A numerical optimization method of the vertical Bridgman growth configuration is presented and developed. It permits to optimize the furnace temperature field and the pulling rate versus time in ...order to decrease the radial thermal gradients in the sample. Some constraints are also included in order to insure physically realistic results. The model includes the two classical non-linearities associated to crystal growth processes, the radiative thermal exchange and the release of latent heat at the solid–liquid interface. The mathematical analysis and development of the problem is shortly described. On some examples, it is shown that the method works in a satisfactory way; however the results are dependent on the numerical parameters. Improvements of the optimization model, on the physical and numerical point of view, are suggested.
We study a mathematical model treating of the dynamic contact line problem, supposed to describe the main features of the advancing triple line (rolling motion and variable contact angle) and to ...remove the singularity. The model is composed by a macroscopic hydrodynamic free surface flow model (HFSM) (Navier–Stokes) coupled with a mesoscopic local surface model (LSM). Detailed mathematical and numerical analysis of the 1D steady-state local surface model are doneexistence and uniqueness of the exact and numerical solutions, extra properties of the derivatives, and convergence of finite element schemes. Some numerical results of the two models treated separately are presented for a 2D plunging tape configuration.
The detection of old house borer larvae (Hylotrupes bajulus L.) in Scots pine wood (Pinus sylvestris L.) was performed using the acoustic emission (AE) method. Laboratory experiments (as preliminary) ...as well as real tests in full-sized building elements were performed. The sound energy of larvae with a mass of 0.011 g to 0.065 g placed in small samples of wood was calculated. A remarkable relationship was found between the calculated sound energy and larva mass. The AE measurement of an old house borer larva in construction element with a cross-section of 11.0 cm × 5.5 cm and a length of 203 cm was also performed. A remarkable drop in calculated sound energy was observed with increasing distance of the sensor from the larval presence. Similar measurements were also conducted in wood with a cross-section of 1.5 cm × 1.5 cm and a length of 203 cm. There was a smaller decline in the calculated energy of sound than in previous studies. For this reason, the AE method should be used in detecting wood-boring insects in furniture.
The acoustic emission analysis method was used to determine the activity of very young Hylotrupes bajulus larvae in their long-term development. In the laboratory conditions the simulated scenario of ...a fresh, intense infestation inside the construction wood was evaluated. The sounds generated by the insects during their feeding on the wooden samples were processed by the measurement system, which was able to detect and count the larva-originated sound pulses and calculate related energy. So far, no one has examined possibilities of detecting infant larvae of Hylotrupes bajulus L. This work is a continuation of research on the influence of the insect mass on its AE-based detection. The experiments performed with multiple wood samples analyzed through the period of one year have shown dependency between the mass of the larva and the intensity of the sound generated by them. The moment of the earliest possible detection of infestation in the wooden structure was evaluated. In the appropriate conditions (large number of young larvae inside the wood and optimal temperature) the insects reach the mass of tens of mg, which makes them detectable using the AE method.
During the filling stage of an injection moulding process, which consists in casting a melt polymer in order to manufacture plastic pieces, the free interface between polymer and air has to be ...precisely described. We set this interface as a zero level set of an unknown function. This function satisfies a transport equation with boundary conditions, where the velocity field has few regularity properties.In a first part, we obtain existence and uniqueness result for these equations, under weaker regularity assumptions than C. Bardos Bar70, and C. Bardos, Y. Leroux and J.C. Nedelec BLN79 in previous articles, but stronger assumptions than R.J. DiPerna and P.L. Lions DL89b who studied the case without boundary condition. We also study some regularity properties of the interface.A second part is devoted to an application to injection molding of melt polymer. We give a numerical experiment which shows that our method leads to an accurate localization of interface, which is robust, since it easily handles changes of topology of the free interface, as bubble formation or fusion of two fronts of melt polymer.
Pseudomonotonicity seems to be the good notion to deal with convergence in nonlinear terms of partial differential equations. Lions 1 used two different definitions of pseudomonotonicity for elliptic ...and parabolic problems, and derived associated existence results. Nonlinear elliptic-parabolic equations are intermediate equations for which an intermediate pseudomonotonicity is defined and an existence result is proved, extending previous results of Alt and Luckhaus 2 and Bermúdez, Durany and Saguez 3.
The paper presented in general characteristics of Danish agriculture, the yields achieved within last century as well as the milking performance of the cows within last five decades. Production level ...and the range of foreign trade with agricultural products were described. Transformations in agrarian structure weer analysed considering also the changes in farming system directed towards production concentration and specialization. The necessary figures were taken from official Danish agricultural statistics as well as from different Danish and Polish publications
Le modèle que nous présentons ici est une version simplifiée tirée de la simulation numérique d’un procédé de cristallogénèse (3, 6). On s’intéresse à la résolution de l’équation de la chaleur dans ...un domaine Ω avec des échanges thermiques par rayonnement sur une partie Γ1 de la frontière de Ω. Ces échanges se font à l’intérieur d’une enceinte fermée Г = Г1 ∪ Г2. La prise en compte de toutes les réflections donne un couplage des températures et une condition de Neumann non linéaire sur Г1. Cette non linéarité n’est pas monotone. On utilise la méthode des sous et sur solutions pour montrer l’existence d’une solution minimale et d’une solution maximale puis on établit l’unicité de la solution avec un principe du maximum.
The model we are presenting here is a simplified version which arises from the numerical simulation of the crystal growth (3, 6). We are interested in the resolution of the heat equation in a domain Ω with thermal exchanges by radiation on a part Γ1 of the boundary of Ω. These exchanges exist inside a closed cavity Γ = Γ1 ∪ Γ2. If we take account of all the reflections we obtain a nonlinear Neumann’s condition with temperatures coupled on Г1. The method using here to prove the existence of a solution to this problem is based on the utilization of lower and upper solutions. We obtain the unicity by a maximum principle.
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