A free boundary problem related to thermal insulation

We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but rather a hypersurface along which a harmonic function satisfies a Robin condition. We show that minimal sets exist, satisfy uniform density estimates, and, under some geometric conditions, have “locally flat” boundaries.     

Existence analysis of an optimal shape design problem with non coercive state equation

In this paper, a shape optimization problem, modelling a welding process, governed by a second order non coercive PDE is considered. The well posedness of the shape optimal design problem is showed using the degree of Leray–Schauder. Then the existence of an optimal solution is proved.     

Dislocations hétéro-interfaciales vis perçant une plaquette mince

A specimen observed in high-resolution transmission electron microscopy is electron transparent and its thickness is often less than about 10 nm. When it contains a linear defect like a screw dislocation, the obtained image can exhibit more or less important perturbations due to elastic relaxation nearby both free surfaces. Therefore, the theoretical interpretation of an image should include this relaxation in the calculation model. In the present work, it is evaluated for screw misfit dislocations piercing normally an elastically heterogeneous bicristalline plate (thickness 2h) from the following assumptions: there is no applied force on the thin plate and any surface stress related to a possible nanometric structure along the two free surfaces is neglected. The solution is found from an appropriate combination of known elastic fields in an infinite medium, which enables total stresses applying on two planes distant of 2h to be cancelled. This solution generalizes for the first time that of Eshelby and Stroh (1951), who consider an isolated screw dislocation normal to a homogeneous plate.     

Verification of the Usefulness of Radiotracing Methods in Hydrodynamic Investigations

In the paper comparison of accuracy of two methods used for investigations of hydrodynamic in continuous flow tanks has been made. Basis for the comparison is the experimental work performed for big industrial wastewater concentration equalization tank. The first method is based on the radiotracer experiment while the second one uses the analysis of response on sudden change of the technological parameters. The radiotracer method has better accuracy connected with the shorter sampling period.

Ks wird die Genauigkeit zweier Methoden zur Untersuchting der Hydrodynamik von kontinuierlich arbeitenden Flüssigkeitsbehältern verglichen. Grundlage dafür sind experimentelle Untersuchungen an groβen Industrieabwasser-Ausgleichsbehältern. Die erste Methode bedient sich der Radiotracertechnik, während die zweite Methode auf einer plötzlichen Veränderung der technologischcn Parameter beruht. Es zeigt sich, daβ die Radiotracermethoden die besseren Ergebnisse liefert, wobei auβerdem noch kürzere Probenaltmeperioden von Vorteil sind.     

The Spin-Coating Process: Analysis of the Free Boundary Value Problem

In this paper, an accurate model of the spin-coating process is presented and investigated from the analytical point of view. More precisely, the spin-coating process is being described as a one-phase free boundary value problem for Newtonian fluids subject to surface tension and rotational effects. It is proved that for T > 0 there exists a unique, strong solution to this problem in (0, T) belonging to a certain regularity class provided the data and the speed of rotation are small enough in suitable norms. The strategy of the proof is based on a transformation of the free boundary value problem to a quasilinear evolution equation on a fixed domain. The keypoint for solving the latter equation is the so-called maximal regularity approach. In order to pursue in this direction one needs to determine the precise regularity classes for the associated inhomogeneous linearized equations. This is being achieved by applying the Newton polygon method to the boundary symbol.     

Properties of cat-eye modulating retro-reflector and its application with piezoelectric transducer

Piezoelectric cat-eye modulating retro-reflector (MRR) is the core component of an acousto-optic retro-identification system. The influence of the optical parameters (link distance l, lens focal length f and the detector diameter r) to the cat-eye effect was analyzed theoretically and experimentally. A piezoelectric cat-eye retro-identification (PCERI) system was built, and an information transmission ratio of 2 kHz was achieved which can satisfy an access control system.     

Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain

This paper concerns with the problem of how to running an insurance company to maximize his total discounted expected dividends. In our model, the dividend rate is limited in $[0,M]$ and the company is allowed to transfer any proportion of risk by reinsuring. So there are two strategies which we call dividend strategy and reinsurance strategy. The objective function and the corresponding optimal two strategies are the solution and the two free boundaries of the following Barenblatt parabolic equation

$v_t?\underset{0\le a\le 1}{\max }?(\frac{1}{2}{a}^2{\sigma }^2{v}_{xx}+a\mu v_x)+cv?\underset{0\le l\le M}{\max }?[(1?v_x)l]=0$

under certain boundary conditions on an angular domain

$Q_T=\{(x,t)|0<x<Mt,0<t\le T\}.$

The main effort is to analyze the properties of the solution and the free boundaries to show the optimal decision for the insurance company.