Hartmut-Loewen.pdf

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σ ) 3 ρ(z) set-up C DDFT (solid curves) and BD (dashed curves) 12 t 0 (a) 0.5 0.4 10 0.3 0.2 8 t 1 0.1 6 4 t 6 t 5 t 4 t 3 t 2 0 -0.1 -0.2 2 -0.3 -0.4 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -0.5 z/σ σ ) 3 S(z) t 6 t 5 t 4 t 0 t 1 t 2 t 3 (b) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 t0 = 0.0 t1 = 0.02 τ B, t 2 = 0.04 τ B, t3 = 0.06 τ B, t4 = 0.08 τ B, t5 = 0.25 τ B, t6 = 15.0τB z/σ
mm (t) ( 2 7.5 5 2.5 0 -2.5 -5 m 2 (t) 0.2 0.1 0 -0.1 -0.2 0 5 t/τ B 10 -7.5 0 0.5 1 t/τ B 1.5 2 short-dashed: slow compression (set-up A) llong-dashed: d h d slow l expansion i (set-up ( t B) full curve: instantaneous expansion (set-up C)
Page 1 and 2:
3rd Warsaw School of Statictical Ph
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1) Density functional theory of fre
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ii) Hansen-Verlet rule of freezing
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Maxwell-double tangent construction
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1.4) Phase diagrams of simple poten
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) plasma (with neutralizing backgro
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e) Lennard-Jones-system phase p dia
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g) ultrasoft interactions repulsive
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exceptions: i) ) soft potentials p
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contour plot of
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approximations on different levels
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3) Ramakrishnan-Youssuf (RY) 1979 i
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5) Rosenfeld functional (for hard s
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advantages - excludes overlapping h
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2) Brownian Dynamics and dynamical
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Thi This is i valid lid for f ffree
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Smoluchowski equation Diffusion in
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linear relation between and One can
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Langevin-picture Smoluchowski-pictu
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with hydrodynamic interactions(HI.)
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integration yields 2-particle densi
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3) in equilibrium, necessarily
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in equilibrium, DFT says: apply com
Page 48 and 49: colloidal particles colloidal dispe
Page 50 and 51: The road map of complexity H. Löwe
Page 52 and 53: particle p configurations g for dif
Page 54 and 55: DDFT, , equilibrium q functional by
Page 56 and 57: imposed nucleation seed cut-out of
Page 58 and 59: no nucleation 0 φ= 60 Aρ = 0.6
Page 60 and 61: Two stage process: - sub-Brownian t
Page 62 and 63: 2.3) Hydrodynamic interactions How
Page 64 and 65: 2) Rotne-Prager-tensor with 3) high
Page 66 and 67: Rotne-Prager expression ( r ) = 0 v
Page 68 and 69: Application: colloids in an oscilla
Page 70 and 71: stroboscopic view t i /t B = 2.5, 2
Page 72 and 73: 3) Density functional theory for ro
Page 74 and 75: density of center-of-masses: orient
Page 76 and 77: (2) nematic phase positions iti are
Page 78 and 79: three eigenvalues with largest eige
Page 80 and 81: (5) columnar phase: (6) plastic cry
Page 82 and 83: 3.2) Simple models hard objects A)
Page 84 and 85: C) Density functional theory There
Page 86 and 87: 3.3) Brownian dynamics of rod-like
Page 88 and 89: “adiabatic“ approximation: assu
Page 90 and 91: Model Gaussian segment-segment segm
Page 93 and 94: full density orientationally averag
Page 95 and 96: σ 3 ρ(z) 10 8 set-up A DDFT (soli
Page 97: expansion compression transient par
Page 101 and 102: From „passive“ to „active“
Page 103 and 104: L. Baraban, private communication m
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