r s sts t ss - - PowerPoint PPT Presentation
r s sts t ss s t stt tt rrts r tt
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✶ ✴ ✸✺
◮ ❙❤❡❛r✲t❤✐♥♥✐♥❣ ❛♥❞ s❤❡❛r✲t❤✐❝❦❡♥✐♥❣ ✭r❤❡♦❧♦❣②✮ ◮ ◆❡❣❛t✐✈❡ r❡s✐st❛♥❝❡ ✭✐♦♥ ❝❤❛♥♥❡❧s✱ ❤♦♠❡♦st❛t✐❝ ❜❛❧❛♥❝❡✳✳✳✮ ◮ ▼❛❝r♦♠♦❧❡❝✉❧❛r ❝r♦✇❞✐♥❣✿ ❛♥♦♠❛❧♦✉s ❞✐✛✉s✐♦♥
◮ ❆♣♣r♦❛❝❤✐♥❣ t❤❡ ❧❛r❣❡✲❞❡✈✐❛t✐♦♥ r❡❣✐♠❡ ◮ ❚✐♠❡✲r❡✈❡rs❛❧ s②♠♠❡tr② ♦❢ ❝✉rr❡♥t ✢✉❝t✉❛t✐♦♥s ◮ ❊✛❡❝t✐✈❡ ✢✉❝t✉❛t✐♥❣ ❤②❞r♦❞②♥❛♠✐❝s ❞❡s❝r✐♣t✐♦♥
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✷ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✸ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✹ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✻ ✴ ✸✺
✷
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✼ ✴ ✸✺
0.02 0.04 0.06 0.08 0.1 0.1 0.2 0.3 0.4 0.5 0.6
J(ρ+, ρ-) ρ+ - ρ-
❈✉rr❡♥t ♠❛①✐♠✉♠ ❛♥❞ ❝♦rr❡s♣♦♥❞✐♥❣ ❞r✐✈✐♥❣ ❢♦r❝❡ ❝❛♥ ❜❡ ❝♦♠♣✉t❡❞ ❜② ▲❛❣r❛♥❣❡ ♠✉❧t✐♣❧✐❡rs ♠❡t❤♦❞✿ ❏♠❛① = ρ✶+φ
❝
✶ + φ (✶ − δ)✶+φ
✶ ✶+φ
φ , (ρ+ − ρ−)♠❛① = ρ❝(✶ − δ) ✶ − δ
✶ φ
✶ − δ
✶+φ φ
. ▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✽ ✴ ✸✺
0.2 0.4 0.6 0.8 1 1 2 3 4 5
0.1 0.2 0.3 0.01 0.1 1 10 100
Jav α
❆s②♠♠❡tr② ♣❛r❛♠❡t❡r α = τ/τ✵ − ✶
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✾ ✴ ✸✺
t✇
t→∞ ❧✐♠ t✇→∞ ❇(t + t✇, t✇) =
t✇→∞ ❧✐♠ t→∞ ❇(t + t✇, t✇)
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✶✵ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✶✷ ✴ ✸✺
❞❡♥s✐t② ♣r♦✜❧❡ ❧♦❝❛❧ ❞❡♥s✐t② ✢✉❝t✉❛t✐♦♥s
0.54 0.61 0.68 0.75 0.82
0.2 0.6 1
<> z /L
L = 50
0.15 0.2 0.25
0.2 0.6 1
(<
2> - <> 2) L 2
z /L
L = 50
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✶✸ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✶✹ ✴ ✸✺
0.1 0.2 2 4 6 8
(a)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11 2 3 4 5 0.2 0.4 0.6 0.8 1
(b)
1 - e-E = 0.1 = 0.2 = 0.3 = 0.4 = 0.5 = 0.6 = 0.7
❋♦r st❛♥❞❛r❞ ❆❙❊P ❏(ρ, ❊) = ρ(✶ − ρ)(✶ − ❡−❊ )/✹. ▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✶✺ ✴ ✸✺
2 4 6 0.25 0.5 0.75 1
TASEP TACEP
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✶✻ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✶✼ ✴ ✸✺
1 2 3 4 2 4 6 8 10
J x 10-3 E
L = 400
ρ = 0.79 ρ = 0.80 ρ = 0.81 ρ = 0.82
2 4 6 8 10 2 4 6 8 10
J x 10-4 E
L = 400
ρ = 0.83 ρ = 0.84 ρ = 0.85 ρ = 0.86
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✶✽ ✴ ✸✺
2 3 4 5 6 1 2 3 4 5 6
log10 τrel
ρ = 0.86 ρ = 0.84 ρ = 0.82 ρ = 0.80 ρ = 0.78
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✶✾ ✴ ✸✺
❞❡♥s✐t② ♦❢ ❜❧♦❝❦❡❞ ♣❛rt✐❝❧❡s ❞❡♥s✐t② ♦❢ ❛❝❝❡ss✐❜❧❡ ❤♦❧❡s
0.7 0.74 0.78 0.82 1 2 3 4 5 6
ρblocked E
ρ = 0.80 ρ = 0.81 ρ = 0.83 0.01 0.03 0.05 0.07 0.09 1 2 3 4 5 6
ρholes E
ρ = 0.80 ρ = 0.81 ρ = 0.83
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✷✵ ✴ ✸✺
▲♦♥❣✐t✉❞✐♥❛❧ ♣❛✐r ❝♦rr❡❧❛t✐♦♥
0.02 1 2 3 4 5 6 7 8
gL r
ρ = 0.86 E = 0.4 E = 0.8 E = 1.2 E = 1.6 E = 2.0
❚r❛♥s✈❡rs❡ ♣❛✐r ❝♦rr❡❧❛t✐♦♥
0.01 0.02 0.03 0.04 1 2 3 4 5 6 7 8 9 10
gT r
ρ = 0.86 E = 0.4 E = 0.8 E = 1.2 E = 1.6 E = 2.0
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✷✶ ✴ ✸✺
1 2 1 2 3 4 5 rescaled current
= 0.70 = 0.81
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✷✷ ✴ ✸✺
0.02 0.04 0.06 0.08 0.1 0.12
1 2 3 4 5 6 7
∆r❘ ❘
2 /t
log10 t
ρ = 0.8, L = 400 E = 0.1 E = 0.3 E = 0.6 E = 1.2 E = 2.8
0.02 0.04 0.06 0.08 0.1
1 2 3 4 5 6 7
∆r❘ ❘
2 /t
log10 t
ρ = 0.8, E = 2.8 L = 50 100 200 400
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✷✸ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✷✺ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✷✻ ✴ ✸✺
2 4 6 8 log10 (στ Πτ)
(Jτ-J)/στ E = 0.1, ρ = 0.4
τ = 1 τ = 2 τ = 4 τ = 8 1 2 3 4 1 2 3 4 log[Πτ(Jτ)/Πτ(-Jτ)]
E Jτ E = 0.1, ρ = 0.4
τ = 1
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✷✼ ✴ ✸✺
2 4 6 8 log10 (στ Πτ)
(Jτ-J)/στ E = 0.1, ρ = 0.8 L = 25 τ = 8
16 32 64
20 25 30 35 40 45 1 10 100 1000 10000
στ
2/J
τ E = 0.1, ρ = 0.8 L = 10 L = 15 L = 25 L = 40 ▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✷✽ ✴ ✸✺
0.4 0.8 1.2 1.6 2 0.4 0.8 1.2 1.6 2 log[Πτ(Jτ)/Πτ(-Jτ)]
E Jτ E = 0.1, ρ = 0.8, L = 25 τ = 2 τ = 8 τ = 32 τ = 128 τ = 512
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✷✾ ✴ ✸✺
2 4 6 8 10 log10 (στ Πτ)
(Jτ-J)/στ E = 2.8, ρ = 0.8 L = 45, τ = 1
0.2 0.4 0.6 0.8 1 1 10 100 1000 10000
τ E = 2.8, ρ = 0.8, L = 45
στ
2/J
skewness kurtosis
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✸✵ ✴ ✸✺
5 10 15 20 25 5 10 15 20 25 log[Πτ(Jτ)/Πτ(-Jτ)]
E Jτ E = 2.8, ρ = 0.8
τ = 1 τ = 4 τ = 8 τ = 16
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✸✶ ✴ ✸✺
❚✉r❝✐ P✐t❛r❞✱ ❊P▲ ✭✷✵✶✶✮
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✸✷ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✸✸ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✸✹ ✴ ✸✺
▼❛✉r♦ ❙❡❧❧✐tt♦ ✭❙✳❯✳◆✳✮ ❉r✐✈❡♥ ❉✐✛✉s✐✈❡ ●❧❛ss② ❙②st❡♠s ❋❧♦r❡♥❝❡✱ ❏✉♥❡ ✷✵✶✹ ✸✺ ✴ ✸✺