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showing 10 items of 7541 documents
Multiple positive normalized solutions for nonlinear Schrödinger systems
2018
We consider the existence of multiple positive solutions to the nonlinear Schr\"odinger systems sets on $H^1(\mathbb{R}^N) \times H^1(\mathbb{R}^N)$, \[ \left\{ \begin{aligned} -\Delta u_1 &= \lambda_1 u_1 + \mu_1 |u_1|^{p_1 -2}u_1 + \beta r_1 |u_1|^{r_1-2} u_1|u_2|^{r_2}, -\Delta u_2 &= \lambda_2 u_2 + \mu_2 |u_2|^{p_2 -2}u_2 + \beta r_2 |u_1|^{r_1} |u_2|^{r_2 -2} u_2, \end{aligned} \right. \] under the constraint \[ \int_{\mathbb{R}^N}|u_1|^2 \, dx = a_1,\quad \int_{\mathbb{R}^N}|u_2|^2 \, dx = a_2. \] Here $a_1, a_2 >0$ are prescribed, $\mu_1, \mu_2, \beta>0$, and the frequencies $\lambda_1, \lambda_2$ are unknown and will appear as Lagrange multipliers. Two cases are studied, the first …
The nature of black stains in Lascaux Cave, France, as revealed by surface-enhanced Raman spectroscopy
2011
We used surface-enhanced Raman spectroscopy to investigate the chemical composition of the black stains threatening the rock-art paintings of Lascaux Cave, Montignac, France. The stains are mainly composed of melanin from the fungus Ochroconis sp. and the faecal pellets of the collembolan Folsomia candida. Surface-enhanced Raman spectroscopy is a useful technique for revealing the structure of unknown macromolecules in cultural heritage research. Copyright © 2011 John Wiley & Sons, Ltd.
Experiments for testing soil texture effects on flow resistance in mobile bed rills
2018
Abstract In this paper a recently theoretically deduced rill flow resistance equation, based on a power-velocity profile, was tested experimentally on plots of varying slopes and soil texture in which mobile bed rills are incised. Measurements of flow velocity, water depth, cross section area, wetted perimeter and bed slope conducted in rill reaches incised on experimental plots, having different slope values (9, 14, 22, 24 and 26%) and soil texture (clay fraction ranging from 42 to 73%), and literature data were used to calibrate the flow resistance equation. In particular, the relationship between the velocity profile parameter Γ, the channel slope, the flow Froude number and texture frac…
A boundary condition for arbitrary shaped inlets in lattice-Boltzmann simulations
2009
We introduce a mass-flux-based inlet boundary condition for the lattice-Boltzmann method. The proposed boundary condition requires minimal amount of boundary data, it produces a steady-state velocity field which is accurate close to the inlet even for arbitrary inlet geometries, and yet it is simple to implement. We demonstrate its capability for both simple and complex inlet geometries by numerical experiments. For simple inlet geometries, we show that the boundary condition provides very accurate inlet velocities when Re less than or similar to 1. Even with moderate Reynolds number, the inlet velocities are accurate for practical purposes. Furthermore, the potential of our boundary condit…
A full‐scale study of Darcy‐Weisbach friction factor for channels vegetated by riparian species
2021
In this article, an open channel flow resistance equation, deduced applying dimensional analysis and incomplete self-similarity condition for the flow velocity distribution, was tested using measurements carried out in a full-scale channel equipped with three types of riparian plants (Salix alba L., Salix caprea L. and Alnus glutinosa L.). In the experimental channel, having banks lined with boulders, the vegetation branches were anchored in a concrete bottom. For each species, the measurements were carried out with plants having different amounts of leaves, different plant density and plant area index. The relationship between the scale factor Γ of the velocity profile and the Froude numbe…
Comparative tests on different multi-electrode arrays using models in near-surface geophysics
2008
In this paper, the response of different synthetic models to geoelectrical multi-electrode surveys is studied. The models considered are related to two main problems, which are very common in geophysical research regarding hydrogeology and engineering. The first class of models represents buried walls, similar archaeological remains or remains of buried foundations; the other class corresponds to a sea-water intrusion of a fresh water aquifer, which is generally studied in hydrogeophysics. A set of 2D simulations, starting from the synthetic models, was carried out to compare the behaviour of the different arrays when acquiring measurements of electrical resistivity tomography. For each mod…
Models as Research Tools: Plücker, Klein, and Kummer Surfaces
2018
In the late summer of 1869, 20-year-old Felix Klein made his way to Berlin, where he planned to attend the renowned seminar founded by Ernst Eduard Kummer and Karl Weierstrass. Klein had already taken his doctorate in Bonn and he would soon be recognized as a leading expert on line geometry, a new approach to 3-space launched by his mentor in Bonn, Julius Plucker. Just before Plucker died in 1868, he entrusted Klein to complete the classic monograph, Neue Geometrie des Raumes gegrundet auf die Betrachtung der geraden Linie als Raumelement. Overall responsibility for this project fell to Alfred Clebsch in Gottingen, which was how Klein first came to the prestigious Georgia Augusta. There he …
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
2003
We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to right-angled Artin groups a result of Lyndon for free groups, we show that the Euler characteristic -1 surface group (given by the relation x^2y^2=z^2) never embeds in a right-angled Artin group.
Many-body Green's function theory for electron-phonon interactions: ground state properties of the Holstein dimer
2015
We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong whereas at smaller interactions only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron de…
Revealing lattice disorder, oxygen incorporation and pore formation in laser induced two-photon oxidized graphene
2019
Abstract Laser induced two-photon oxidation has proven to be a reliable method to pattern and control the level of oxidation of single layer graphene, which in turn allows the development of graphene-based electronic and optoelectronic devices with an all-optical method. Here we provide a full structural and chemical description of modifications of air-suspended graphene during the oxidation process. By using different laser irradiation doses, we were able to show via transmission electron microscopy, electron energy loss spectroscopy, electron diffraction and Raman spectroscopy how graphene develops from its pristine form up to a completely oxidized, porous and amorphous carbon layer. Furt…