Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term

The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient which is usually small in comparison to the other physical constants. The main feature of this equation is the fact that even a globally bounded nonlinearity is "supercritical" in the case of two and three space dimensions. Thus the standard methods used for studying semilinear hyperbolic equations are not very effective in the present case. Nevertheless, we have recently proven the global existence and dissipativity of strong solutions in the 2D case (with a cubic controlled growth nonlinearity) and for the 3D case with small inertial coefficient and arbitrary growth rate of the nonlinearity. The present contribution studies the long-time behavior of rather weak (energy) solutions of that equation and it is a natural complement of the results of our previous papers. Namely, we prove here that the attractors for energy and strong solutions coincide for both the cases mentioned above. Thus, the energy solutions are asymptotically smooth. In addition, we show that the non-smooth part of any energy solution decays exponentially in time and deduce that the (smooth) exponential attractor for the strong solutions constructed previously is simultaneously the exponential attractor for the energy solutions as well

Giant Coulomb broadening and Raman lasing on ionic transitions

CW generation of anti-Stokes Raman laser on a number of blue-green argon-ion lines (4p-4s, 4p-3d) has been demonstrated with optical pumping from metastable levels 3d'^2G, 3d^4F. It is found, that the population transfer rate is increased by a factor of 3-5 (and hence, the output power of such Raman laser) owing to Coulomb diffusion in the velocity space. Measured are the excitation and relaxation rates for the metastable level. The Bennett hole on the metastable level has been recorded using the probe field technique. It has been shown that the Coulomb diffusion changes shape of the contour to exponential cusp profile while its width becomes 100 times the Lorentzian one and reaches values close to the Doppler width. Such a giant broadening is also confirmed by the shape of the absorption saturation curve.Comment: RevTex 18 pages, 5 figure

On Asymptotic Completeness of Scattering in the Nonlinear Lamb System, II

We establish the asymptotic completeness in the nonlinear Lamb system for hyperbolic stationary states. For the proof we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ODE) converging to a hyperbolic stationary point using the Inverse Function Theorem in a Banach space. We give the counterexamples showing nonexistence of such trajectories for nonhyperbolic stationary points

Random raman fiber laser based on a twin-core fiber with FBGs inscribed by femtosecond radiation

Narrowband Raman lasing in a polarization-maintaining two-core fiber (TCF) is demonstrated. Femtosecond point-by-point inscription of fiber Bragg gratings (FBGs) in individual cores produces a half-open cavity with random distributed feedback. The laser linewidth in the cavity with a single FBG inscribed in one core of the TCF reduced by ∼2 times with respect to the cavity with a fiber loop mirror. It is shown that the inscription of two FBGs in different cores leads to the formation of a Michelson-type interferometer, leading to the modulation of generation spectra near threshold. This technique offers new possibilities for spectral filtering or multi-wavelength generation

Vortical and Wave Modes in 3D Rotating Stratified Flows: Random Large Scale Forcing

Utilizing an eigenfunction decomposition, we study the growth and spectra of energy in the vortical and wave modes of a 3D rotating stratified fluid as a function of $\epsilon = f/N$. Working in regimes characterized by moderate Burger numbers, i.e. $Bu = 1/\epsilon^2 < 1$ or $Bu \ge 1$, our results indicate profound change in the character of vortical and wave mode interactions with respect to $Bu = 1$. As with the reference state of $\epsilon=1$, for $\epsilon < 1$ the wave mode energy saturates quite quickly and the ensuing forward cascade continues to act as an efficient means of dissipating ageostrophic energy. Further, these saturated spectra steepen as $\epsilon$ decreases: we see a shift from $k^{-1}$ to $k^{-5/3}$ scaling for $k_f < k < k_d$ (where $k_f$ and $k_d$ are the forcing and dissipation scales, respectively). On the other hand, when $\epsilon > 1$ the wave mode energy never saturates and comes to dominate the total energy in the system. In fact, in a sense the wave modes behave in an asymmetric manner about $\epsilon = 1$. With regard to the vortical modes, for $\epsilon \le 1$, the signatures of 3D quasigeostrophy are clearly evident. Specifically, we see a $k^{-3}$ scaling for $k_f < k < k_d$ and, in accord with an inverse transfer of energy, the vortical mode energy never saturates but rather increases for all $k < k_f$. In contrast, for $\epsilon > 1$ and increasing, the vortical modes contain a progressively smaller fraction of the total energy indicating that the 3D quasigeostrophic subsystem plays an energetically smaller role in the overall dynamics.Comment: 18 pages, 6 figs. (abbreviated abstract

Bioecology of a major pest of Arabica coffee in Eastern Africa highlands, the african coffee white stem borer, Monochamus leuconotus (Coleoptera: Cerambycidae)

For the last 50 years, coffee production has been in constant decline for major producing countries of Eastern Africa, like Kenya and Tanzania. Factors explaining this decline include high production costs, especially costs for fertilizers and pesticides, which led many smallholders to phase out of coffee farming. The African coffee white stem borer (CWSB), Monochamus leuconotus (Pascoe) (Coleoptera: Cerambycidae) appears to be a growing threat in those countries and a significant cause of coffee farming abandonment. CWSB damages coffee trees, mainly by ring barking and wood boring, leading to low yields and dieback under high infestation. Insecticides that have proven to be effective for CWSB control in the past are banned today, and coffee smallholders are poorly equipped to resolve the threat. An urgent need for action has been recognized in different countries of the region to provide scientifically-sound and practical strategies for the management of CWSB. However, available knowledge of the pest bioecology still suffers gaps that need to be filled to achieve this objective. For 4 years now, the coffee pest project at International Centre of Insect Physiology and Ecology (icipe) in Kenya has undertaken research dedicated to CWSB bioecology. The present communication reviews this research and gives some basic unpublished life history traits. A rearing method with an artificial diet has been developed that allowed the description of CWSB life cycle and feeding and reproductive behaviours, and the assessment of the pest demographic parameters. Field surveys in smallholder coffee farms located on elevation gradients on Kilimanjaro, Tanzania allowed the characterization of the pest population dynamics and showed impact of agro-ecological factors such as elevation, shade and microclimate. Recommendations for a more efficient and sustainable management of this major pest are proposed based on existing knowledge along with results obtained at icipe. (Résumé d'auteur

Optical Characterisation of Suspended Particles in the Mackenzie River Plume (Canadian Arctic Ocean) and Implications for Ocean Colour Remote Sensing

Climate change significantly impacts Arctic shelf regions in terms of air temperature, ultraviolet radiation, melting of sea ice, precipitation, thawing of permafrost and coastal erosion. Direct consequences have been observed on the increasing Arctic river flow and a large amount of organic carbon sequestered in soils at high latitudes since the last glacial maximum can be expected to be delivered to the Arctic Ocean during the coming decade. Monitoring the fluxes and fate of this terrigenous organic carbon is problematic in such sparsely populated regions unless remote sensing techniques can be developed and proved to be operational. The main objective of this study is to develop an ocean colour algorithm to operationally monitor dynamics of suspended particulate matter (SPM) on the Mackenzie River continental shelf (Canadian Arctic Ocean) using satellite imagery. The water optical properties are documented across the study area and related to concentrations of SPM and particulate organic carbon (POC). Robust SPM and POC : SPM proxies are identified, such as the light backscattering and attenuation coefficients, and relationships are established between these optical and biogeochemical parameters. Following a semi-analytical approach, a regional SPM quantification relationship is obtained for the inversion of the water reflectance signal into SPM concentration. This relationship is reproduced based on independent field optical measurements. It is successfully applied to a selection of MODIS satellite data which allow estimating fluxes at the river mouth and monitoring the extension and dynamics of the Mackenzie River surface plume in 2009, 2010 and 2011. Good agreement is obtained with field observations representative of the whole water column in the river delta zone where terrigenous SPM is mainly constrained (out of short periods of maximum river outflow). Most of the seaward export of SPM is observed to occur within the west side of the river mouth. Future work will require the validation of the developed SPM regional algorithm based on match-ups with field measurements, then the routine application to ocean colour satellite data in order to better estimate the fluxes and fate of SPM and POC delivered by the Mackenzie River to the Arctic Ocean