Magnetic granular matter: A review of phenomena and modeling approaches

Magnetic granular matter extends classical granular physics through the introduction of tunable, long-range dipolar interactions. These interactions give rise to a wide range of collective phenomena, including field-aligned chain formation, enhanced cohesion, anisotropic stress transmission, field and modified flow behaviour. This review summarizes recent experimental, numerical, and theoretical developments in magnetic granular systems, with particular emphasis on the distinction between quasi-static and dynamically driven systems. Existing modeling approaches are discussed, including discrete particle simulations, continuum descriptions, and reduced-order frameworks for capturing the interplay between magnetic interactions and granular dynamics. As an illustrative example, we discuss a minimal lattice-based model motivated by experimentally observed field-induced structural transitions in magnetic granular mounds. The model provides a conceptual framework for exploring how long-range interactions can modify threshold dynamics and instability mechanisms in cohesive granular systems. Finally, we highlight open questions concerning instability thresholds, rheology, avalanche dynamics, multiphysics coupling, and the development of predictive models, and identify promising directions for future experimental and theoretical research.