In this paper, we use the fading regularization method to solve a biharmonic inverse problem, represented by the Cauchy problem. Two formulations are studied and implemented numerically using a finite element method (FEM). We present numerical reconstructions of the missing data on the inaccessible part of the boundary from the knowledge of over-prescribed noisy data for both smooth and piecewise smooth two-dimensional geometries. Numerical examples validate the convergence, stability and efficiency of the proposed numerical algorithm, as well as its capability to deblur the noisy data. 相似文献
The presence of interfaces in fluid/solid biphasic media is known to strongly influence their behavior both in terms of solid deformation and fluids flow. Mathematical models have traditionally represented these interfaces as lines of no-thickness and whose behavior is given in terms of effective permeabilities whose physical meaning is often disconnected to the microscopic nature of the interface. This article aims to reconcile macroscopic and microscopic interface representations by investigating how the nature of microscopic flows and pressures in the interface can be used to explain its macroscopic behavior. By invoking a proper thickness average operation, we derive an closed form expression that relates the effective interfaces permeabilities to its microscopic properties. In particular, we find that the effective interface permeabilities are strongly influenced by three factors: the ratio of bulk and interface permeabilities, the fluid viscosity, and the physical thickness of the interface.
Microcystins (MCs), a group of cyclic heptapeptides produced by common cyanobacteria (blue green algae), cause both acute and chronic toxicity. Due to their toxicity, constant monitoring in drinking water, recreational waters as well as other potential exposure through ingestion of contaminated sea food, is very important. In this context, an immunochromatographic test (ICT) using a monoclonal antibody labeled with fluorescent liposomes (immunoliposomes) as tracer was developed, allowing a rapid and simple detection of a large number of MC and nodularin variants in field samples. The present ICT using immunoliposomes proved to be ten times more sensitive than the ICT using colloidal gold for labeling. To achieve quantitative measurement, this ICT was improved by including a stable signal on the control band allowing the expression of the results as a ratio of the fluorescence signals of the specific band versus the control band (SB/CB). Very low concentrations of MC-LR were detected in the analysis buffer (0.06 ng/ml), well below the guideline value of 1 ng/ml proposed by the World Health Organization (WHO), with a dynamic range from 0.06 to 1.5 ng/ml of MC-LR. This method was also validated using a hand-held commercial fluorometer (from ESE®), providing the same performances obtained via the analysis station (from Kodak®) used in our laboratory. Repeatability tests performed with both devices showed good accuracy (CV?13%). Furthermore, quantification of MCs in natural samples (water bloom and Microcystis culture) was achieved using ICT, leading to similar results obtained via an EIA previously described. All these results demonstrate that this new fluorescent ICT could be used not only as a sensitive detection tool but also to quantify MCs in field samples. 相似文献
We propose a new approximate Bayesian computation (ABC) algorithm that aims at minimizing the number of model runs for reaching a given quality of the posterior approximation. This algorithm automatically determines its sequence of tolerance levels and makes use of an easily interpretable stopping criterion. Moreover, it avoids the problem of particle duplication found when using a MCMC kernel. When applied to a toy example and to a complex social model, our algorithm is 2–8 times faster than the three main sequential ABC algorithms currently available. 相似文献