Refined approximation for a class of Landau-de Gennes energy minimizers

We study a class of Landau-de Gennes energy functionals in the asymptotic regime of small elastic constant $L>0$. We revisit and sharpen the results in [18] on the convergence to the limit Oseen-Frank functional. We examine how the Landau-de Gennes global minimizers are approximated by the Oseen-Frank ones by determining the first order term in their asymptotic expansion as $L\to 0$. We identify the appropriate functional setting in which the asymptotic expansion holds, the sharp rate of convergence to the limit and determine the equation for the first order term. We find that the equation has a ``normal component'' given by an algebraic relation and a ``tangential component'' given by a linear system

Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations

We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single standard bubble in a universal positive distance around each blow-up point, and (iii) the heights of these bubbles are comparable by a universal factor. As an application of this result, we establish a quantitative Liouville theorem

A degree theory for second order nonlinear elliptic operators with nonlinear oblique boundary conditions

In this paper we introduce an integer-valued degree for second order fully nonlinear elliptic operators with nonlinear oblique boundary conditions. We also give some applications to the existence of solutions of certain nonlinear elliptic equations arising from a Yamabe problem with boundary and reflector problems

Existence and uniqueness to a fully non-linear version of the Loewner-Nirenberg problem

We consider the problem of finding on a given Euclidean domain $\Omega$ of dimension $n \geq 3$ a complete conformally flat metric whose Schouten curvature $A$ satisfies some equation of the form $f(\lambda(-A)) = 1$. This generalizes a problem considered by Loewner and Nirenberg for the scalar curvature. We prove the existence and uniqueness of such metric when the boundary $\partial\Omega$ is a smooth bounded hypersurface (of codimension one). When $\partial\Omega$ contains a compact smooth submanifold $\Sigma$ of higher codimension with $\partial\Omega\setminus\Sigma$ being compact, we also give a `sharp' condition for the divergence to infinity of the conformal factor near $\Sigma$ in terms of the codimension

Many-body physics of intersubband polaritons

Intersubband polaritons are light-matter excitations originating from the strong coupling between an intersubband quantum well electronic transition and a microcavity photon mode. In this paper we study how the Coulomb electron-electron interaction and the Pauli saturation of the electronic transitions affect the physics of intersubband polaritons. We develop a microscopic many-body theory for the physics of such composite bosonic excitations in a microcavity-embedded two-dimensional electron gas. As a first application, we calculate the modification of the depolarization shifts and the efficiency of intersubband polariton-polariton scattering processes

APPLYING EXERCISES TO IMPROVE SPEED ENDURANCE IN 100 METERS SPRING FOR MALE STUDENTS AT VINH UNIVERSITY, VIETNAM

The purpose of this study was to select and apply selected exercises to develop speed endurance in 100 meter sprint for male students. 20 male students (aged 18.8 ± 0.9 years), non-specializing in physical education and sports, regularly attended physical education courses. The participants were divided into two groups: an exercise group and a control group. All subjects were informed of the experimental protocol prior to testing and signed an informed consent form. Participants in the exercise group followed a new exercise program for 8 weeks. Participants in the control group maintained regular physical exercises which were yearly assigned by the department and were asked to not do any new exercise program. After 8-week exercise training, the exercise group showed better performance in two tests in comparison with the control group. It can be concluded that selected exercises had good impacts on improving speed endurance and performance of 100 meter sprint for male students.  Article visualizations

Data-driven discovery of the heat equation in an induction machine via sparse regression

Discovery of natural laws through input-output data analysis has been of considerable interest during the past decade. Various approach among which the increasingly growing body of sparsity-based algorithms have been recently proposed for the purpose of free-form system identification. There has however been limited discussion on the performance of these approaches when applied on experimental datasets. The aim of this paper is to study the capability of this technique for identifying the heat equation as the natural law of heat distribution from experimental data, obtained using a Totally-Enclosed-Fan-Cooled (TEFC) induction machine, with and without active cooling. The results confirm the usefulness of the algorithm as a method to identify the underlying natural law in a physical system in the form of a Partial Differential Equation (PDE)