This work deals with a free boundary identification problem in a steady viscoplastic flow. We provide a novel identification model based on a non-linear optimization. The fluid motion is governed by the incompressible Norton–Hoff model coupled with the heat equation. The viscosity of the fluid is modeled by the non-linear Arrhenius law. Our point of view is to treat the problem as a shape sensitivity of a cost functional formulated on the free boundary and governed by the normal component of the velocity of the flow. We analyze the mathematical statement of the forward problem. The equations related to the free boundary are simplified. Various properties of this optimization are proved. Since the state of Norton–Hoff model is not regular enough we introduce a parameter penalization. The shape gradient of the considered cost functional is given in the strong sense up to the parameter of penalization. We supply the expression of the shape gradient in a weak sense. 相似文献
We report on ideas, problems and results, which occupied us during the past decade and which seem to extend the frontiers of information theory in several directions. The main contributions concern information transfer by channels. There are also new questions and some answers in new models of source coding. While many of our investigations are in an explorative state, there are also hard cores of mathematical theories. In particular we present a unified theory of information transfer, which naturally incorporates Shannon's theory of information transmission and the theory of identification in the presence of noise as extremal cases. It provides several novel coding theorems. On the source coding side we introduce data compression for identification. Finally we are led beyond information theory to new concepts of solutions for probabilistic algorithms.
The original paper [R. Ahlswede, General theory of information transfer, Preprint 97-118, SFB 343 Diskrete Strukturen in der Mathematik, Universität Bielefeld, 1997] gave to and received from the ZIF-project essential stimulations which resulted in contributions added as GTIT-Supplements “Search and channels with feedback” and “Noiseless coding for multiple purposes: a combinatorial model”.
Other contributions—also to areas initiated—are published in the recent book [R. Ahlswede et al. (Eds.), General Theory of Information Transfer and Combinatorics, Lecture Notes in Computer Science, vol. 4123, Springer, Berlin, 2006].
The readers are advised to study always the pioneering papers in a field—in this case the papers [R. Ahlswede, G. Dueck, Identification via channels, IEEE Trans. Inform. Theory 35 (1989) 15–29; R. Ahlswede, G. Dueck, Identification in the presence of feedback—a discovery of new capacity formulas, IEEE Trans. Inform. Theory 35 (1989) 30–39] on identification. It is not only the most rewarding way to come to new ideas, but it also helps to more quickly grasp the more advanced formalisms without going through too many technicalities. Perhaps also the recent Shannon Lecture [R. Ahlswede, Towards a General Theory of Information Transfer, Shannon Lecture at ISIT in Seattle 13th July 2006, IEEE Information Theory Society Newsletter, 2007], aiming at an even wider scope, gives further impetus. 相似文献
This work proposes a methodology of identifying linear parameter varying (LPV) models for nonlinear systems. First, linear local models in some operating points, by applying standard identifications procedures for linear systems in time domain, are obtained. Next, a LPV model with linear fractional dependence (LFR) with respect to measured variables is fitted with the condition of containing all the linear models identified in previous step (differential inclusion). The fit is carried out using nonlinear least squares algorithms. Finally, this identification methodology will then be applied to a nonlinear turbocharged diesel engine. 相似文献