Collective Dynamics & Molecular Operators

← Back to Domain-Specific Families

Abstractions about interacting particles, molecular and Coulomb operators, nonlinear many-body dynamics, reversible propagation, and field-based material models.

6 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Clustering of Self-Propelled Particles — The nonequilibrium formation of finite dynamic clusters or dense active phases when self-propulsion and interaction-dependent retention make motile particles accumulate faster than they escape or fragment.
• Coulomb Operator — The Hartree–Fock one-electron operator that averages the pairwise Coulomb kernel over an occupied-orbital density and multiplies a test orbital by the resulting local repulsive potential.
• Fermi–Pasta–Ulam–Tsingou problem — The nonlinear-lattice problem in which energy placed in a few modes nearly recurs instead of rapidly equipartitioning as naive ergodic expectations predicted.
• Kaplan–Yorke map — A two-dimensional skew-product chaotic map coupling the doubling map x↦2x mod 1 to a driven contraction or expansion y↦αy+cos(4πx), with dynamics controlled by one parameter α.
• Reversible reference system propagation algorithm — Integrate molecular dynamics with a symmetric multiple-time-step factorization that evaluates fast force components frequently and slow components less often while preserving time reversibility.
• Scheutjens–Fleer theory — A lattice self-consistent-field framework for computing equilibrium segment-density profiles of polymers near interfaces under incompressibility and mean-field interaction assumptions.