Active Matter: Run-and-Tumble in Confinement

Self-propelled particles perform run-and-tumble motion (like E. coli) — accumulate at walls, form motility-induced phases, and probe active pressure.

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Run-and-tumble: straight runs at v₀ interrupted by Poisson tumbles (rate λ). Run length ℓ = v₀/λ.

Wall accumulation: active particles pile up at boundaries — purely kinematic, no equilibrium analogue. Wall density ∝ v₀/λ.

Active pressure: P_active = ρv₀²τ/(d) where τ=1/λ. Exceeds thermal pressure for strong swimmers.
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