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Adsorption isotherms are the most important parameters in rigorous models of chromatographic processes. In this paper, in order to recover adsorption isotherms, we consider a coupled complex boundary method (CCBM), which was previously proposed for solving an inverse source problem [2]. With CCBM, the original boundary fitting problem is transferred to a domain fitting problem. Thus, this method has advantages regarding robustness and computation in reconstruction. In contrast to the traditional CCBM, for the sake of the reduction of computational complexity and computational cost, the recovered adsorption isotherm only corresponds to the real part of the solution of a forward complex initial boundary value problem. Furthermore, we take into account the position of the profiles and apply the momentum criterion to improve the optimization progress. Using Tikhonov regularization, the well-posedness, convergence properties and regularization parameter selection methods are studied. Based on an adjoint technique, we derive the exact Jacobian of the objective function and give an algorithm to reconstruct the adsorption isotherm. Finally, numerical simulations are given to show the feasibility and efficiency of the proposed regularization method.

Competitive adsorption isotherms must be estimated in order to simulate and optimize modern continuous modes of chromatography in situations where experimental trial-and-error approaches are too co ...

How to determine adsorption isotherms is an issue of significant importance in chromatography. A modern technique of obtaining adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides with actual experimental results. In this work, as well as the natural least-square approach, we consider a Kohn–Vogelius type formulation for the reconstruction of adsorption isotherms in chromatography, which converts the original boundary fitting problem into a domain fitting problem. Moreover, using the first momentum regularizing strategy, a new regularization algorithm for both the Equilibrium-Dispersive model and the Transport-Dispersive model is developed. The mass transfer resistance coefficients in the Transport-Dispersive model are also estimated by the proposed inverse method. The computation of the gradients of objective functions for both of the two models is derived by the adjoint method. Finally, numerical simulations for both a synthetic problem and a real-world pr...

In this work, based on the collage theorem, we develop a new numerical approach to reconstruct the locations of discontinuity of the conduction coefficient in elliptic partial differential equations (PDEs) with inaccurate measurement data and coefficient value. For a given conductivity coefficient, one can construct a contraction mapping such that its fixed point is just the gradient of a solution to the elliptic system. Therefore, the problem of reconstructing a conductivity coefficient in PDEs can be considered as an approximation of the observation data by the fixed point of a contraction mapping. By collage theorem, we translate it to seek a contraction mapping that keeps the observation data as close as possible to itself, which avoids solving adjoint problems when applying the gradient descent method to the corresponding optimization problem. Moreover, the total variation regularizing strategy is applied to tackle the ill-posedness and the parametric level set technique is adopted to represent the discontinuity of the conductivity coefficient. Various numerical simulations are given to show the efficiency of the proposed method., Funding Agencies:Alexander von Humboldt-StiftungNational Natural Science Foundation of China (NSFC) 11571311

Determining competitive adsorption isotherms is an open problem in liquid chromatography. Since traditional experimental trial-and-error approaches are too complex and expensive, a modern technique ...

Web relevance is one of the important indicators to reflect website characteristics from the semantic perspective. To users and constructors of the website, whether web relevance is good or not will affect their use and construction of the website. This paper makes use of the keywords extraction method for web page content and web relevance comparison way to do the research of Chinese web relevance evaluation. A small-scale experiment has been done to verify the feasibility of this evaluation method.