Pattern Selection in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing

We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe or hexagon patterns are linearly stable, whereas square patterns and patterns involving more than three modes are unstable. In the case of hexagon patterns up- and down-hexagons can be simultaneously stable. The third-order, weakly nonlinear analysis predicts stable square patterns and super-hexagons for larger amplitudes. Direct simulations show, however, that in this regime the third-order weakly nonlinear analysis is insufficient, and these patterns are, in fact unstable

Solitons in combined linear and nonlinear lattice potentials

We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons. Under the direct commensurability (equal periods of the lattices, the family of ordinary solitons is similar to its counterpart in the free space. The situation is different in the case of the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or incommensurability. In those cases, there is an existence threshold for the solitons, and the scaling relation between their amplitude and width is different from that in the free space. GS families demonstrate a bistability, unless the direct commensurability takes place. Specific scaling relations are found for them too. Ordinary solitons can be readily set in motion by kicking. GSs are mobile too, featuring inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion, while the stability of GS families follows an inverted ("anti-VK") criterion, which is explained by means of the averaging approximation.Comment: 9 pages, 6 figure

Bayesian Sea Ice Detection With the ERS Scatterometer and Sea Ice Backscatter Model at C-Band

This paper describes the adaptation of a Bayesian sea ice detection algorithm for the scatterometer on-board the European Remote Sensing (ERS) satellites (ERS-1 and ERS-2). The algorithm is based on statistics of distances to ocean wind and sea ice geophysical model functions (GMFs) and its performance is validated against coincident active and passive microwave data. We furthermore propose a new model for sea ice backscatter at the C-band in vertical polarization based on the sea ice GMFs derived from ERS and advanced scatterometer data. The model characterizes the dependence of sea ice backscatter on the incidence angle and the sea ice type, allowing a more precise incidence angle correction than afforded by the usual linear transformation. The resulting agreement between the ERS, QuikSCAT, and special sensor microwave imager sea ice extents during the year 2000 is high during the fall and winter seasons, with an estimated ice edge accuracy of about 20 km, but shows persistent biases between scatterometer and radiometer extents during the melting period, with scatterometers being more sensitive to summer (lower concentration and rotten) sea ice types

Instantaneous cell migration velocity may be ill-defined

Cell crawling is critical to biological development, homeostasis and disease. In many cases, cell trajectories are quasi-random-walk. In vitro assays on flat surfaces often described such quasi-random-walk cell trajectories as approximations to a solution of a Langevin process. However, experiments show quasi-diffusive behavior at small timescales, indicating that instantaneous velocity and velocity autocorrelations are not well-defined. We propose to characterize mean-squared cell displacement using a modified F\"urth equation with three temporal and spatial regimes: short- and long-time/range diffusion and intermediate time/range ballistic motion. This analysis collapses mean-squared displacements of previously published experimental data onto a single-parameter family of curves, allowing direct comparison between movement in different cell types, and between experiments and numerical simulations. Our method also show that robust cell-motility quantification requires an experiment with a maximum interval between images of a few percent of the cell-motion persistence time or less, and a duration of a few orders-of-magnitude longer than the cell-motion persistence time or more.Comment: 5 pages, plus Supplemental materia

Effect of quick-dip with increasing doses of IBA on rooting of five grapevine rootstocks grafted with 'Cabernet Sauvignon'

The establishment of a vineyard depends on clonal propagation of grapevine woody cuttings. The successful plant propagation relies on adventitious root formation, but it is affected by the scion-rootstock interaction. Synthetic auxins are used in the nursery to improve rooting of woody cuttings. We tested the effect of a quick dip (30 seconds) of increasing doses of indole-3-butyric acid (IBA) solutions (0, 500, 750, 1000, 1250, 1500 ppm) on rooting of grafted woody cuttings. We tested 5 rootstocks grafted with V. vinifera 'Cabernet Sauvignon': SO4 (V. berlandieri x V. riparia), 110 Richter and 1103 Paulsen (V. berlandieri x V. rupestris), 101-14 Mgt (V. riparia x V. rupestris) and Cereza (V. vinifera L.). After 21 days in the callus chamber, we examined the quality of the root system by means of different rooting parameters (callusing and rooting percentage and number, length and biomass of roots per cutting). Among all the rooting parameters evaluated, Cereza presented the highest values in relation to the rest of the rootstocks, followed by 101-14 Mgt, SO4, 110R and 1103P. The quality of the root system was improved in terms of number of roots, length and the total biomass on four rootstocks: Cereza, 110R, 101-14 Mgt and SO4, but not in 1103P whose rooting was unaffected by treatments. The optimal dose of IBA through quick-dip at improving rooting was rootstock-dependent, being 750 ppm for 110R, 101-14 Mgt and SO4; and 1000 ppm for Cereza. These results will contribute in reducing costs during clonal propagation in the nursery, which is associated with the use of costly synthetic hormones and a lower production of bare-root vines

Comportamiento tribológico de materiales cerámicos de nitruro de silicio texturados

Se han fabricado materiales densos de nitruro de silicio (Si3N4) texturados incorporando semillas de β- Si3N4, favoreciendo su alineación mediante extrusión de las piezas en verde y prensado en caliente. Estos materiales presentan elevada anisotropía microestructural que conduce a un comportamiento anisótropo de sus propiedades, tanto mecánicas como tribológicas. Se han realizado ensayos de desgaste en seco mediante movimiento recíproco lineal de pares homólogos con geometría esfera-placa. El material texturado presenta mayor resistencia al desgaste que el de referencia, sin texturar, identificándose como principal mecanismo de desgaste la abrasión debida a microfractura y arranque de granos de Si3N4. En este material, además, se desarrolla un tercer cuerpo que protege la superficie del material