Inverse Design and Boundary Controllability for the Chromatography System

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-09-04 DOI:10.1007/s00032-024-00402-y

Giuseppe Maria Coclite, Nicola De Nitti, Carlotta Donadello, Florian Peru

引用次数: 0

Abstract

We consider the prototypical example of the \(2\times 2\) liquid chromatography system and characterize the set of initial data leading to a given attainable profile at \(t=T\). For profiles that are not attainable at time T, we study a non-smooth optimization problem: recovering the initial data that lead as close as possible to the target in the \(L^2\)-norm. We then study the system on a bounded domain and use a boundary control to steer its dynamics to a given trajectory. Finally, we implement a suitable finite volumes scheme to illustrate these results and show its numerical convergence. Minor modifications of our arguments apply to the Keyfitz–Kranzer system.

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色谱系统的逆向设计和边界可控性

我们考虑了液相色谱系统的原型，并描述了在 \(t=T\) 时导致给定可实现剖面的初始数据集的特征。对于在 T 时无法实现的剖面，我们研究了一个非平滑优化问题：恢复初始数据，使其尽可能接近 \(L^2\)-norm 中的目标。然后，我们在有界域上研究该系统，并使用边界控制将其动态转向给定轨迹。最后，我们采用合适的有限体积方案来说明这些结果，并展示其数值收敛性。我们对Keyfitz-Kranzer系统的论证稍作修改即可应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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