Search results for " mathematical & earth Sciences]"
showing 10 items of 34 documents
Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three
2020
International audience; We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case.
Reversed polarized emission in highly strained a-plane GaN/AlN multiple quantum wells
2010
The polarization of the emission from a set of highly strained $a$-plane GaN/AlN multiple quantum wells of varying well widths has been studied. A single photoluminescence peak is observed that shifts to higher energies as the quantum well thickness decreases due to quantum confinement. The emitted light is linearly polarized. For the thinnest samples the preferential polarization direction is perpendicular to the wurtzite $c$ axis with a degree of polarization that decreases with increasing well width. However, for the thickest well the preferred polarization direction is parallel to the $c$ axis. Raman scattering, x-ray diffraction, and transmission electron microscopy studies have been p…
Viewpoint: Atomic-Scale Design Protocols toward Energy, Electronic, Catalysis, and Sensing Applications
2019
Nanostructured materials are essential building blocks for the fabrication of new devices for energy harvesting/storage, sensing, catalysis, magnetic, and optoelectronic applications. However, because of the increase of technological needs, it is essential to identify new functional materials and improve the properties of existing ones. The objective of this Viewpoint is to examine the state of the art of atomic-scale simulative and experimental protocols aimed to the design of novel functional nanostructured materials, and to present new perspectives in the relative fields. This is the result of the debates of Symposium I "Atomic-scale design protocols towards energy, electronic, catalysis…
Electronic structure and optical properties of III-N nanowires
2011
The term III-N nanowire (NW) will refer throughout this work to the free-standing nanowires made of group-III-nitrides semiconductors, namely InN, GaN and AlN. These nanostructures have a large length/diameter ratio, of the order of 100 (sev- eral micrometers versus tenths of nanometers). The term free-standing highlights the fact that the NWs are not embedded in another material. The improvement of the epitaxial techniques, and in particular, those based on III-N semiconductors, has lead an important part of the Solid State Physics community to concentrate the attention in the last years towards a better understanding of the physical properties of those NWs. Nanowires present several di er…
Description of hard-sphere crystals and crystal-fluid interfaces: a comparison between density functional approaches and a phase-field crystal model.
2012
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three--dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a …
Connectivity percolation in suspensions of hard platelets
2012
We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single--particle cell model. It is commonly assumed that the percolation threshold of anisotropic objects scales as their inverse aspect ratio. While this rule has been shown to hold for rod-like particles, we find that for hard plate-like particles the percolation threshold is non-monotonic in the aspect ratio. It exhibits a shallow minimum at intermediate aspect ratios and then saturates to a constant value. This effect is caused by the isotropic-nematic transition pre-empting the percolation tran…
Isotropic-nematic interface in suspensions of hard rods: Mean-field properties and capillary waves
2006
We present a study of the isotropic-nematic interface in a system of hard spherocylinders. First we compare results from Monte Carlo simulations and Onsager density functional theory for the interfacial profiles of the orientational order parameter and the density. Those interfacial properties that are not affected by capillary waves are in good agreement, despite the fact that Onsager theory overestimates the coexistence densities. Then we show results of a Monte Carlo study of the capillary waves of the interface. In agreement with recent theoretical investigations (Eur.Phys.J. E {\bf 18} 407 (2005)) we find a strongly anistropic capillary wave spectrum. For the wave-numbers accessed in o…
Tight-binding study of the optical properties of GaN/AlN polar and nonpolar quantum wells
2009
The electronic structure of wurtzite semiconductor superlattices (SLs) and quantum wells (QWs) is calculated by using the empirical tight-binding method. The basis used consists of four orbitals per atom (sp3 model), and the calculations include the spin-orbit coupling as well as the strain and electric polarization effects. We focus our study on GaN/AlN QWs wells grown both in polar (C) and nonpolar (A) directions. The band structure, wave functions and optical absorption spectrum are obtained and compared for both cases.
Hard-sphere fluids in annular wedges: density distributions and depletion potentials.
2009
We analyze the density distribution and the adsorption of solvent hard spheres in an annular slit formed by two large solute spheres or a large solute and a wall at close distances by means of fundamental measure density functional theory, anisotropic integral equations and simulations. We find that the main features of the density distribution in the slit are described by an effective, two--dimensional system of disks in the vicinity of a central obstacle. For large solute--solvent size ratios, the resulting depletion force has a straightforward geometrical interpretation which gives a precise "colloidal" limit for the depletion interaction. For intermediate size ratios 5...10 and high sol…
Stochastic differential equations with coefficients in Sobolev spaces
2010
We consider It\^o SDE $\d X_t=\sum_{j=1}^m A_j(X_t) \d w_t^j + A_0(X_t) \d t$ on $\R^d$. The diffusion coefficients $A_1,..., A_m$ are supposed to be in the Sobolev space $W_\text{loc}^{1,p} (\R^d)$ with $p>d$, and to have linear growth; for the drift coefficient $A_0$, we consider two cases: (i) $A_0$ is continuous whose distributional divergence $\delta(A_0)$ w.r.t. the Gaussian measure $\gamma_d$ exists, (ii) $A_0$ has the Sobolev regularity $W_\text{loc}^{1,p'}$ for some $p'>1$. Assume $\int_{\R^d} \exp\big[\lambda_0\bigl(|\delta(A_0)| + \sum_{j=1}^m (|\delta(A_j)|^2 +|\nabla A_j|^2)\bigr)\big] \d\gamma_d0$, in the case (i), if the pathwise uniqueness of solutions holds, then the push-f…