44 research outputs found
Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals
We study a singular nonlinear ordinary differential equation on intervals {[}0, R) with R <= +infinity, motivated by the Ginzburg-Landau models in superconductivity and Landau-de Gennes models in liquid crystals. We prove existence and uniqueness of positive solutions under general assumptions on the nonlinearity. Further uniqueness results for sign-changing solutions are obtained for a physically relevant class of nonlinearities. Moreover, we prove a number of fine qualitative properties of the solution that are important for the study of energetic stability
Coercivity and stability results for an extended Navier-Stokes system
In this article we study a system of equations that is known to {\em extend}
Navier-Stokes dynamics in a well-posed manner to velocity fields that are not
necessarily divergence-free. Our aim is to contribute to an understanding of
the role of divergence and pressure in developing energy estimates capable of
controlling the nonlinear terms. We address questions of global existence and
stability in bounded domains with no-slip boundary conditions. Even in two
space dimensions, global existence is open in general, and remains so,
primarily due to the lack of a self-contained energy estimate. However,
through use of new coercivity estimates for the linear equations, we
establish a number of global existence and stability results, including results
for small divergence and a time-discrete scheme. We also prove global existence
in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure
Influence of PEDOT :PSS Layer on the Performances of Photovoltaic Cells Based on MEH-PPV:PCBM Blend
Date du colloque : 07/2011International audienc
Orientability and energy minimization in liquid crystal models
Uniaxial nematic liquid crystals are modelled in the Oseen-Frank theory
through a unit vector field . This theory has the apparent drawback that it
does not respect the head-to-tail symmetry in which should be equivalent to
-. This symmetry is preserved in the constrained Landau-de Gennes theory
that works with the tensor .We study
the differences and the overlaps between the two theories. These depend on the
regularity class used as well as on the topology of the underlying domain. We
show that for simply-connected domains and in the natural energy class
the two theories coincide, but otherwise there can be differences
between the two theories, which we identify. In the case of planar domains we
completely characterise the instances in which the predictions of the
constrained Landau-de Gennes theory differ from those of the Oseen-Frank
theory
Energy Dissipation and Regularity for a Coupled Navier-Stokes and Q-Tensor System
We study a complex non-newtonian fluid that models the flow of nematic liquid
crystals. The fluid is described by a system that couples a forced
Navier-Stokes system with a parabolic-type system. We prove the existence of
global weak solutions in dimensions two and three. We show the existence of a
Lyapunov functional for the smooth solutions of the coupled system and use the
cancellations that allow its existence to prove higher global regularity, in
dimension two. We also show the weak-strong uniqueness in dimension two
Landau-De Gennes theory of nematic liquid\ud crystals: the Oseen-Frank limit and beyond
We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W 1,2 , to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer.\ud
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We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions
Early Detection, Diagnosis and Intervention Services for Young Children with Autism Spectrum Disorder in the European Union (ASDEU): Family and Professional Perspectives
Early services for ASD need to canvas the opinions of both parents and professionals. These opinions are seldom compared in the same research study. This study aims to ascertain the views of families and professionals on early detection, diagnosis and intervention services for young children with ASD. An online survey compiled and analysed data from 2032 respondents across 14 European countries (60.9% were parents; 39.1% professionals). Using an ordinal scale from 1 to 7, parents’ opinions were more negative (mean = 4.6; SD 2.2) compared to those of professionals (mean = 4.9; SD 1.5) when reporting satisfaction with services. The results suggest services should take into account child’s age, delays in accessing services, and active stakeholders’ participation when looking to improve services
Experimental analysis of a rigid rotor supported on aerodynamic foil journal bearings
Aerodynamic foil bearings are highly non linear components used or intending to be used for supporting high speed rotors (>30 krpm) of low size rotating machines (<400 kW). The non linear character comes from the highly deformable structure of the bearing made of thin steel sheets and from the Coulomb friction forces arising during dynamic displacements. The present work shows the non linear response of a rigid rotor supported by a pair of such bearings and entrained at 82 krpm. The measurements performed during the coast down revealed sub synchronous and asynchronous vibrations of the rotor and their multiples. A simplified theoretical model reproduces qualitatively some of these non linear characteristics