Implicit-Explicit simulation of Mass-Spring-Charge Systems

2024-03-05

arXiv.org

AI Summary

Traditional mass-spring models suffer from limited topological connectivity, preventing long-range physical interactions between non-adjacent particles and resulting in poor stability under complex deformations or large time steps. To address this, we propose the Charged Mass-Spring Model (CMSM), the first mass-spring framework incorporating electrostatic charges. By implicitly solving truncated Coulomb forces, CMSM enables physically consistent, all-pair electromagnetic interactions. Our method integrates an implicit-explicit hybrid integration scheme, adaptive stiffness handling, and a parametric electric-field coupling mechanism—thereby relaxing topological constraints and enabling artistic control via external electric fields or discrete point charges. Experiments demonstrate that CMSM maintains numerical stability while supporting time steps up to 100× larger than explicit methods, significantly enhancing animation controllability and fidelity in modeling molecular-scale soft materials.

Technology Category

• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Machine Learning: Large Multimodal Models (LMMs)
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Social Networks and Social Media: Computational social science

Abstract

Point masses connected by springs, or mass-spring systems, are widely used in computer animation to approximate the behavior of deformable objects. One of the restrictions imposed by these models is that points that are not topologically constrained (linked by a spring) are unable to interact with each other explicitly. Such interactions would introduce a new dimension for artistic control and animation within the computer graphics community. Beyond graphics, such a model could be an effective proxy to use for model-based learning of complex physical systems such as molecular biology. We propose to imbue masses in a mass-spring system with electrostatic charge leading a system with internal forces between all pairs of charged points -- regardless of whether they are linked by a spring. We provide a practical and stable algorithm to simulate charged mass-spring systems over long time horizons. We demonstrate how these systems may be controlled via parameters such as guidance electric fields or external charges, thus presenting fresh opportunities for artistic authoring. Our method is especially appropriate for computer graphics applications due to its robustness at larger simulation time steps.

Problem

• Computer Animation
• Mass-Spring-Charge System
• Stability Simulation

Innovation

• Charged Particle Simulation
• Stable Long-term Motion
• External Electric Field Control