Hartmut-Loewen.pdf

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“adiabatic“ approximation: assume the pair correlations in nonequilibrium are the same as those for an equilibrium system with v the same one-body density profile (established by a suitable V ˆ ext (r, ω,t)) v ∂ρ( r, ˆ ω, t) v t v ⎡ v v δF = ∇ v • D( ˆ) • ⎢ ( r, ˆ r ω ρ ω, t) ∇ v r ∂ t ⎢ ⎣ δδρ ( r, ˆ ω, t ) v ⎡ [ ] ⎤ + ˆ v ˆ δF ρ( r, ˆ ω, t) D ⎢ ( , ˆ r rR⎢ ρρ ( r, ω , t ) R v ⎥⎦ ⎣ δ ( ˆ ) ⎥ ⎣ δρ( r, ˆ ω, t) ⎦ [ ρ( r, ˆ ω, t) ] ⎤ v ⎥⎦ ⎥ ⎦ DDFT with the equilibrium Helmholtz free energy density functional v v 3 v v [ ( ) ] [ ] d r d ˆ ωρ( r, ˆ ω) V ( r, ˆ ω, t) 3 3 [ ρ] = k T d r d ˆ ( r, ˆ ) ln ( r, ˆ B ∫ ∫ ωρ ω Λ ρ ω) − 1 + Fext ρ + ∫ F ext (M. Rex, H.H. Wensink, H.L., PRE 76, 021403 (2007)) ∫
approximation for the density functional mean mean-field field F exc 1 v v v = ω ) 2 3 3 [ ρ] ∫ d r ∫ d r′ ∫ d ˆ ω ∫ dω′ ρ( r, ˆ ω′ ) v ( , ′ , ˆ, ˆ′ 2 r r ω (caveat: ( brings g ideal rotational dynamics) y ) time t e independent depe de t
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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
Page 37 and 38: Langevin-picture Smoluchowski-pictu
Page 39 and 40: with hydrodynamic interactions(HI.)
Page 41 and 42: integration yields 2-particle densi
Page 44 and 45: 3) in equilibrium, necessarily
Page 46 and 47: 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 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 and 98: expansion compression transient par
Page 99 and 100: mm (t) ( 2 7.5 5 2.5 0 -2.5 -5 m 2
Page 101 and 102: From „passive“ to „active“
Page 103 and 104: L. Baraban, private communication m
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