Grundforskningscenteret “Glas & Tid”, Roskilde Universitet.

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1 Grundforskningscenteret “Glas & Tid”, Roskilde Universitet.
Lidt om “den fjerde tilstandform”, viskøse væsker, og vores forskning i disse Ulf Rørbæk Pedersen Thomas Schrøder, Grundforskningscenteret “Glas & Tid”, Roskilde Universitet. ATU, April 2015

2 Fase-diagram for vand:

3 The Pitch Drop Experiment (http://www.theninthwatch.com/)
- a derivative of tar once used for waterproofing boats

4 Viscocity: Resistance to flow
Pitch (tar) Honey: T=-10°C T= 20°C Water (20°C) [Angell 2002]

5 At high viscocity response functions become frequency dependent.
Dielectric relaxation [K. Niss]: At high viscocity response functions become frequency dependent. Frequency dependent shear modulus: [Christensen & Olsen, 1995] Real part Imaginary part Low frequencies ~ Liquid behavior High frequencies ~ Solid-like behavior

6 Computer-simulering af væsker
1) Beregn alle kræfter 2) Beregn acceleration (F=m*a) 3) Beregn nye hastigheder (dv/dt=a) 4) Beregn nye positioner (dr/dt=v) 5) Gå til punkt 1) “Molecular Dynamics”:

7 Vi simulerer simple systemer, feks: toluene:

8 The need for speed: To test theories and investigate new phenomena, we want to simulate liquids on the millisecond timescale and beyond. 𝑡 1 𝑇,ρ Simulation timescale today (CPU) CUDA...

9 1992: Wolfenstein 2007: Crysis

10 CPU vs. GPU 2007: CUDA (C + extensions) GPU computing

11 The Glass and Time GPU Cluster
85 GPU's (mostly Gtx780 Ti and Gtx Titan) Total theoretical peak perfomance: ~ 390 TFlops Vestas: 180 TFlops

12 eventually crystallizes !
Dynamics becomes slow as the system is cooled Mean Square Displacement: ... but the system eventually crystallizes ! Diffusive NVE Ballistic [Kob & Andersen, PRE, 1994] T=0.400 Long time diffusive behavior: Der sker altid noget uventet I forskning! 〈Δ 𝑟 2 𝑡 〉=6Dt A characteristic time: 〈Δ 𝑟 2 𝑡 1 〉=1

13 Jeres “computer eksperiment”:
Faseopførslen af 864 Lennard-Jones partikler Hvornår sker der en faseovergang og mellem hvilke faser? Strukturen af en væske (rdf): Φ 𝐿𝐽 𝑟 =4ε   σ 𝑟  12 −  σ 𝑟  6  𝑟 𝑐𝑢𝑡 Hver gruppe: En densitet – vi sammenligner resultaterne til sidst

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15 The glass transition and ultra viscous liquids
Relaxation time = 1000s Relaxation time: τ α = η 𝐺 ∞ ∝η Goal of research: Understand the ultra viscous (supercooled) liquid state 1ns [Angell 2002] Viscocity: Resistance to flow

16 Viscositet (sejhed, træghed...)
Viscocitet = konstant * tid det tager boblen at flyde en bestemt afstand

17 Relaxation times in molecular liquids:
τ α = η 𝐺 ∞ ∝η τ= τ 0 𝑒 Δ𝐸 𝑘 𝐵 𝑇 [Hecksher et al., Nature Physics, 2008] Arrhenius behavior: The first non: Non-Arrhenius relaxation times

18 From these building blocks very complex molecules can be simulated:
satellite tobacco mosaic virus, complete with protein, RNA, ions, and a small water box [

19 Simulating viscous liquids: Kob & Andesen Binary LJ liquid
Φ αβ 𝑟 =4 ε αβ   σ αβ 𝑟  12 −  σ αβ 𝑟  6  BB [Kob & Andersen, PRE, 1994] AA σ 𝐴𝐴 =1.00 ε 𝐴𝐴 =1.00 α,β∈ 𝐴,𝐵 σ 𝐵𝐵 =0.88 ε 𝐵𝐵 =0.50 AB σ 𝐴𝐵 =0.80 ε 𝐴𝐵 =1.50 𝑚 𝐴 = 𝑚 𝐵 =1 𝑁=1000, 𝑁 𝐴 =800, 𝑁 𝐵 =200 AA AB BB Radial distribution function

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21 “Leap Frog” integration method
[V. Molinaro] “Leap Frog” integration method

22 From these building blocks very complex molecules can be simulated:
satellite tobacco mosaic virus, complete with protein, RNA, ions, and a small water box Water permeation through membrane water channels [

23 The hardware: CPU vs. GPU

24 The software - Specialized hardware needs specialized software (CUDA).
“Harvesting graphics power for MD simulations”, van Meel et al., Molecular Simulation, (2008): Our program: Optimized for small samples. Speed-up compared to optimized CPU programs: ~ 20