Kardar-Parisi-Zhang growth on one-dimensional decreasing substrates

Recent experimental works on one-dimensional (1D) circular Kardar-Parisi-Zhang (KPZ) systems whose radii decrease in time have reported controversial conclusions about the statistics of their interfaces. Motivated by this, we investigate here several 1D KPZ models on substrates whose size changes in time as $L(t)=L_0 + \omega t$, focusing on the case $\omega<0$. From extensive numerical simulations, we show that for $L_0 \gg 1$ there exists a transient regime in which the statistics is consistent with that of flat KPZ systems (the $\omega=0$ case), for both $\omega0$. Actually, for a given model, $L_0$ and $|\omega|$, we observe that a difference between ingrowing ($\omega0$) systems arises only at long times ($t \gtrsim t_c=L_0/|\omega|$), when the expanding surfaces cross over to the statistics of curved KPZ systems, whereas the shrinking ones become completely correlated. A generalization of the Family-Vicsek scaling for the roughness of ingrowing interfaces is presented. Our results demonstrate that a transient flat statistics is a general feature of systems starting with large initial sizes, regardless their curvature. This is consistent with their recent observation in ingrowing turbulent liquid crystal interfaces, but it is in contrast with the apparent observation of curved statistics in colloidal deposition at the edge of evaporating drops. A possible explanation for this last result, as a consequence of the very small number of monolayers analyzed in this experiment, is given. This is illustrated in a competitive growth model presenting a few-monolayer transient and an asymptotic behavior consistent, respectively, with the curved and flat statistics.Comment: 5 pages, 3 figure

Width and extremal height distributions of fluctuating interfaces with window boundary conditions

We present a detailed study of squared local roughness (SLRDs) and local extremal height distributions (LEHDs), calculated in windows of lateral size $l$, for interfaces in several universality classes, in substrate dimensions $d_s = 1$ and $d_s = 2$. We show that their cumulants follow a Family-Vicsek type scaling, and, at early times, when $\xi \ll l$ ($\xi$ is the correlation length), the rescaled SLRDs are given by log-normal distributions, with their $n$th cumulant scaling as $(\xi/l)^{(n-1)d_s}$. This give rise to an interesting temporal scaling for such cumulants $\left\langle w_n \right\rangle_c \sim t^{\gamma_n}$, with $\gamma_n = 2 n \beta + {(n-1)d_s}/{z} = \left[ 2 n + {(n-1)d_s}/{\alpha} \right] \beta$. This scaling is analytically proved for the Edwards-Wilkinson (EW) and Random Deposition interfaces, and numerically confirmed for other classes. In general, it is featured by small corrections and, thus, it yields exponents $\gamma_n$'s (and, consequently, $\alpha$, $\beta$ and $z$) in nice agreement with their respective universality class. Thus, it is an useful framework for numerical and experimental investigations, where it is, usually, hard to estimate the dynamic $z$ and mainly the (global) roughness $\alpha$ exponents. The stationary (for $\xi \gg l$) SLRDs and LEHDs of Kardar-Parisi-Zhang (KPZ) class are also investigated and, for some models, strong finite-size corrections are found. However, we demonstrate that good evidences of their universality can be obtained through successive extrapolations of their cumulant ratios for long times and large $l$'s. We also show that SLRDs and LEHDs are the same for flat and curved KPZ interfaces.Comment: 11 pages, 10 figures, 4 table

Aproximative solutions to the neutrino oscillation problem in matter

We present approximative solutions to the neutrino evolution equation calculated by different methods. In a two neutrino framework, using the physical parameters which gives the main effects to neutrino oscillations from nu{e} to another flavors for L=3000Km and E=1GeV, the results for the transition probability calculated by using series solutions, by to take the neutrino evolution operator as a product of ordered partial operators and by numerical methods, for a linearly and sinusoidally varying matter density are compared. The extension to an arbitrary density profile is discussed and the evolution operator as a product of partial operators in the three neutrino case is obtained.Comment: 12 pages, 5 figure

Newtonian Perturbations on Models with Matter Creation

Creation of Cold Dark Matter (CCDM) can macroscopically be described by a negative pressure, and, therefore, the mechanism is capable to accelerate the Universe, without the need of an additional dark energy component. In this framework we discuss the evolution of perturbations by considering a Neo-Newtonian approach where, unlike in the standard Newtonian cosmology, the fluid pressure is taken into account even in the homogeneous and isotropic background equations (Lima, Zanchin and Brandenberger, MNRAS {\bf 291}, L1, 1997). The evolution of the density contrast is calculated in the linear approximation and compared to the one predicted by the $\Lambda$CDM model. The difference between the CCDM and $\Lambda$CDM predictions at the perturbative level is quantified by using three different statistical methods, namely: a simple $\chi^{2}$-analysis in the relevant space parameter, a Bayesian statistical inference, and, finally, a Kolmogorov-Smirnov test. We find that under certain circumstances the CCDM scenario analysed here predicts an overall dynamics (including Hubble flow and matter fluctuation field) which fully recovers that of the traditional cosmic concordance model. Our basic conclusion is that such a reduction of the dark sector provides a viable alternative description to the accelerating $\Lambda$CDM cosmology.Comment: Physical Review D in press, 10 pages, 4 figure