Physically Inspired Particle Framework for Recalescence-Induced Self-Jumping Ice Dynamics

Technical Summary: Physically Inspired Particle Framework for Recalescence-Induced Self-Jumping Ice Dynamics

Problem Statement
While computer graphics has extensively modeled the geometric growth and static appearance of ice (e.g., icicles, speleothems, and surface opacity), existing methods largely fail to capture the transient, nonequilibrium dynamics occurring during the early stages of freezing. Specifically, the phenomenon of recalescence-induced self-jumping—where a supercooled droplet spontaneously detaches and jumps due to rapid latent-heat release and asymmetric vaporization—remains unaddressed in lightweight simulation frameworks. Fully resolving this behavior requires expensive multiphase thermo-fluid solvers that couple heat transfer, phase change, vapor flow, and rigid-body dynamics, which are computationally prohibitive for real-time graphics applications. There is a lack of a reduced-order, controllable model that captures the essential impulse-generation mechanism without solving full fluid equations.

Methodology
The author proposes a reduced-order, particle-based physical model that simulates self-jumping by approximating the dominant momentum-generation mechanism: asymmetric vaporization flux near the recalescence front. The framework operates through a four-stage pipeline:

1. Automatic Nucleation: The system simulates surface cooling using a Schrage-based evaporative cooling model with a directional bias (stronger cooling on upward-facing surfaces). Nucleation is triggered automatically when a surface particle's temperature drops below a critical supercooling threshold ($T_{nuc} = T_m - \Delta T_{nuc}$). The location of this first crossing defines the nucleation seed.
2. Recalescence-Front Propagation: Upon nucleation, a freezing front propagates bidirectionally from the seed along the surface. The model employs a "Mushy band" thermal clamp to stabilize temperatures near the melting point ($T_m$) and gradually reduces the liquid fraction ($\alpha$) to simulate the phase transition from liquid to solid.
3. Arc-Limited Directional Impulse Accumulation: To capture the jump, the model calculates the evaporation flux difference between the ice/mushy surface ($J_i$) and the liquid surface ($J_w$). Crucially, instead of integrating over the entire surface (which would cancel out horizontal components), the framework restricts impulse accumulation to a narrow arc-limited region (or geodesic band in 3D) around the front tip. This selective integration preserves the asymmetric momentum imbalance, generating a net linear impulse ($J_{acc}$) and angular impulse ($\tau_{acc}$).
4. Rigid-Body Detachment: Once the accumulated impulse exceeds a threshold, the frozen droplet transitions to rigid-body motion. The accumulated impulse is converted into a jump force ($F_{jump}$) and torque ($\tau_{jump}$), propelling the object in a direction opposite to the nucleation seed while preserving its original shape.

Generalization to Arbitrary Geometries
The framework extends from a 2D circular base model to arbitrary 2D image masks and 3D triangular meshes.

• 2D Masks: The circular angular coordinate is replaced by a boundary arc-length parameterization derived from a surface graph.
• 3D Meshes: The front propagation is parameterized using geodesic distances on the mesh surface. The impulse accumulation region becomes a geodesic band around the front tip. This allows the model to handle complex topologies (e.g., dragons, bunnies, teapots) while maintaining the same front-based logic.

Key Contributions

1. Front-Aware Phase-Transition Model: A unified structure that couples automatic nucleation, bidirectional front propagation, and Mushy-band thermal stabilization, enabling the simulation of the recalescence stage without full thermo-fluid coupling.
2. Arc-Limited Impulse Integration: A novel scheme that accumulates directional impulse only within a narrow region near the front tip. This effectively suppresses horizontal cancellation and reproduces the experimentally observed jump direction (opposite to the nucleation site).
3. Shape-Independent Extensibility: The successful generalization of the 2D particle formulation to arbitrary 3D triangular meshes via geodesic parameterization, demonstrating that self-jumping dynamics are independent of surface topology or curvature.
4. Computational Efficiency: A lightweight implementation (PyCUDA-based) that achieves near-real-time performance (approx. 1.16 ms/frame for 2D, 3.08 ms/frame for 3D) by avoiding full multiphysics solvers.

Experimental Results
The author validated the framework through:

• 2D Simulations: Demonstrating that the model reproduces asymmetric freezing patterns where the upper surface cools faster and nucleates first. Results showed that jump direction is consistently opposite to the seed, and the magnitude varies based on shape symmetry (e.g., asymmetric spirals produce stronger jumps than symmetric hearts).
• Sampling Robustness: The method remained stable under both grid sampling and Poisson-disk sampling, with only minor variations in impulse magnitude due to local density irregularities.
• 3D Mesh Applications: Applied to complex models (Dino, Bunny, Dragon, Teapot, etc.), the system produced geometry-dependent jump vectors that aligned with the local curvature and front propagation paths.
• User Control: The framework supports both automatic nucleation and user-defined seed positions, allowing artists to control the freezing and jumping direction interactively.

Significance and Claims
The paper claims to bridge the gap between fluid-mechanics research on recalescence and computer graphics simulation. Its primary significance lies in providing a computationally tractable, reduced-order representation of recalescence-driven impulse generation. The author asserts that their framework:

• Captures the essential physics of self-jumping (thermal asymmetry $\to$ vaporization recoil $\to$ detachment) without the cost of full thermo-fluid solvers.
• Offers a shape-independent and controllable tool for visual effects, games, and scientific visualization, enabling the generation of plausible phase-change dynamics.
• Serves as a "recalescence-stage impulse module" that can be integrated into broader freezing animation pipelines, rather than replacing them.

The author explicitly notes limitations, acknowledging that the model is a phenomenological approximation. It does not quantitatively predict exact temperature or velocity fields, relies on empirically tuned parameters (e.g., impulse gain, arc width), and does not resolve 3D volumetric phase changes, gas interactions, or impurity transport. However, they argue that for the purpose of visually plausible, real-time graphics simulation, the proposed framework successfully reproduces the dominant mechanism of recalescence-induced self-jumping.