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In this study, a novel application of the Koopman operator for control-oriented modeling of proton exchange membrane fuel cell (PEMFC)stacks is proposed. The primary contributions of this paper are: (1) the design of Koopman-based models for a fuel cell stack, incorporating K-fold cross-validation, varying lifted dimensions, radial basis functions (RBFs), and prediction horizons; and (2) comparison of the performance of Koopman based approach with a more traditional physics-based model. The results demonstrate the high accuracy of the Koopman-based model in predicting fuel cell stack behavior, with an error of less than 3%. The proposed approach offers several advantages, including enhanced computational efficiency, reduced computational burden, and improved interpretability. This study demonstrates the suitability of the Koopman operator for the modeling and control of PEMFCs and provides valuable insights into a novel control-oriented modeling approach that enables accurate and efficient predictions for fuel cell stacks. 

Accurate modeling is crucial for the effective design and control of fuel cell stacks. Although physics-based models are widely used, data-driven methods such as the Koopman operator have not been fully explored for fuel cell modeling. In this paper, a Koopman-based approach is utilized to model the thermal dynamics of a 5 kW open cathode proton exchange membrane fuel cell stack. A physics-based model is used as the baseline for comparison. By varying the cooling fan rotational speed, the dynamics of the fuel cell stack were measured from the low load of near 0 kW to about 5 kW. Compared to experimental results, the steady-state absolute errors of Koopman-based models are within 3%. Additionally, once given sufficient dimension, the development effort required for the Koopman-based model is relatively low compared to the traditional physics-based approach, while still achieving a high level of accuracy. These findings suggest the Koopman operator may be a suitable alternative approach for fuel cell stack modeling that enables the development of more accurate and efficient modeling methods for fuel cell systems and facilitates the implementation of the linear optimal algorithms. 

Precious metals represent some of the least abundant elements in the earth’s crust. There is an urgent need to maximize the utilization efficiency of these metals and thereby attain affordable and sustainable products. One approach for achieving this goal is based on the development of hollow nanocrystals with a well-controlled surface structure, together with a wall thickness kept below 2 nm, or roughly 10 layers of atoms. The hollow structure eliminates the waste of interior atoms and creates an inner surface, while the controllable surface structures contribute to the optimization of catalytic activity and selectivity. In this article, we begin with a brief introduction to two methods that have been developed for the synthesis of hollow nanocrystals: the first relying on the galvanic replacement with a sacrificial template, and the second involving layer-by-layer deposition of metal atoms followed by etching. We then showcase some remarkable properties and applications of this novel class of nanostructures, including their use as effective catalysts for energy conversion, photoresponsive carriers for controlled release and drug delivery, and theranostic agents. A discussion of the existing barriers to their commercialization is also presented. 

As a class of biocompatible and biodegradable phase‐change materials, natural fatty acids have received considerable interest in recent years for temperature‐controlled release of drugs. However, the poor dispersibility and colloidal stability of their nanoparticles under physiological conditions place a major limitation on their applications in biomedicine. Herein, we report a facile method for encapsulating a mixture of two natural fatty acids (with a eutectic melting point at 39 °C) in a biocompatible, silica‐based nanocapsule to achieve both stable dispersion and controllable release of drugs. The nanocapsules have a well‐defined hole in the wall to ensure easy loading of fatty acids, together with multiple types of functional components such as therapeutics and near‐infrared dyes. The payloads can be released through the hole when the fatty acids are melted upon photothermal heating. The release profile can be controlled by varying the size of the hole and/or the duration of laser irradiation.

 

As a class of biocompatible and biodegradable phase‐change materials, natural fatty acids have received considerable interest in recent years for temperature‐controlled release of drugs. However, the poor dispersibility and colloidal stability of their nanoparticles under physiological conditions place a major limitation on their applications in biomedicine. Herein, we report a facile method for encapsulating a mixture of two natural fatty acids (with a eutectic melting point at 39 °C) in a biocompatible, silica‐based nanocapsule to achieve both stable dispersion and controllable release of drugs. The nanocapsules have a well‐defined hole in the wall to ensure easy loading of fatty acids, together with multiple types of functional components such as therapeutics and near‐infrared dyes. The payloads can be released through the hole when the fatty acids are melted upon photothermal heating. The release profile can be controlled by varying the size of the hole and/or the duration of laser irradiation.