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Ampere-Maxwell's Law: Problem-Solving

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
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Accelerating self-consistent field theoretic simulations for disordered systems with deep learning.

Dongqi Zhao¹, Qingquan Bao², Robert A Riggleman¹

¹Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.

The Journal of Chemical Physics

|October 30, 2025

Summary

This summary is machine-generated.

A new machine learning approach speeds up polymer self-assembly predictions using self-consistent field theory (SCFT). This method bypasses computationally intensive steps, offering significant efficiency gains for polymer science simulations.

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Area of Science:

Polymer science and computational materials science.
Application of machine learning in theoretical physics.

Background:

Polymer thermodynamics and self-assembly are crucial for advanced materials and drug delivery.
Self-consistent field theory (SCFT) is a powerful tool for predicting polymer behavior.
Standard SCFT methods face computational challenges with complex systems like anisotropic and worm-like chains.

Purpose of the Study:

To develop a computationally efficient machine learning approach for SCFT simulations.
To predict polymer density fields directly from potential fields, bypassing computationally expensive propagator calculations.
To enhance the speed and scalability of large-scale SCFT simulations.

Main Methods:

Integration of various neural network models into the SCFT framework.
Direct prediction of density fields from potential fields using machine learning.
Comparative analysis of different neural network architectures for performance evaluation.
Focus on Gaussian chain models forming disordered, microphase-separated structures.

Main Results:

A robust and computationally efficient machine learning model for SCFT was developed.
The model achieves speedups of over 3x for similar system sizes and up to 100x for larger systems.
Demonstrated the feasibility of using deep learning to accelerate SCFT simulations.
The developed methods show potential for extension to more complex and computationally demanding models.

Conclusions:

Machine learning offers a viable strategy to significantly improve the efficiency of SCFT simulations.
The developed approach alleviates computational bottlenecks in predicting polymer thermodynamics and self-assembly.
This work paves the way for more extensive and complex simulations in polymer science.