On soccer balls and linearized inverse statistical mechanics

DOI10.1007/s00332-012-9132-7zbMath1302.82032OpenAlexW2139431382MaRDI QIDQ1935546

James H. von Brecht, David Uminsky

Publication date: 18 February 2013

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-012-9132-7

zbMATH Keywords

inverse problemspattern formationself assembly

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Inverse problems for PDEs (35R30) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) Initial value problems for nonlinear first-order PDEs (35F25) Inverse problems for systems of particles (70F17) Pattern formations in context of PDEs (35B36)

Related Items (27)

Regularity of local minimizers of the interaction energy via obstacle problems ⋮ Swarming on random graphs ⋮ Well-posedness theory for aggregation sheets ⋮ Explicit flock solutions for Quasi-Morse potentials ⋮ Convergence of a linearly transformed particle method for aggregation equations ⋮ Dimensionality of local minimizers of the interaction energy ⋮ The Filippov characteristic flow for the aggregation equation with mildly singular potentials ⋮ Localization and vector spherical harmonics ⋮ Long-time behaviour of interaction models on Riemannian manifolds with bounded curvature ⋮ An anisotropic interaction model for simulating fingerprints ⋮ On global minimizers of repulsive–attractive power-law interaction energies ⋮ Anisotropic assembly and pattern formation ⋮ Small inertia regularization of an anisotropic aggregation model ⋮ Pattern formation of a nonlocal, anisotropic interaction model ⋮ Nonlocal interactions by repulsive-attractive potentials: radial ins/stability ⋮ Singular patterns for an aggregation model with a confining potential ⋮ A second-order numerical method for the aggregation equations ⋮ Confinement for repulsive-attractive kernels ⋮ Two-species particle aggregation and stability of co-dimension one solutions ⋮ First-order aggregation models and zero inertia limits ⋮ Nonlinear stability of flock solutions in second-order swarming models ⋮ Stability Analysis of Line Patterns of an Anisotropic Interaction Model ⋮ Metastable States for an Aggregation Model with Noise ⋮ From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials ⋮ Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds ⋮ Stability and clustering of self-similar solutions of aggregation equations ⋮ Existence of compactly supported global minimisers for the interaction energy

Cites Work

• Do travelling band solutions describe cohesive swarms? An investigation for migratory locusts
• A note on optimal unimodular lattices
• PREDICTING PATTERN FORMATION IN PARTICLE INTERACTIONS
• A Primer of Swarm Equilibria
• Lp theory for the multidimensional aggregation equation
• Point vortex equilibria and optimal packings of circles on a sphere
• Swarm dynamics and equilibria for a nonlocal aggregation model
• Universally optimal distribution of points on spheres
• The N -vortex problem on a rotating sphere. II. Heterogeneous Platonic solid equilibria
• Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
• Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
• Asymptotic Dynamics of Attractive-Repulsive Swarms
• Local and Global Existence for an Aggregation Equation
• The N -vortex problem on a rotating sphere. III. Ring configurations coupled to a background field

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