On our theory of self-organisation
Move them to jostle and shear them to slide
Granules constantly rub and collide
Cells split and diffuse
Theorists to bemuse
But now we can see how they self-organise
RB, April 2019
Research
The deeper concern running through all this work is how disordered many-body systems organise structure, transmit stress, evolve under driving, and admit reduced descriptions that are both physically honest and mathematically useful.
Granular matter is the main laboratory, but not the only one. The questions reach into soft condensed matter, cellular structures, porous materials, biological systems, and any setting where disorder, force mediation, and multiscale description matter.
The research spans four decades and includes both tightly focused theoretical programmes and broader excursions into fracture, polymers, complex fluids, and nonlinear media. The older programmes remain part of the intellectual map even when they are not currently the main focus.
Current research themes
Core programme
Stress transmission & force chains
A first-principles approach to stress transmission in granular solids, treating force chains as structural consequences of the governing stress equations. Central ideas include isostatic stress states, marginal rigidity, coarse-graining from grain scale to continuum, and the two-phase composite picture of real granular materials.
- Force chains as structural predictions, not just visual motifs
- Isostaticity theory from single grains to continuum
- Two-phase composite model for realistic granular solids
2024 Granular solids transmit stress as two-phase composites Reframes granular solids as two-phase composites for stress transmission, continuing Blumenfeld's long-running programme on constitutive description beyond conventional elastic assumptions.
2020 The unusual problem of upscaling isostaticity theory for granular matter Addresses the long-standing difficulty of carrying isostaticity theory from particle-scale structure to macroscopic description without losing the geometry-dependent constitutive content.
Statistical mechanics
Entropy, detailed balance & athermal ensembles
Can driven granular systems be described with something as principled as statistical mechanics? This programme investigates Edwards-style volume-stress ensembles, entropy, detailed balance in quasi-static steady states, and the distinction between typicality and mere possibility.
- Coupled volume and stress ensembles
- Detailed balance in quasi-static granular steady states
- Stability and lifespan as selectors of typical states
2012 Inter-dependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems Shows that the volume and stress ensembles in granular statistical mechanics are not independent and derives an equipartition result for granular systems from that coupled structure.
2020 Friction-controlled entropy-stability competition in granular systems Examines how friction mediates the competition between entropy and stability in granular systems, with implications for state selection and configurational statistics.
2025 Self-organisation - the underlying principle and a general model Proposes a general model for self-organisation, framing it as a unifying principle rather than a topic tied to a single material system.
Flow & response
Dense granular flow & penetration
The "da Vinci fluid" model pushes a friction-dominated view of dense granular flow, where plug formation and catch-up dynamics emerge from the governing equations rather than being bolted on. Related work shows how a modified Archimedes law can survive inside granular media.
- Dense flow via solid friction, not viscous closure
- Plug regions as generically emerging structures
- Penetration as a bridge between discrete and continuum physics
2010 Da Vinci Fluids, catch-up dynamics and dense granular flow Introduces a continuum picture in which dissipation is dominated by solid friction, producing plug formation and catch-up dynamics characteristic of dense granular flow.
2019 Archimedes' law explains penetration of solids into granular media Shows that a modified Archimedes-style framework can account for how solids penetrate granular media, linking granular response to a familiar continuum principle in a nontrivial way.
2026 Gravity-dependent rate sensitivity in granular intrusion: microgravity experiments and simulations Examines how granular intrusion depends on gravity level and rate by combining microgravity experiments with simulations, extending Blumenfeld's granular-matter work into space-related impact and mobility problems.
Cross-disciplinary
Cellular, auxetic & biological systems
The same structural-statistical ideas extend to cellular systems, auxetic materials, porous structures, and biological problems where force mediation or structural transitions matter — including bacterial phase transitions and cell surface fluctuations.
- Cellular and foam-like structural analogues
- Auxetic and non-affine constitutive behaviour
- Biophysical applications in living matter
2014 On universal structural characteristics of granular packs Argues for structural regularities that persist across granular packings, identifying universal features that survive changes in preparation and frictional details.
2022 Phase transitions in bacteria - From structural transitions in free living bacteria to phenotypic transitions in bacteria within biofilms A review-oriented paper extending statistical-physics ideas into living matter, from structural transitions in free bacteria to phenotypic transitions inside biofilms.
Through-line
Self-organisation as a unifying principle
The most promising unifying idea across the recent work is that self-organisation can be framed in terms of stability, disorder, and the selective survival of configurations — connecting the older granular-statistical programme to broader claims about driven systems.
- Granular media as the concrete proving ground
- The target is a wider framework for self-organising systems
- The intellectual spine connecting four decades of work
Earlier programmes
Earlier work
Fracture, growth & morphology
Slow and fast cracking, Laplacian growth, fractal morphology, and the relation between dynamics and roughness. Substantial earlier programmes preserved in the archive.
Earlier work
Polymers, complex fluids & mesoscale modelling
Polymer chain pullout, complex fluids near the glass transition, porous-media transport, and multiscale coarse-graining methods.
Earlier work
Magnetic systems & nonlinear media
Work on spin systems, nonlinear materials, and geometric curve dynamics showing the mathematical breadth behind the later granular emphasis.