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Mathematical modelling of flow and adsorption in a gas chromatograph

Partial Differential Equations in applied mathematics 2025年 13卷

作者： Cabrera-Codony, A. Valverde, A. Born, K. Noreldin, O.A.I. Myers, T.G. LEQUIA Institute of the Environment Universitat de Girona Spain Department of Chemical Engineering Universitat Politècnica de Catalunya Spain School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa Department of Mathematical Sciences University of Zululand South Africa Centre de Recerca Matemàtica Barcelona Spain

In this paper, a mathematical model is developed to describe the evolution of the concentration of compounds through a gas chromatography column. The model couples mass balances and kinetic equations for all components. Both single and multiple-component cases are considered with constant or variable velocity. Dimensional analysis is employed to identify negligible terms and so reduce the problem to the solution of a single integral equation. From this the concentration profile for all components may be determined (since they are scaled versions of each other). The full governing equations are also solved numerically to verify the analytical approach. Finally the analytical results are compared with experimental data, showing excellent agreement. This novel method is highly efficient and is significantly faster and simpler than previous numerical approaches. © 2025

关键词： Advection–diffusion equation Column adsorption Compounds separation Gas chromatography Mathematical model

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Efficient Power Transfer via Induced Virtual Critical Coupling in an Overcoupled Silicon Nitride Microresonator

Efficient Power Transfer via Induced Virtual Critical Coupli...

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Conference on Lasers and Electro-Optics (CLEO)

作者： Jakob Hinney Seunghwi Kim Graydon J. K. Flatt Ipshita Datta Andrea Alù Michal Lipson Department of Electrical Engineering Columbia University New York NY USA Photonics Initiative Advanced Science Research Center City University of New York New York NY USA Department of Applied Physics and Applied Mathematics Columbia University New York NY USA Physics Program Graduate Center City University of New York New York NY USA

We induce virtual critical coupling in an overcoupled photonic microresonator using complex-frequency pulses. We observe efficient cavity storage as an incident pulse of time constant 138 ps suppresses the resonant tr... 详细信息

ISBN: (纸本)9781957171258

关键词： Continuous wave operation Coupled mode theory Electrooptical modulators Optical resonators Pulse shaping Silicon nitride

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State Estimation for Continuous-Discrete-Time Nonlinear Stochastic Systems

arXiv

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arXiv 2022年

作者： Nielsen, Marcus Krogh Ritschel, Tobias K.S. Christensen, Ib Dragheim, Jess Huusom, Jakob Kjøbsted Gernaey, Krist V. Jørgensen, John Bagterp Department of Applied Mathematics and Compute Science DTU Compute Technical University of Denmark Kgs. LyngbyDK-2800 Denmark Department of Chemical and Biochemical Engineering DTU Chemical Engineering Technical University of Denmark Kgs. LyngbyDK-2800 Denmark Unibio A/S RoskildeDK-4000 Denmark

State estimation incorporates the feedback in optimization based advanced process control systems and is very important for the performance of model predictive control. We describe the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and a particle filter for continuous-discrete time nonlinear systems involving stochastic differential equations. Continuous-discrete time nonlinear systems is a natural way to model physical systems controlled by digital controllers. We implement the state estimation methods in Matlab, illustrate and evaluate their performance using simulations of the modified four-tank system. This system is non-stiff and the state estimation methods are implemented numerically using an explicit numerical integration scheme. We evaluate the accuracy of the state estimation methods in terms of the mean absolute percentage error over the simulation horizon. Each method successfully estimates the states and unmeasured disturbances of the simulated modified four-tank system. The key contribution is an overview and comparison of state estimation methods for continuous-discrete time nonlinear stochastic systems. This can guide efficient implementations. Copyright © 2022, The Authors. All rights reserved.

关键词： State estimation

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Foundation Models for Atomistic Simulation of Chemistry and Materials

arXiv

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arXiv 2025年

作者： Yuan, Eric C.-Y. Liu, Yunsheng Chen, Junmin Zhong, Peichen Raja, Sanjeev Kreiman, Tobias Vargas, Santiago Xu, Wenbin Head-Gordon, Martin Yang, Chao Blau, Samuel M. Cheng, Bingqing Krishnapriyan, Aditi Head-Gordon, Teresa Kenneth S. Pitzer Theory Center Department of Chemistry United States Department of Chemical and Biomolecular Engineering United States Electrical Engineering and Computer Science United States Bakar Institute of Digital Materials for the Planet University of California BerkeleyCA94720 United States Chemical Sciences Division United States Applied Mathematics and Computational Research Division United States Energy Technologies Area United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

Given the power of large language and large vision models, it is of profound and fundamental interest to ask if a foundational model based on data and parameter scaling laws and pre-training strategies is possible for learned simulations of chemistry and materials. The scaling of large and diverse datasets and highly expressive architectures for chemical and materials sciences should result in a foundation model that is more efficient and broadly transferable, robust to out-of-distribution challenges, and easily fine-tuned to a variety of downstream observables, when compared to specific training from scratch on targeted applications in atomistic simulation. In this Perspective we aim to cover the rapidly advancing field of machine learned interatomic potentials (MLIP), and to illustrate a path to create chemistry and materials MLIP foundation models at larger scale. © 2025, CC BY-SA.

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High-speed and low-power molecular dynamics processing unit(MDPU)with ab initio accuracy

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npj Computational Materials 2024年第1期10卷 559-568页

作者： Pinghui Mo Yujia Zhang Zhuoying Zhao Hanhan Sun Junhua Li Dawei Guan Xi Ding Xin Zhang Bo Chen Mengchao Shi Duo Zhang Denghui Lu Yinan Wang Jianxing Huang Fei Liu Xinyu Li Mohan Chen Jun Cheng Bin Liang Weinan E Jiayu Dai Linfeng Zhang Han Wang Jie Liu College of Integrated Circuits Hunan UniversityChangsha410082P.R.China College of Electrical and Information Engineering Hunan UniversityChangsha410082P.R.China College of Computer National University of Defense TechnologyChangsha410073P.R.China Department of Physics National University of Defense TechnologyChangsha410073P.R.China DP Technology 100080 BeijingP.R.China AI for Science Institute 100080 BeijingP.R.China Academy for Advanced Interdisciplinary Studies Peking University100871 BeijingP.R.China HEDPS CAPTCollege of EngineeringPeking University100871 BeijingP.R.China School of Mathematical Science Peking University100871 BeijingP.R.China State Key Laboratory of Physical Chemistry of Solid Surfaces iChEMCollege of Chemistry and Chemical EngineeringXiamen UniversityXiamen361005P.R.China School of Integrated Circuits Peking University100871 BeijingP.R.China Center for Machine Learning Research Peking University100871 BeijingP.R.China Institute of Applied Physics and Computational Mathematics 100088 BeijingP.R.China Greater Bay Area Institute for Innovation Hunan UniversityGuangzhou511300P.R.China Department of Electrical and Computer Engineering University of WashingtonSeattleWA98195USA

Molecular dynamics(MD)is an indispensable atomistic-scale computational tool widely-used in various *** the past decades,nearly all ab initio MD and machine-learning MD have been based on the general-purpose central/graphics processing units(CPU/GPU),which are well-known to suffer from their intrinsic“memory wall”and“power wall”***,nowadays MD calculations with ab initio accuracy are extremely time-consuming and power-consuming,imposing serious restrictions on the MD simulation size and *** solve this problem,here we propose a special-purpose MD processing unit(MDPU),which could reduce MD time and power consumption by about 103 times(109 times)compared to state-of-the-art machine-learningMD(ab initio MD)based on CPU/GPU,while keeping ab initio *** significantly-enhanced performance,the proposed MDPU may pave a way for the accurate atomistic-scale analysis of large-size and/or longduration problems which were impossible/impractical to compute before.

关键词： consuming power MDP

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Cementing the grain boundary defects in the strain relaxed mixed Sn-Pb perovskite solar cells

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chemical engineering Journal 2025年 516卷

作者： Kumar, Abhishek Ansari, Zeeshan Alam Hanmandlu, Chintam Banerjee, Soumallya Chen, Yu-Te Yang, Po-Yu Musa, Ahmed Fouad You, Yun-Wen Pao, Chun-Wei Wei, Tzu-Chien Shyue, Jing-Jong Lu, Yu-Jung Chu, Chih-Wei Department of Physics National Taiwan University Sec. 4 Roosevelt Road Taipei106 Taiwan Research Center for Applied Sciences Academia Sinica 128 Academia Road Section 2 Taipei Nangang11529 Taiwan Nano-Science and Technology Program Taiwan International Graduate Program Academia Sinica Taipei106 Taiwan Department of Materials Science and Engineering National Yang Ming Chiao Tung University Hsinchu300 Taiwan Department of Chemical Engineering National Tsing Hua University 101 Section 2 Kuang-Fu Road Hsinchu City300044 Taiwan College of Engineering Center for Green Technology Chang Gung University Taoyuan City333002 Taiwan Department of Photonics National Yang Ming Chiao Tung University Hsinchu City30010 Taiwan Institute of Applied Mechanics National Taiwan University Sec. 4 Roosevelt Road Taipei106 Taiwan

Mixed Tin-lead (Sn-Pb) perovskite solar cells (PSCs) offer a promising avenue for achieving high power conversion efficiencies (PCEs) due to their narrow bandgaps and substantial optical absorption in the visible–near-infrared region. However, the disparated reaction kinetics of PbI2 and SnI2 with organic salts, resulting in an uneven spatial distribution of Sn2+ and Pb2+ within the perovskite lattice, inducing micro-strain in the film and a Sn-rich surface vulnerable to oxidation-Sn2+ to Sn4+, thereby elevating nonradiative recombination. Here, we report the incorporation of 2,5-Dibromo-3,4-pyridinediamine (DBPDA) as an additive in the mixed Sn-Pb perovskite precursor solution, designed to mitigate micro-strain formation, reduce defect density by suppressing Sn4+ formation, and enhance the passivation of undercoordinated Sn/Pb species through synergistic bonding interaction. The best performing PSCs achieved an impressive PCE of 21.24 % with a high open circuit voltage (Voc) of 0.85 V, alongside significantly improved long-term stability, retaining near 80 % of their initial PCE after 1,008 h in a nitrogen-filled glovebox without encapsulation. In contrast, the control devices retained only 18 % of their initial efficiency under identical conditions. Additionally, an enhanced field effect hole mobility, increasing from 0.18 cm2/V-s in the control film to 1.43 cm2/V-s in the target film, was achieved in mixed Sn-Pb perovskite thin film transistors (TFTs) using these films as active layers. These findings present a viable strategy for strain-relieved perovskite films, enabling stable and high-performance mixed Sn-Pb PSCs and TFTs. © 2025 Elsevier B.V.

关键词： Crystallization kinetics

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Robust State-of-Charge Estimator for Lithium-Ion Batteries Enabled By a Physics-Driven Dual-Stage Attention Mechanism

SSRN

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SSRN 2023年

作者： Zhang, Kai Bai, Dongxin Song, Ke Li, Yong Zheng, Bailin Yang, Fuqian School of Aerospace Engineering and Applied Mechanics Tongji University Shanghai200092 China School of Intelligent Manufacturing and Control Engineering Shanghai Polytechnic University Shanghai201209 China School of Automotive Studies Tongji University Shanghai201804 China Materials Program Department of Chemical and Materials Engineering University of Kentucky LexingtonKY40506 United States

The current deep state-of-charge (SOC) estimators face a challenge in extracting short-time-domain multi-scale features, which makes it difficult to capture important driving variables in multi-channel battery measurement features and invariant features in the time and frequency domains of the historical hidden states. This limitation leads to the tradeoff between the ability of the estimators to be trained at a lower cost and the higher error peaks and cumulative errors in the SOC estimation. A hybrid approach, which combines the physics-based characteristics of SOC changes with real-time measured data, is likely an effective solution to address this issue. In this work, we propose a novel SOC estimator, which is based on physics-driven dual-stage attention-based bidirectional recurrent neural network (PDA-BRNN). This estimator consists of two stages. In the first stage, the physics-driven input attention (PIA) mechanism synthesizes historical information and radial strains of the electrode particles of a battery, which are calculated via a physics-based analytical model, from numerous input channels. This synthesis helps identify the main driving variables and suppress local error peaks and cumulative errors in the estimation process. In the second stage, dual-temporal attention (DTA) mines, amplifies, and correlates effective time-varying information from different dimensions in the historical hidden states that benefits the current estimation process for reducing the error levels and improving the overall estimation accuracy. Experimental results demonstrate that the proposed PDA-BRNN is more accurate and robust than the state-of-the-art deep estimators under coherent multi-scale disturbances or Gaussian noise in measurements. © 2023, The Authors. All rights reserved.

关键词： Errors

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Utilizing probabilistic entanglement between sensors in quantum networks

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Physical Review applied 2024年第6期22卷 064085-064085页

作者： Emily A. Van Milligen Christos N. Gagatsos Eneet Kaur Don Towsley Saikat Guha Department of Physics The University of Arizona 1630 East University Boulevard Tucson Arizona 85721 USA Department of Electrical and Computer Engineering The University of Arizona 1630 East University Boulevard Tucson Arizona 85721 USA Wyant College of Optical Sciences The University of Arizona 1630 East University Boulevard Tucson Arizona 85721 USA Program in Applied Mathematics The University of Arizona Tucson Arizona 85721 USA Cisco Quantum Lab Los Angeles USA College of Computer Science University of Massachusetts Amherst Massachusetts USA Department of Electrical and Computer Engineering The University of Maryland College Park Maryland 20742 USA

One of the most promising applications of quantum networks is entanglement-assisted sensing. The field of quantum metrology exploits quantum correlations to improve the precision bound for applications such as precision timekeeping, field sensing, and biological imaging. When measuring multiple spatially distributed parameters, current literature focuses on quantum entanglement in the discrete-variable case and quantum squeezing in the continuous-variable case, distributed amongst all of the sensors in a given network. However, it can be difficult to ensure that all sensors preshare entanglement of sufficiently high fidelity. This work probes the space between fully entangled and fully classical sensing networks by modeling a star network with probabilistic entanglement generation that is attempting to estimate the average of local parameters. The quantum Fisher information is used to determine which protocols best utilize entanglement as a resource for different network conditions. It is shown that without entanglement distillation there is a threshold fidelity below which classical sensing is preferable. For a network with a given number of sensors and links characterized by a certain initial fidelity and probability of success, this work outlines when and how to use entanglement, when to store it, and when it needs to be distilled.

关键词： Quantum entanglement

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Polysaccharide nanocomposites in wastewater treatment: A review

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Chemosphere 2024年 347卷 140578页

作者： Al-Hazmi, Hussein E. Luczak, Justyna Habibzadeh, Sajjad Hasanin, Mohamed S. Mohammadi, Ali Esmaeili, Amin Kim, Seok-Jhin Khodadadi Yazdi, Mohsen Rabiee, Navid Badawi, Michael Saeb, Mohammad Reza Department of Sanitary Engineering Faculty of Civil and Environmental Engineering Gdańsk University of Technology Gdańsk80-233 Poland Department of Process Engineering and Chemical Technology Faculty of Chemistry Gdańsk University of Technology Gdańsk80-233 Poland Tehran Iran Cellulose and Paper Department National Research Centre Cairo Dokki12622 Egypt Department of Engineering and Chemical Sciences Karlstad University Karlstad65188 Sweden Department of Chemical Engineering School of Engineering Technology and Industrial Trades College of the North Atlantic—Qatar Doha Qatar School of Chemical Engineering Oklahoma State University StillwaterOK74078 United States Division of Electrochemistry and Surface Physical Chemistry Faculty of Applied Physics and Mathematics Gdańsk University of Technology Narutowicza 11/12 Gdańsk80-233 Poland Centre for Molecular Medicine and Innovative Therapeutics Murdoch University PerthWA6150 Australia School of Engineering Macquarie University SydneyNSW2109 Australia Université de Lorraine CNRS L2CM F-57000 Metz France Department of Pharmaceutical Chemistry Medical University of Gdańsk J. Hallera 107 Gdańsk80-416 Poland

In modern times, wastewater treatment is vital due to increased water contamination arising from pollutants such as nutrients, pathogens, heavy metals, and pharmaceutical residues. Polysaccharides (PSAs) are natural, renewable, and non-toxic biopolymers used in wastewater treatment in the field of gas separation, liquid filtration, adsorption processes, pervaporation, and proton exchange membranes. Since addition of nanoparticles to PSAs improves their sustainability and strength, nanocomposite PSAs has gained significant attention for wastewater treatment in the past decade. This review presents a comprehensive analysis of PSA-based nanocomposites used for efficient wastewater treatment, focusing on adsorption, photocatalysis, and membrane-based methods. It also discusses potential future applications, challenges, and opportunities in adsorption, filtration, and photocatalysis. Recently, PSAs have shown promise as adsorbents in biological-based systems, effectively removing heavy metals that could hinder microbial activity. Cellulose-mediated adsorbents have successfully removed various pollutants from wastewater, including heavy metals, dyes, oil, organic solvents, pesticides, and pharmaceutical residues. Thus, PSA nanocomposites would support biological processes in wastewater treatment plants. A major concern is the discharge of antibiotic wastes from pharmaceutical industries, posing significant environmental and health risks. PSA-mediated bio-adsorbents, like clay polymeric nanocomposite hydrogel beads, efficiently remove antibiotics from wastewater, ensuring water quality and ecosystem balance. The successful use of PSA-mediated bio-adsorbents in wastewater treatment depends on ongoing research to optimize their application and evaluate their potential environmental impacts. Implementing these eco-friendly adsorbents on a large scale holds great promise in significantly reducing water pollution, safeguarding ecosystems, and protecting human health. © 2023 The

关键词： Wastewater treatment

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A Physics-informed Deep Learning Approach for Minimum Effort Stochastic Control of Colloidal Self-Assembly

arXiv

引用

arXiv 2022年

作者： Nodozi, Iman O’Leary, Jared Mesbah, Ali Halder, Abhishek The Department of Electrical and Computer Engineering University of California Santa CruzCA95064 United States The Department of Chemical and Biomolecular Engineering University of California BerkeleyCA94720 United States The Department of Applied Mathematics University of California Santa CruzCA95064 United States

We propose formulating the finite-horizon stochastic optimal control problem for colloidal self-assembly in the space of probability density functions (PDFs) of the underlying state variables (namely, order parameters). The control objective is formulated in terms of steering the state PDFs from a prescribed initial probability measure towards a prescribed terminal probability measure with minimum control effort. For specificity, we use a univariate stochastic state model from the literature. Both the analysis and the computational steps for control synthesis as developed in this paper generalize for multivariate stochastic state dynamics given by generic nonlinear in state and non-affine in control models. We derive the conditions of optimality for the associated optimal control problem. This derivation yields a system of three coupled partial differential equations together with the boundary conditions at the initial and terminal times. The resulting system is a generalized instance of the so-called Schrödinger bridge problem. We then determine the optimal control policy by training a physics-informed deep neural network, where the "physics" are the derived conditions of optimality. The performance of the proposed solution is demonstrated via numerical simulations on a benchmark colloidal self-assembly problem. Copyright © 2022, The Authors. All rights reserved.

关键词： Probability density function

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