arXiv subjects

Juan M. López

Publications and source records attributed to Juan M. López.

25 records · Page 2Linked to original sources

arXiv2008

Structure of characteristic Lyapunov vectors in spatiotemporal chaos

We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in systems with spatiotemporal chaos. We focus on characteristic LVs and compare the results with backward LVs obtained via successive Gram-Schmidt orthonormalizations. Systems of a very different nature such as coupled-map lattices and the (continuous-time) Lorenz `96 model exhibit the same features in quantitative and qualitative terms. Additionally we propose a minimal stochastic model that reproduces the results for chaotic systems. Our work supports the claims about universality of our earlier results [I. G. Szendro et al., Phys. Rev. E 76, 025202(R) (2007)] for a specific coupled-map lattice.

nlin.CD↗

arXiv2007

Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices

The spatiotemporal dynamics of Lyapunov vectors (LVs) in spatially extended chaotic systems is studied by means of coupled-map lattices. We determine intrinsic length scales and spatiotemporal correlations of LVs corresponding to the leading unstable directions by translating the problem to the language of scale-invariant growing surfaces. We find that the so-called 'characteristic' LVs exhibit spatial localization, strong clustering around given spatiotemporal loci, and remarkable dynamic scaling properties of the corresponding surfaces. In contrast, the commonly used backward LVs (obtained through Gram-Schmidt orthogonalization) spread all over the system and do not exhibit dynamic scaling due to artifacts in the dynamical correlations by construction.

nlin.CD↗

arXiv2007

Pseudospectral versus finite-differences schemes in the numerical integration of stochastic models of surface growth

We present a comparison between finite differences schemes and a pseudospectral method applied to the numerical integration of stochastic partial differential equations that model surface growth. We have studied, in 1+1 dimensions, the Kardar, Parisi and Zhang model (KPZ) and the Lai, Das Sarma and Villain model (LDV). The pseudospectral method appears to be the most stable for a given time step for both models. This means that the time up to which we can follow the temporal evolution of a given system is larger for the pseudospectral method. Moreover, for the KPZ model, a pseudospectral scheme gives results closer to the predictions of the continuum model than those obtained through finite difference methods. On the other hand, some numerical instabilities appearing with finite difference methods for the LDV model are absent when a pseudospectral integration is performed. These numerical instabilities give rise to an approximate multiscaling observed in the numerical simulations. With the pseudospectral approach no multiscaling is seen in agreement with the continuum model.

cond-mat.stat-mech↗

arXiv2007

Time dependent couplings and crossover length scales in non-equilibrium surface roughening

We show that time dependent couplings may lead to nontrivial scaling properties of the surface fluctuations of the asymptotic regime in non-equilibrium kinetic roughening models . Three typical situations are studied. In the case of a crossover between two different rough regimes, the time-dependent coupling may result in anomalous scaling for scales above the crossover length. In a different setting, for a crossover from a rough to either a flat or damping regime, the time dependent crossover length may conspire to produce a rough surface, despite the most relevant term tends to flatten the surface. In addition, our analysis sheds light into an existing debate in the problem of spontaneous imbibition, where time dependent couplings naturally arise in theoretical models and experiments.

cond-mat.stat-mech↗

arXiv2005

Universal Critical Behavior of the Synchronization Transition in Delayed Chaotic Systems

We numerically investigate the critical behavior of the synchronization transition of two unidirectionally coupled delayed chaotic systems. We map the problem to a spatially extended system to show that the synchronization transition in delayed systems exhibits universal critical properties. We find that the synchronization transition is absorbing and generically belongs to the universality class of the bounded Kardar-Parisi-Zhang equation, as occurs in the case of extended systems. We also argue that directed percolation critical behavior may emerge for systems with strong nonlinearities

cond-mat.stat-mech↗

arXiv2005

Scaling of Local Slopes, Conservation Laws and Anomalous Roughening in Surface Growth

We argue that symmetries and conservation laws greatly restrict the form of the terms entering the long wavelength description of growth models exhibiting anomalous roughening. This is exploited to show by dynamic renormalization group arguments that intrinsic anomalous roughening cannot occur in local growth models. However some conserved dynamics may display super-roughening if a given type of terms are present.

cond-mat.stat-mech↗

arXiv1992

Lack of Self-affinity and Anomalous Roughening in Growth Processes

We contrast analytical results of a variety of growth models involving subdiffusion, thermal noise and quenched disorder with simulations of these models, concluding that the assumed self-affinity property is more an exception than a rule. In our two dimensional models, self-affine surfaces may only appear when the roughness exponent is $χ= 1/2$ or $χ= 1$. A new scaling picture, which leads to more suitable ways of determining the scaling exponents, is proposed when lack of self-affinity exists.

cond-mat↗