Physics of mesoscopic condensed matter where thermal energy k_BT competes with elastic and interaction energies: colloids, polymers, liquid crystals, granular media, active matter. The regime where statistical mechanics, continuum…
soft-matter
Colloid physics
Dispersions of mesoscopic particles (1 nm–1 μm) in a fluid, where Brownian motion keeps them suspended and pairwise DLVO (van der Waals +…
Liquid crystal
Phases with orientational order but partial or no positional order: nematic (directional only), smectic (layered), cholesteric (helical).…
Polymer physics
Long chains treated as random walks in dilute solution (ideal R ~ N^{1/2}, self-avoiding R ~ N^{3/5} Flory). Gaussian chains give rubber…
Granular physics
Assemblies of macroscopic athermal particles (sand, grains, powders) that are dissipative and out of thermal equilibrium. Exhibit jamming…
Jamming transition
Sharp rigidity transition at packing fraction φ_J ≈ 0.64 (random close packing) for frictionless spheres: below, system is fluid-like;…
Brownian motion (mesoscale)
Stochastic motion of suspended particles driven by solvent kicks. Langevin equation m ẍ = -γẋ + ξ(t) with ⟨ξ(t)ξ(t')⟩ = 2γk_BTδ(t–t')…
Active matter
Systems of self-propelled agents consuming energy locally (bacteria, motor proteins, birds, self-phoretic colloids). Break detailed…
Rheology of complex fluids
Stress–strain response of non-Newtonian fluids: shear-thinning/thickening, viscoelasticity (Maxwell model η(ω) = G∞τ/(1+iωτ)), yield stress…
Self-assembly
Spontaneous organisation of building blocks into ordered structures driven by weak, reversible interactions (hydrogen bonds, depletion, DNA…
Critical Casimir forces
Long-range effective interactions between surfaces immersed in a near-critical binary solvent, caused by confined thermal fluctuations.…
Ericksen–Leslie equations for nematic liquid crystals (soft-matter)
Soft-matter application of L0 partial-differential-equation theory and variation-of-parameters. Liquid-crystal nematics are described by a…
Cahn–Hilliard spinodal decomposition and instability threshold (soft-matter)
Soft-matter application of L0 reaction-diffusion equation theory and initial-value-problem theory. The Cahn–Hilliard equation ∂_t φ =…