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

Fase-diagram for vand:

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

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

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

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”:

Vi simulerer simple systemer, feks: toluene:

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...

1992: Wolfenstein 2007: Crysis

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

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

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

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

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

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

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

From these building blocks very complex molecules can be simulated: satellite tobacco mosaic virus, complete with protein, RNA, ions, and a small water box [http://www.ks.uiuc.edu/Gallery/]

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

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

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 [http://www.ks.uiuc.edu/Gallery/]

The hardware: CPU vs. GPU

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