Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension.

We show that the theoretical machinery developed for the Kardar-Parisi-Zhang (KPZ) class in low dimensions is obeyed by the restricted solid-on-solid model for substrates with dimensions up to d=6. Analyzing different restriction conditions, we show that the height distributions of the interface are universal for all investigated dimensions. It means that fluctuations are not negligible and, consequently, the system is still below the upper critical dimension at d=6. The extrapolation of the data to dimensions d≥7 predicts that the upper critical dimension of the KPZ class is infinite.

Feelings of powerlessness and hope for cure in patients with chronic lower-limb ulcers.

OBJECTIVE: To assess feelings of powerlessness and hope for cure in patients with chronic venous leg ulcers (VLUs) and diabetic foot ulcers (DFUs). METHOD: A clinical, analytical, descriptive study was conducted from April to September 2012 in a wound-care clinic in Brazil, on consecutive patients presenting withVLUs and DFUs. The Powerlessness AssessmentTool for Adult Patients (PAT) and the Herth Hope Index (HHI) were used.Total PAT scores range 12-60 and the higher the score, the stronger the feelings of powerlessness. The HHI ranges 12-48, with higher scores indicating higher levels of hope RESULTS: In total, 80 consecutive patients were recruited (40 VLU and 40 DFU). Mean PAT score was 53.3 +/- 9.6 (range 21-60) for DFU patients and 34.3 +/- 7.7 (range 21-60; p = 0.001) forVLU patients, suggesting these individuals had strong feelings of powerlessness. The mean HHI was 16.5 +/- 16.5 (range 12-40) for DFU patients and 27.5 +/- 27.5 (range 12-40; p = 0.001) for patients with VLUs, indicating low levels of hope. CONCLUSION: The results suggest that patients with DFUs had stronger feelings of powerlessness regarding their condition and less hope of recovery compared with patients with VLUs.

Kardar-Parisi-Zhang universality class in (2+1) dimensions: universal geometry-dependent distributions and finite-time corrections.

The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different from their Tracy-Widom counterpart in one dimension, were found. Distributions exhibit finite-time corrections hallmarked by a shift in the mean decaying as t(-ß), where ß is the growth exponent. Our results support a generalization of the ansatz h=v(∞)t+(Γt)(ß)χ+η+ζt(-ß) to higher dimensions, where v(∞), Γ, ζ, and η are nonuniversal quantities whereas ß and χ are universal and the last one depends on the surface geometry. Generalized Gumbel distributions provide very good fits of the distributions in at least four orders of magnitude around the peak, which can be used for comparisons with experiments. Our numerical results call for analytical approaches and experimental realizations of the KPZ class in two-dimensional systems.

Universal fluctuations in Kardar-Parisi-Zhang growth on one-dimensional flat substrates.

We present a numerical study of the evolution of height distributions (HDs) obtained in interface growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. The growth is done on an initially flat substrate. The HDs obtained for all investigated models are very well fitted by the theoretically predicted Gaussian orthogonal ensemble (GOE) distribution. The first cumulant has a shift that vanishes as t(-1/3), while the cumulants of order 2≤n≤4 converge to GOE as t(-2/3) or faster, behaviors previously observed in other KPZ systems. These results yield evidences for the universality of the GOE distribution in KPZ growth on flat substrates. Finally, we further show that the surfaces are described by the Airy(1) process.

Explaining the high number of infected people by dengue in Rio de Janeiro in 2008 using a susceptible-infective-recovered model.

An epidemiological model for dengue propagation using cellular automata is constructed. Dependence on temperature and rainfall index are taken into account. Numerical results fit pretty well with the registered cases of dengue for the city of Rio de Janeiro for the period from 2006 to 2008. In particular, our approach explains very well an abnormally high number of cases registered in 2008. A phase transition from endemic to epidemic regimes is discussed.

Effects of the mean free path and relaxation in a model for the aggregation of particles in superfluid media.

In this paper, we study a two-dimensional model for the growth of molecular clusters in superfluid helium at low temperature. In the model, particles of diameter a follow random ballistic moves of length delta = a - 256a. Upon attachment on the cluster surface, particles allow one-step relaxation to the nearest twofold coordinated site. Average coordination numbers of particles show that in the presence of relaxation the screening for incoming particles modifies the microscopic structure of the cluster. These results are in qualitative agreement with experimental aggregation of methane in He droplets, in which large abundance of fully coordinated sites is observed. The average coordination number increases with delta, showing that screening is relevant when relaxation is present. As the cluster size increases, the corresponding structure clusters changes from a compact to a fractal, typical of ballistic and diffusion limited models, respectively. A scaling ansatz describing the crossover between the two regimes is proposed.

Contact process on a Voronoi triangulation.

We study the continuous absorbing-state phase transition in the contact process on the Voronoi-Delaunay lattice. The Voronoi construction is a natural way to introduce quenched coordination disorder in lattice models. We simulate the disordered system using the quasistationary simulation method and determine its critical exponents and moment ratios. Our results suggest that the critical behavior of the disordered system is unchanged with respect to that on a regular lattice, i.e., that of directed percolation.

Granular fingers on jammed systems: new fluidlike patterns arising in grain-grain invasion experiments.

In this Letter we report spontaneous pattern formation in dense granular assemblies confined to a Hele-Shaw cell and quasistatic regime. Varied unexpected patterns, ranging from rounded to fingered, are observed due to the displacement of one granular material by another. Computer simulations reproduce the major features observed in these experiments. Two mechanisms are responsible for the pattern formation: crystallization of the injected grains and plastic deformation of the displaced grains. The experiment suggests analogies with viscous fingering and jamming transition experiments.

Aggregation in a mixture of Brownian and ballistic wandering particles.

In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the patterns, as well as their gap distributions. The particles added to the cluster can follow either ballistic trajectories, with probability Pba, or random ones, with probability Prw=1-Pba. The patterns were characterized through several quantities, including those related to the radial and angular scaling. The fractal dimension as a function of Pba continuously increases from df approximately 1.72 (DLA dimensionality) for Pba=0 to df approximately 2 (BA dimensionality) for Pba. However, the lacunarity and the active zone width exhibit a distinct behavior: they are convex functions of Pba with a maximum at Pba approximately 1/2. Through the analysis of the angular correlation function, we found that the difference between the radial and angular exponents decreases continuously with increasing Pba and rapidly vanishes for Pba>1/2, in agreement with recent results concerning the asymptotic scaling of DLA clusters.

Morphological transition between diffusion-limited and ballistic aggregation growth patterns.

In this work, the transition between diffusion-limited (DLA) and ballistic aggregation (BA) models was reconsidered using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter lambda, which assumes the value lambda=0 (1) for the ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, an efficient algorithm was developed. For lambda (not equal to) 0 , the patterns are fractal on small length scales, but homogeneous on large ones. We evaluated the mean density of particles (-)rho in the region defined by a circle of radius r centered at the initial seed. As a function of r, (-)rho reaches the asymptotic value rho(0)(lambda) following a power law (-)rho = rho(0) +Ar(-gamma) with a universal exponent gamma=0.46 (2) , independent of lambda . The asymptotic value has the behavior rho(0) approximately |1-lambda|(beta) , where beta=0.26 (1) . The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by xi approximately |1-lambda|(-nu) , where nu=0.61 (1) , while the cluster mass at the crossover follows a power law M(xi) approximately |1-lambda(-alpha) , where alpha=0.97 (2) . We deduce the scaling relations beta=nugamma and beta=2nu-alpha between these exponents.

Cellular automata model for citrus variegated chlorosis.

A cellular automata model is proposed to analyze the progress of citrus variegated chlorosis epidemics in São Paulo orange plantations. In this model epidemiological and environmental features, such as motility of sharpshooter vectors that perform Lévy flights, level of plant hydric and nutritional stress, and seasonal climatic effects, are included. The observed epidemic data were quantitatively reproduced by the proposed model on varying the parameters controlling vector motility, plant stress, and initial population of diseased plants.