find two different behaviours for the density of nearest-neighbour occupied sites r against the density of particles p. These behaviours correspond to the diffusion-limited regime (p + 0) and to the reaction-limited regime ( p -1). Using a scaling ansak for r against p we derive an approximation for p as a function of 6 and p that agrees well with Monte Carlo numerical results.
Journal of Physics A-mathematical and General, 1995
Coupled Ginzburg-Landau equations appear in a variety of contexts involving instabilities in osci... more Coupled Ginzburg-Landau equations appear in a variety of contexts involving instabilities in oscillatory media. When the relevant unstable mode is of vectorial character (a common situation in nonlinear optics), the pair of coupled equations has special symmetries and can be written as a vector complex Ginzburg-Landau (CGL) equation. Dynamical properties of localized structures of topological character in this vector-field case are considered. Creation and annihilation processes of different kinds of vector defects are described, and some of them interpreted in theoretical terms. A transition between different regimes of spatiotemporal dynamics is described.
Physical Review A, 2000
We consider a model for a Kerr medium in a planar resonator, which takes into account the vectori... more We consider a model for a Kerr medium in a planar resonator, which takes into account the vectorial character of the radiation field. We analyze the spatial behavior of quantum fluctuations around a steady state, with a roll-pattern configuration in the beam cross section, using a Langevin treatment based on the Wigner representation. The spatial distribution of the quantum fluctuations around the roll pattern is dominated by the neutral ͑or Goldstone͒ mode, corresponding to rigid spatial displacements of the pattern. The spatial configuration of the field immediately outside the cavity input-output mirror depends on the time window over which fluctuations are averaged: only when the time window is on the order of the cavity lifetime the output field fluctuations are qualitatively similar to that of the intracavity field. The quantum correlations among the fields in play, as described by the full multimode model, turn out to be in good agreement with those predicted by a simple three-mode model.
Physica D-nonlinear Phenomena, 2003
Coupled Ginzburg-Landau equations appear in a variety of contexts involving instabilities in osci... more Coupled Ginzburg-Landau equations appear in a variety of contexts involving instabilities in oscillatory media. When the relevant unstable mode is of vectorial character (a common situation in nonlinear optics), the pair of coupled equations has special symmetries and can be written as a vector complex Ginzburg-Landau (CGL) equation. Dynamical properties of localized structures of topological character in this vector-field case are considered. Creation and annihilation processes of different kinds of vector defects are described, and some of them interpreted in theoretical terms. A transition between different regimes of spatiotemporal dynamics is described.
European Physical Journal D, 2003
We analyze the quantum fluctuations of the degenerate optical parametric oscillator close to an i... more We analyze the quantum fluctuations of the degenerate optical parametric oscillator close to an instability for the formation of a square pattern. While strong correlations between the fluctuations of the signal modes emitted at the critical wave number and with opposite wave vector are present both below and above threshold, no features signaling the square character of the pattern forming above threshold have been identified below threshold in the spatio-temporal second-order coherence. We also explore in which regimes a reduced few mode model gives meaningful results.
International Journal of Bifurcation and Chaos, 1999
We study the spatiotemporal dynamics, in one and two spatial dimensions, of two complex fields wh... more We study the spatiotemporal dynamics, in one and two spatial dimensions, of two complex fields which are the two components of a vector field satisfying a vector form of the complex Ginzburg-Landau equation. We find synchronization and generalized synchronization of the spatiotemporally chaotic dynamics. The two kinds of synchronization can coexist simultaneously in different regions of the space, and they are mediated by localized structures. A quantitative characterization of the degree of synchronization is given in terms of mutual information measures.
We study spatiotemporal pattern formation associated with the polarization degree of freedom of t... more We study spatiotemporal pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a Kerr medium in a cavity with flat mirrors and driven by a coherent plane-wave field. We consider linearly as well as elliptically polarized driving fields, and situations of self-focusing and self-defocusing. For the case of self-defocusing and a linearly polarized driving field, there is a stripe pattern orthogonally polarized to the driving field. Such a pattern changes into a hexagonal pattern for an elliptically polarized driving field. The range of driving intensities for which the pattern is formed shrinks to zero with increasing ellipticity. For the case of self-focusing, changing the driving field ellipticity leads from a linearly polarized hexagonal pattern ͑for linearly polarized driving͒ to a circularly polarized hexagonal pattern ͑for circularly polarized driving͒. Intermediate situations include a modified Hopf bifurcation at a finite wave number, leading to a time dependent pattern of deformed hexagons and a codimension 2 Turing-Hopf instability resulting in an elliptically polarized stationary hexagonal pattern. Our numerical observations of different spatiotemporal structures are described by appropriate model and amplitude equations.
Physical Review E, 1998
We study spatiotemporal pattern formation associated with the polarization degree of freedom of t... more We study spatiotemporal pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a Kerr medium in a cavity with flat mirrors and driven by a coherent plane-wave field. We consider linearly as well as elliptically polarized driving fields, and situations of self-focusing and self-defocusing. For the case of self-defocusing and a linearly polarized driving field, there is a stripe pattern orthogonally polarized to the driving field. Such a pattern changes into a hexagonal pattern for an elliptically polarized driving field. The range of driving intensities for which the pattern is formed shrinks to zero with increasing ellipticity. For the case of self-focusing, changing the driving field ellipticity leads from a linearly polarized hexagonal pattern ͑for linearly polarized driving͒ to a circularly polarized hexagonal pattern ͑for circularly polarized driving͒. Intermediate situations include a modified Hopf bifurcation at a finite wave number, leading to a time dependent pattern of deformed hexagons and a codimension 2 Turing-Hopf instability resulting in an elliptically polarized stationary hexagonal pattern. Our numerical observations of different spatiotemporal structures are described by appropriate model and amplitude equations.
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Papers by Miguel Hoyuelos