Dewetting dynamics of stressed viscoelastic thin polymer films

Ultrathin polymer films that are produced e.g. by spin-coating are believed to be stressed since polymers are 'frozen in' into out-of-equilibrium configurations during this process. In the framework of a viscoelastic thin film model, we study the effects of lateral residual stresses on the dewetting dynamics of the film. The temporal evolution of the height profiles and the velocity profiles inside the film as well as the dissipation mechanisms are investigated in detail. Both the shape of the profiles and the importance of frictional dissipation vs. viscous dissipation inside the film are found to change in the course of dewetting. The interplay of the non-stationary profiles, the relaxing initial stress and changes in the dominance of the two dissipation mechanisms caused by nonlinear friction with the substrate is responsible for the rich behavior of the system. In particular, our analysis sheds new light on the occurrence of the unexpected maximum in the rim width obtained recently in experiments on PS-PDMS systems.Comment: 11 pages, 10 figure

Stable self similar blow up dynamics for slightly L^2 supercritical NLS equations

We consider the focusing nonlinear Schr\"odinger equations $i\partial_t u+\Delta u +u|u|^{p-1}=0$ in dimension $1\leq N\leq 5$ and for slightly $L^2$ supercritical nonlinearities p_c with $p_c=1+\frac{4}{N}$ and 0<\e\ll 1. We prove the existence and stability in the energy space $H^1$ of a self similar finite time blow up dynamics and provide a qualitative description of the singularity formation near the blow up tim

Growth rings in tropical trees : role of functional traits, environment, and phylogeny

Acknowledgments Financial support of the Centre National de la Recherche Scientifique (USR 3330), France, and from the Rufford Small Grants Foundation (UK) is acknowledged. We thank the private farmers and coffee plantation companies of Kodagu for providing permissions and logistical support for this project. We are grateful to N. Barathan for assistance with slide preparation and data entry, S. Aravajy for botanical assistance, S. Prasad and G. Orukaimoni for technical inputs, and A. Prathap, S. Shiva, B. Saravana, and P. Shiva for field assistance. The corresponding editor and three anonymous reviewers provided insightful comments that improved the manuscript.Peer reviewedPostprin

Anderson Model out of equilibrium: decoherence effects in transport through a quantum dot

The paper deals with the nonequilibrium two-lead Anderson model, considered as an adequate description for transport through a d-c biased quantum dot. Using a self-consistent equation-of-motion method generalized out of equilibrium, we calculate a fourth-order decoherence rate $\gamma^{(4)}$ induced by a bias voltage $V$. This decoherence rate provides a cut-off to the infrared divergences of the self-energy showing up in the Kondo regime. At low temperature, the Kondo peak in the density of states is split into two peaks pinned at the chemical potential of the two leads. The height of these peaks is controlled by $\gamma^{(4)}$. The voltage dependence of the differential conductance exhibits a zero-bias peak followed by a broad Coulomb peak at large $V$, reflecting charge fluctuations inside the dot. The low-bias differential conductance is found to be a universal function of the normalized bias voltage $V/T_K$, where $T_K$ is the Kondo temperature. The universal scaling with a single energy scale $T_K$ at low bias voltages is also observed for the renormalized decoherence rate $\gamma^{(4)}/T_K$. We discuss the effect of $\gamma^{(4)}$ on the crossover from strong to weak coupling regime when either the temperature or the bias voltage is increased.Comment: 23 pages, 10 figure

"Marginal pinching" in soap films

We discuss the behaviour of a thin soap film facing a frame element: the pressure in the Plateau border around the frame is lower than the film pressure, and the film thins out over a certain distance lambda(t), due to the formation of a well-localized pinched region of thickness h(t) and extension w(t). We construct a hydrodynamic theory for this thinning process, assuming a constant surface tension: Marangoni effects are probably important only at late stages, where instabilitites set in. We find lambda(t) ~ t^{1/4}, and for the pinch dimensions h(t) ~ t^{-1/2}$ and w(t) ~ t^{-1/4}. These results may play a useful role for the discussion of later instabilitites leading to a global film thinning and drainage, as first discussed by K. Mysels under the name ``marginal regeneration''.Comment: 7 pages, 2 figure

Stable self-similar blow-up dynamics for slightly L2L^2-supercritical generalized KdV equations

In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . We will prove the existence and stability of a blow-up dynamic with self-similar blow-up rate in the energy space $H^1$ and give a specific description of the formation of the singularity near the blow-up time.Comment: 38 page

Predicting tropical forest stand structure parameters from Fourier transform of very high-resolution remotely sensed canopy images

1. Predicting stand structure parameters for tropical forests from remotely sensed data has numerous important applications, such as estimating above-ground biomass and carbon stocks and providing spatial information for forest mapping and management planning, as well as detecting potential ecological determinants of plant species distributions. As an alternative to direct measurement of physical attributes of the vegetation and individual tree crown delineation, we present a powerful holistic approach using an index of canopy texture that can be extracted from either digitized air photographs or satellite images by means of two-dimensional spectral analysis by Fourier transform. 2. We defined an index of canopy texture from the ordination of the Fourier spectra computed for 3545 1-ha square images of an undisturbed tropical rain forest in French Guiana. This index expressed a gradient of coarseness vs. fineness resulting from the relative importance of small, medium and large spatial frequencies in the Fourier spectra. 3. Based on 12 1-ha control plots, the canopy texture index showed highly significant correlations with tree density (R2 = 0·80), diameter of the tree of mean basal area (R2 = 0·71), distribution of trees into d.b.h. classes (R2 = 0·64) and mean canopy height (R2 = 0·57), which allowed us to produce reasonable predictive maps of stand structure parameters from digital aerial photographs. 4. Synthesis and applications. Two-dimensional Fourier analysis is a powerful method for obtaining quantitative characterization of canopy texture, with good predictive ability on stand structure parameters. Forest departments should use routine forest inventory operations to set up and feed regional databases, featuring both tree diameter figures and digital canopy images, with the ultimate aims of calibrating robust regression relationships and deriving predictive maps of stand structure parameters over large areas of tropical forests. Such maps would be particularly useful for forest classification and to guide field assessment of tropical forest resources and biodiversity