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. PACS numbers: 81.15.Aa,64.60.Ht,05.70.Ln Recent theoretical and experimental studies of self-affine kinetic roughening have uncovered a rich variety of novel features [1]. In particular, the existence of anomalous roughening has received much attention. Anomalous roughening refers to the observation that local and global surface fluctuations may have distinctly different scaling exponents. This leads to the existence of an independent local roughness exponent α loc that characterizes the local interface fluctuations and differs from the global roughness exponent α. More precisely, global fluctuations are measured by the global interface width, which for a system of total lateral size L scales according to the Family-Vicsek ansatz [2] aswhere the scaling function f (u) behaves asThe roughness exponent α and the dynamic exponent z characterize the universality class of the model under study. The ratio β = α/z is the time exponent. In contrast, local surface fluctuations are given by either the height-height correlation function,, where the average is calculated over all x (overline) and noise (brackets), or the local width,where · · · l denotes an average over x in windows of size l. For growth processes in which an anomalous roughening takes place these functions scale as w(l, t) ∼ G(l, t) = t β f A (l/t 1/z ), with an anomalous scaling function [3,4] given byinstead of Eq.(2). The standard self-affine Family-Vicsek scaling [2] is then recovered when α = α loc . This singular phenomenon was first noticed in numerical simulations of both continuous and discrete models of ideal molecular beam epitaxial growth [3,4,5,6,7,8,9,10,11]. Anomalous roughening has later on been reported to occur in growth models in the presence of disorder [12,13] Nowadays it has become clear [3,23] that anomalous kinetic roughening is related to a non-trivial dynamics of the average surface gradient (local slope), so that (∇h) 2 ∼ t 2κ . Anomalous scaling occurs whenever κ > 0, which leads to the existence of a local roughness scaling with exponent α loc = α − zκ [23]. Also, it has recently been shown that the existence of power-law scaling of the correlation functions (i.e. scale invariance) does not determine a unique dynamic scaling form of the correlation functions [24]. On the one hand, there are super-rough processes, α > 1, for which α loc = 1 always. On the other hand, there are intrinsically anomalous roughened surfaces, for which the local roughness α loc < 1 is actually an independent exponent and α may take values larger or smaller than one depending on the universality class (see [4,24] and references therein). T...

We study domain growth in a nonlinear optical system useful to explore different scenarios that might occur in systems which do not relax to thermodynamic equilibrium. Domains correspond to equivalent states of different circular polarization of light. We describe three dynamical regimes: a coarsening regime in which dynamical scaling holds with a growth law dictated by curvature effects, a regime in which localized structures form, and a regime in which polarization domain walls are modulationally unstable and the system freezes in a labyrinthine pattern. Typeset using REVT E X

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 earlier numerical simulations. With the pseudospectral approach no multiscaling is seen in agreement with the continuum model.

Fifty years ago Arthur Winfree proposed a deeply influential mean-field model for the collective synchronization of large populations of phase oscillators. Here we provide a detailed analysis of the model for some special, analytically tractable cases. Adopting the thermodynamic limit, we derive an ordinary differential equation that exactly describes the temporal evolution of the macroscopic variables in the Ott-Antonsen invariant manifold. The low-dimensional model is then thoroughly investigated for a variety of pulse types and sinusoidal phase response curves (PRCs). Two structurally different synchronization scenarios are found, which are linked via the mutation of a Bogdanov-Takens point. From our results, we infer a general rule of thumb relating pulse shape and PRC offset with each scenario. Finally, we compare the exact synchronization threshold with the prediction of the averaging approximation given by the Kuramoto-Sakaguchi model. At the leading order, the discrepancy appears to behave as an odd function of the PRC offset.

Populations of heterogeneous phase oscillators with frustrated random interactions exhibit a quasiglassy state in which the distribution of local fields is volcanoshaped. In a recent work [Phys. Rev. Lett. 120, 264102 (2018)], the volcano transition was replicated in a solvable model using a low-rank, random coupling matrix M. We extend here that model including tunable nonreciprocal interactions, i.e., M T = M. More specifically, we formulate two different solvable models. In both of them the volcano transition persists if matrix elements M jk and M k j are enough correlated. Our numerical simulations fully confirm the analytical results. To put our work in a wider context, we also investigate numerically the volcano transition in the analogous model with a full-rank random coupling matrix.