Stochastic enhancement of absolute negative mobility Lukasz Machura - - PowerPoint PPT Presentation

Stochastic enhancement of absolute negative mobility

Lukasz Machura

Jakub Spiechowicz, Jerzy Luczka Department of Theoretical Physics Univeristy of Silesia, Katowice

Barcelona, 2015

LM (IF U´ S) Noise induced ANM

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Motivation

m¨ x(t) + γ ˙ x(t) + dU(x) dx = F + A cos(Ωt + φ) + ξ(t) v

−0.05 −0.025 0.025 0.05 −0.2 −0.1 0.1 0.2

F

F −

stall

F +

stall

LM, Kostur, Talkner, Luczka, H¨ anggi

• Phys. Rev. Lett. 98, 040601 (2007)

LM (IF U´ S) Noise induced ANM

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Motivation

m¨ x(t) + γ ˙ x(t) + dU(x) dx = F + A cos(Ωt + φ) + ξ(t) v

−0.05 −0.025 0.025 0.05 −0.2 −0.1 0.1 0.2

F

F −

stall

F +

stall

LM, Kostur, Talkner, Luczka, H¨ anggi

• Phys. Rev. Lett. 98, 040601 (2007)

Nagel, Speer, Gaber, Sterck, Eichhorn, Reimann, Ilin, Siegel, Koelle, Kleiner

• Phys. Rev. Lett. 100, 217001 (2008)

LM (IF U´ S) Noise induced ANM

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Main question

Is it possible to enlarge the mean velocity reduce the fluctuations improve the quality of transport ?

LM (IF U´ S) Noise induced ANM

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Main question

Is it possible to enlarge the mean velocity reduce the fluctuations improve the quality of transport ?

• r in general

Is it possible to improve the transport properties?

LM (IF U´ S) Noise induced ANM

• 7. UPON 2015

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Main question

Is it possible to enlarge the mean velocity reduce the fluctuations improve the quality of transport ?

• r in general

Is it possible to improve the transport properties? ”New operating principle: consider replacing the constant force by nonequilibrium noise!”

”Brownian motors in the micro-scale domain: Enhancement of efficiency by noise” → Monday talk by Jakub Spiechowicz

• J. Spiechowicz, P. H¨

anggi and J. Luczka, Phys. Rev. E 90, 032104 (2014) LM (IF U´ S) Noise induced ANM

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Main question

• r in general

Is it possible to improve the transport properties?

• 0.015
• 0.01
• 0.005

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.05 0.1 0.15 0.2 v f λ = 4 λ = 16 λ = 64 λ = 512 deterministic

LM (IF U´ S) Noise induced ANM

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The idea:

deterministic → dichotomic

¨ x(t) + γ ˙ x(t) + dV (x) dx = η(t) + a cos(ωt + φ) + ξ(t) dichotomic noise η(t) = {−d, u}, d, u > 0, probabilities of transition per unit time from one state to another Pr(−d → u) = µd = 1 τd , Pr(u → −d) = µu = 1 τu

start end

t

−d u

η(t)

LM (IF U´ S) Noise induced ANM

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The idea:

deterministic → dichotomic

¨ x(t) + γ ˙ x(t) + dV (x) dx = η(t) + a cos(ωt + φ) + ξ(t) dichotomic noise η(t) = {−d, u}, d, u > 0, probabilities of transition per unit time from one state to another Pr(−d → u) = µd = 1 τd , Pr(u → −d) = µu = 1 τu with one essential condition η(t) = F

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Let’s see...

Comprehensive and fast numerical simulations (for poor) CUDA environment on a modern desktop GPU speed–up of order 3000x

GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA

• J. Spiechowicz, M. Kostur and LM, Comput. Phys. Commun. 191, 140 (2015)

LM (IF U´ S) Noise induced ANM

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simulations

0.0 0.1 0.2 0.3 0.4 0.5

f =

• η(t)
• 0.05

0.00 0.05 0.10 0.15 0.20

v

deterministic d =0.010,µd =0.100,µu =0.010 d =0.010,µd =0.010,µu =1.000 d =0.010,µd =10.000,µu =1.000 d =0.001,µd =10.000,µu =0.001 d =−0.010,µd =0.010,µu =0.010 LM (IF U´ S) Noise induced ANM

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a simple idea, T = 2π/ω ≃ 1.28

¨ x(t) + γ ˙ x(t) + dV (x) dx = u + a cos(ωt + φ) + ξ(t)

u

LM (IF U´ S) Noise induced ANM

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a simple idea, T = 2π/ω ≃ 1.28

¨ x(t) + γ ˙ x(t) + dV (x) dx = −d + a cos(ωt + φ) + ξ(t)

u

• d

LM (IF U´ S) Noise induced ANM

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a simple idea, T = 2π/ω ≃ 1.28

state u = 0.15: average residence time τu = 1 ≃ 0.78T state d = 0.3: average residence time τd = 1/8 ≃ 0.1T η(t) = 0.1

u

• d

start end

t

−0.3 η(t) =−0.1 0.15

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a simple idea

t

−0.30 −0.1 0.15

d =0.3,µd =8.00,u =0.15,µu =1.00

t

−0.30 −0.1 0.15

d =0.3,µd =0.80,u =0.15,µu =0.10

• 0.015
• 0.01
• 0.005

0.005

v d =0.3 µb =8 u =0.15 µu =1 d =0.3 µb =0.8 u =0.15 µu =0.1 d =0.3 µb =0.08 u =0.15 µu =0.01 d =0.3 µb =80 u =0.15 µu =10 d =0.5 µb =12 u =0.15 µu =1 deterministic f =0.1 dichotomic

t

−0.30 −0.1 0.15

d =0.3,µd =0.08,u =0.15,µu =0.01

t

−0.30 −0.1 0.15

d =0.3,µd =80.00,u =0.15,µu =10.00

t

−0.50 −0.1 0.15

d =0.5,µd =12.00,u =0.15,µu =1.00

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Two state noise can also be better than deterministic force

d = 0.85, µd = 8.7, µu = 0.708, a = 8.95, ω = 3.77, γ = 1.546, D = 0.001

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Efficiency

• H. Linke, Appl. Phys. A 75, 167 (2002), Kostur, et. al, Physica A 371, 20, (2006)

Stokes efficiency (against the friction force γv) εS = Pout Pin = γv2 γ(v2 + σ2

v − D)

Efficiency of the energy conversion Pout =?

t

−0.30 −0.1 0.15

d =0.3,µd =0.08,u =0.15,µu =0.01

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Thank you for your attention!

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