A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model

The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for breaking waves and dry areas. The dispersive part is treated with a classical finite difference approach. Extensive numerical validations are then performed in one horizontal dimension, relying both on analytical solutions and experimental data. The results show that our approach gives a good account of all the processes of wave transformation in coastal areas: shoaling, wave breaking and run-up

Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model

We investigate here the ability of a Green-Naghdi model to reproduce strongly nonlinear and dispersive wave propagation. We test in particular the behavior of the new hybrid finite-volume and finite-difference splitting approach recently developed by the authors and collaborators on the challenging benchmark of waves propagating over a submerged bar. Such a configuration requires a model with very good dispersive properties, because of the high-order harmonics generated by topography-induced nonlinear interactions. We thus depart from the aforementioned work and choose to use a new Green-Naghdi system with improved frequency dispersion characteristics. The absence of dry areas also allows us to improve the treatment of the hyperbolic part of the equations. This leads to very satisfying results for the demanding benchmarks under consideration

Методические особенности управления туристскими потоками в регионе (на примере Автономной Республики Крым)

Экономическая жизнь, начиная от простых жителей сел и городов, до экономики полуострова в целом зависит от количества туристов, приехавших в Крым на отдых и лечениеЕкономічне життя, починаючи від простих мешканців сіл і міст, до економіки півострова в цілому залежить від кількості туристів, що приїхали до Криму на відпочинок і лікуванн

Large time existence for 3D water-waves and asymptotics

We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a ``variable'' nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a well-posedness theorem, uniformly with respect to all the parameters. Its validity ranges therefore from shallow to deep-water, from small to large surface and bottom variations, and from fully to weakly transverse waves. The physical regimes corresponding to the aforementioned models can therefore be studied as particular cases; it turns out that the existence time and the energy bounds given by the theorem are always those needed to justify the asymptotic models. We can therefore derive and justify them in a systematic way.Comment: Revised version of arXiv:math.AP/0702015 (notations simplified and remarks added) To appear in Inventione

A model for the periodic water wave problem and its long wave amplitude equations

We are interested in the validity of the KdV and of the long wave NLS approximation for the water wave problem over a periodic bottom. Approximation estimates are non-trivial, since solutions of order O(ε^2 ), resp. O(ε), have to be controlled on an O(1/ε^3 ), resp. O(1/ε^2 ), time scale. In contrast to the spatially homogeneous case, in the periodic case new quadratic resonances occur and make a more involved analysis necessary. For a phenomenological model we present some results and explain the underlying ideas. The focus is on results which are robust in the sense that they hold under very weak non-resonance conditions without a detailed discussion of the resonances. This robustness is achieved by working in spaces of analytic functions. We explain that, if analyticity is dropped, the KdV and the long wave NLS approximation make wrong predictions in case of unstable resonances and suitably chosen periodic boundary conditions. Finally we outline, how, we think, the presented ideas can be transferred to the water wave problem

Role of protein kinase C and epidermal growth factor receptor signalling in growth stimulation by neurotensin in colon carcinoma cells

<p>Abstract</p> <p>Background</p> <p>Neurotensin has been found to promote colon carcinogenesis in rats and mice, and proliferation of human colon carcinoma cell lines, but the mechanisms involved are not clear. We have examined signalling pathways activated by neurotensin in colorectal and pancreatic carcinoma cells.</p> <p>Methods</p> <p>Colon carcinoma cell lines HCT116 and HT29 and pancreatic adenocarcinoma cell line Panc-1 were cultured and stimulated with neurotensin or epidermal growth factor (EGF). DNA synthesis was determined by incorporation of radiolabelled thymidine into DNA. Levels and phosphorylation of proteins in signalling pathways were assessed by Western blotting.</p> <p>Results</p> <p>Neurotensin stimulated the phosphorylation of both extracellular signal-regulated kinase (ERK) and Akt in all three cell lines, but apparently did so through different pathways. In Panc-1 cells, neurotensin-induced phosphorylation of ERK, but not Akt, was dependent on protein kinase C (PKC), whereas an inhibitor of the β-isoform of phosphoinositide 3-kinase (PI3K), TGX221, abolished neurotensin-induced Akt phosphorylation in these cells, and there was no evidence of EGF receptor (EGFR) transactivation. In HT29 cells, in contrast, the EGFR tyrosine kinase inhibitor gefitinib blocked neurotensin-stimulated phosphorylation of both ERK and Akt, indicating transactivation of EGFR, independently of PKC. In HCT116 cells, neurotensin induced both a PKC-dependent phosphorylation of ERK and a metalloproteinase-mediated transactivation of EGFR that was associated with a gefitinib-sensitive phosphorylation of the downstream adaptor protein Shc. The activation of Akt was also inhibited by gefitinib, but only partly, suggesting a mechanism in addition to EGFR transactivation. Inhibition of PKC blocked neurotensin-induced DNA synthesis in HCT116 cells.</p> <p>Conclusions</p> <p>While acting predominantly through PKC in Panc-1 cells and via EGFR transactivation in HT29 cells, neurotensin used both these pathways in HCT116 cells. In these cells, neurotensin-induced activation of ERK and stimulation of DNA synthesis was PKC-dependent, whereas activation of the PI3K/Akt pathway was mediated by stimulation of metalloproteinases and subsequent transactivation of the EGFR. Thus, the data show that the signalling mechanisms mediating the effects of neurotensin involve multiple pathways and are cell-dependent.</p

Delithiation/lithiation behavior of LiNi<inf>0.5</inf>Mn<inf>1.5</inf>O<inf>4</inf> studied by in situ and ex situ ^6,7Li NMR spectroscopy

Delithiation and lithiation behaviors of ordered spinel LiNi0.5Mn1.5O4 and disordered spinel LiNi0.4Mn1.6O4 were investigated by using in situ (in operando) 7Li NMR and ex situ 6Li MAS NMR spectroscopy. The in situ 7Li monitoring of the ordered spinel revealed a clear appearance and subsequent disappearance of a new signal from the well-defined phase Li0.5Ni0.5Mn1.5O4, suggesting the two-phase reaction processes among Li1.0Ni0.5Mn1.5O4, Li0.5Ni0.5Mn1.5O4, and Li0.0Ni0.5Mn1.5O4. Also, for the disordered spinel, Li0.5Ni0.4Mn1.6O4 was identified with a broad distribution in Li environment. High-resolution 6Li MAS NMR spectra were also acquired for the delithiated and lithiated samples to understand the detailed local structure around Li ions. We suggested that the nominal Li-free phase Li0.0Ni0.5Mn1.5O4 can accommodate a small amount of Li ions in its structure. The tetragonal phases Li2.0Ni0.5Mn1.5O4 and Li2.0Ni0.4Mn1.6O4, which occurred when the cell was discharged down to 2.0 V, were very different in the Li environment from each other. It is found that 6, 7Li NMR is highly sensitive not only to the Ni/Mn ordering in LiNi0.5Mn1.5O4 but also to the valence changes of Ni and Mn on charge-discharge process