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Two key frameworks are employed to analyze mass, energy, and momentum transfer: the control volume approach and the system approach. These frameworks offer different perspectives, depending on whether the focus is on a specific region in space (control volume approach) or a defined mass of fluid (system approach).
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
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Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
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Updated: Jan 23, 2026

High Resolution Physical Characterization of Single Metallic Nanoparticles
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MolCluster: An Unsupervised Framework for Multiscale Molecular Representations with Physically Consistent Resolution

Zhixuan Zhong1,2, Linbo Ma3, Jian Jiang1,2

  • 1Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China.

Journal of Chemical Theory and Computation
|January 21, 2026
PubMed
Summary
This summary is machine-generated.

MolCluster, an unsupervised model, creates accurate coarse-grained (CG) molecular models using graph neural networks. This novel approach overcomes limitations of traditional methods, enabling customizable resolution for complex systems.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Biophysics

Background:

  • Traditional coarse-grained (CG) modeling faces challenges with diverse chemical structures and fixed mapping rules.
  • Supervised CG methods are limited by small labeled datasets and lack of resolution control for multiscale modeling.

Purpose of the Study:

  • To develop an unsupervised model, MolCluster, for extracting customizable coarse-grained representations.
  • To enable precise control over mapping resolution for diverse molecular systems.

Main Methods:

  • Integration of graph neural networks and community detection for unsupervised CG representation extraction.
  • Implementation of a predefined group pair loss for target group preservation.
  • Utilization of a bisection strategy for customizable resolution control.

Main Results:

  • MolCluster demonstrates superior performance in CG mapping and bead type prediction compared to traditional and supervised models on the MARTINI2 dataset.
  • The label-free pretraining strategy significantly enhances MolCluster's effectiveness.

Conclusions:

  • MolCluster offers a novel, unsupervised approach for chemically consistent and customizable CG mapping.
  • This model shows significant potential for applications in polymers, proteins, and complex multiscale systems.