supporting icf by quantum and orbital-free...

Supporting ICF by quantum andorbital-free molecular dynamics

by F. Lambert

from CEA DAM DIF

at Computational challenges in warm dense matter, May 25th

Quantum Physics makes me so happy.It’s like looking at the Universe naked.

S. Cooper

Contents

Inertial confinementfusion

Quantum andorbital-free methods

Adiabatic approximation & molecular dynamicsQuantum and semi-classical treatment

Numerical features:the geek section

The OFMD codeThe regularization procedureThe parallelization paradigm

Microscopic physicsand ICF

Hydrogen thermal conductivity: let’s burn!EOS building: mixing rulesRayleigh-Taylor instability: physics of the ablator

Challenges

Inertial confinement fusion

• Compression of a Deuterium/Tritium layer to reach nuclear fusion;


• Compression of a Deuterium/Tritium layer to reach nuclear fusion;• laser heating of a gold cavity (indirect drive);

• X-ray (black body) radiation (like an oven at 3.5 MK);• rocket effect: explosion/implosion of an outer plastic layer (generation of

moderate shocks);• quasi-isentropic compression of the DT layer (shocks and final implosion);• ignition: 100 low-fat-yogurt energy and 20 billions nuclear-power-plant power;

..

gaseous fuel

.

solid fuel

.

ablator

.

abla

tion

.

compression


• Compression of a Deuterium/Tritium layer to reach nuclear fusion;• laser heating of a gold cavity (indirect drive);• X-ray (black body) radiation (like an oven at 3.5 MK);

• rocket effect: explosion/implosion of an outer plastic layer (generation ofmoderate shocks);

• quasi-isentropic compression of the DT layer (shocks and final implosion);• ignition: 100 low-fat-yogurt energy and 20 billions nuclear-power-plant power;

..

gaseous fuel

.

solid fuel

.

ablator

.

abla

tion

.

compression


• Compression of a Deuterium/Tritium layer to reach nuclear fusion;• laser heating of a gold cavity (indirect drive);• X-ray (black body) radiation (like an oven at 3.5 MK);• rocket effect: explosion/implosion of an outer plastic layer (generation of

moderate shocks);

• quasi-isentropic compression of the DT layer (shocks and final implosion);• ignition: 100 low-fat-yogurt energy and 20 billions nuclear-power-plant power;

..

gaseous fuel

.

solid fuel

.

ablator

.

abla

tion

.

compression



moderate shocks);• quasi-isentropic compression of the DT layer (shocks and final implosion);

• ignition: 100 low-fat-yogurt energy and 20 billions nuclear-power-plant power;

..

gaseous fuel

.

solid fuel

.

ablator

.

abla

tion

.

compression



moderate shocks);• quasi-isentropic compression of the DT layer (shocks and final implosion);• ignition: 100 low-fat-yogurt energy and 20 billions nuclear-power-plant power;

..

gaseous fuel

.

solid fuel

.

ablator

.

abla

tion

.

compression



• What about the underlying physics?• hydrodynamics of radiating flows, e.g. equation of energy conservation;• large thermodynamic domain: kT ∈ [0 : 10 keV], ρ ∈

[10−3 : 103 g cm−3];

• What must be provided by electronic structure calculations?

• complex microscopic physics: low temperature solids or amorphous, partiallyelectronic delocalization, strong correlations of electrons and nuclei, role ofthe radiation, etc;

ρ∂

∂t

(e +

1

ρσT4

)+

(p +

1

3σT4

)∇ · u = ∇ ·

(κ∇T +

λRc3σT4

)

..Radiative hydrodynamics (1 cm, 20 ns)

.target design: 300 simulations, from 30 min to 15 days



• What about the underlying physics?• hydrodynamics of radiating flows, e.g. equation of energy conservation;• large thermodynamic domain: kT ∈ [0 : 10 keV], ρ ∈

[10−3 : 103 g cm−3];

• What must be provided by electronic structure calculations?• complex microscopic physics: low temperature solids or amorphous, partially

electronic delocalization, strong correlations of electrons and nuclei, role ofthe radiation, etc;

ρ∂

∂t

(e +

1

ρσT4

)+

(p +

1

3σT4

)∇ · u = ∇ ·

(κ∇T +

λRc3σT4

)

..Radiative hydrodynamics (1 cm, 20 ns)

.target design: 300 simulations, from 30 min to 15 days.

fast approximate models

.

routine call: 1 ms

.

Microscopic physics (10 nm, 1 ps)

.

thermodynamic equilibrium simulation: a few hours

What does it mean in terms of simulations?

• Several methods developed for solid, liquid or plasma physics:• one-center (average-atom like): quantum, computationally inexpensive;• multicenter:• quantum Monte-Carlo: electronic many-body;• molecular-dynamics based on either classical, quantum or semi-classical

description.

• Material constraints in the high-energy-density regime:• low and high Z elements;• single or multi-specie;• low atomic fractions;• very different thermodynamic conditions;

Contents








Challenges

Outline








Challenges

Adiabatic approximation & molecular dynamics

• Adiabatic approximation:• instantaneous response of electronic fluid;• T-dependent electronic screening of nuclear coulomb interactions;

• Nuclei described as classical particles;

L(R , P

)=

1

2

∑ℓ

P2ℓ

Mℓ−

∑ℓ =ℓ′

ZℓZℓ′∣∣Rℓ − Rℓ′∣∣ − Fe[R

]

• Euler-Lagrange equations in the DFT framework;

minn(r)

Fe[n(r), R ]

and dPℓ

dt=

∑ℓ′ =ℓ

ZℓZℓ′Rℓ − Rℓ′∣∣Rℓ − Rℓ′

∣∣3 −∇RℓFe[R

]

• Basic idea of molecular dynamics:

R(t) −→Coulomb potential V(R(t) ) −→

Free energy minimization Fe[n(r)] −→Newton’s equations R(t +∆t)




L(R , P

)=

1

2

∑ℓ

P2ℓ

Mℓ−

∑ℓ =ℓ′


]


minn(r)

Fe[n(r), R ]

and dPℓ

dt=

∑ℓ′ =ℓ



]


R(t) −→

Coulomb potential V(R(t) ) −→Free energy minimization Fe[n(r)] −→

Newton’s equations R(t +∆t)




L(R , P

)=

1

2

∑ℓ

P2ℓ

Mℓ−

∑ℓ =ℓ′


]


minn(r)

Fe[n(r), R ]

and dPℓ

dt=

∑ℓ′ =ℓ



]







L(R , P

)=

1

2

∑ℓ

P2ℓ

Mℓ−

∑ℓ =ℓ′


]


minn(r)

Fe[n(r), R ]

and dPℓ

dt=

∑ℓ′ =ℓ



]



Free energy minimization Fe[n(r)] −→

Newton’s equations R(t +∆t)




L(R , P

)=

1

2

∑ℓ

P2ℓ

Mℓ−

∑ℓ =ℓ′


]


minn(r)

Fe[n(r), R ]

and dPℓ

dt=

∑ℓ′ =ℓ



]




Outline








Challenges

Quantum treatment

• Independent particle model: the Kohn-Sham scheme;

Fe[n(r)] = ∑ℓ

(fℓ∫

dr∣∣∇ψℓ

∣∣2 −1

β

[fℓ ln fℓ + (1− fℓ) ln(1− fℓ)

])

+1

2

∫∫dr dr′ n(r)n(r′)

|r − r′|−

Na∑ℓ=1

Zℓ

∫dr n(r)

|Rℓ − r|

+

∫dr εxc

[n(r)

]

minn(r)

Fe[n(r)] ⇔ [p2

2+ VH[n] + Vxc[n] + Vext

]|ψℓ⟩ = εℓ |ψℓ⟩

n(r) =∑ℓ

2

1 + expβ(εℓ − µ)

∣∣ψℓ(r)∣∣2

High-energy -density and semi-classical treatment

• Limitation in temperature and density:• Fermi-Dirac distribution: flat when kT ∼ µ;• pseudo-potential and delocalization: frozen-core-electron approximation down

(Mazevet et al PRE 2007);

• Only one term involving quantum states in LDA

• Semi-classical expansion: first term in ℏ (Brack, 2007);

Fe[n(r)] = 1

2


|r − r′|−

Na∑ℓ=1

Zℓ

∫dr n(r)

|Rℓ − r|

+

∫dr εxc

[n(r)

]+

∑ℓ

(fℓ∫

dr∣∣∇ψℓ

∣∣2 −1

β


])

+∑ℓ

(fℓ∫

dr∣∣∇ψℓ

∣∣2 −1

β


])

n(r) =∑ℓ

2

1 + expβ(εℓ − µ)

∣∣ψℓ(r)∣∣2




• Only one term involving quantum states in LDA: let’s get rid of it!• Semi-classical expansion: first term in ℏ (Brack, 2007);

Fe[n(r)] = 1

2


|r − r′|−

Na∑ℓ=1

Zℓ

∫dr n(r)

|Rℓ − r|

+

∫dr εxc

[n(r)

]+

∫dr

(n(r)Φ

[n(r)

]−

2√2

3π2β32

I 32

(Φ[n(r)

]))+

∑ℓ

(fℓ∫

dr∣∣∇ψℓ

∣∣2 −1

β


])

n(r) =√2

π2β32

I 32

(Φ[n(r)

])




• Only one term involving quantum states in LDA• Semi-classical expansion: first term in ℏ (Brack, 2007);

Ee[n(r)] = 353 π

43

10

∫dr n(r)

53

+1

2


|r − r′|−

Na∑ℓ=1

Zℓ

∫dr n(r)

|Rℓ − r|

Contents








Challenges

Outline








Challenges

Orbital Free Molecular Dynamics

• Microcanonical (N,Ω, E) and isokinetic (N,Ω,K) statistical ensembles:• isokinetic: time reversal algorithm (Minary et al, JCP 2003);

• Periodic boundary conditions:• Ewald sums for the nuclei;• FFT for the electronic fluid: parallel FFTW 2.1.5 and FFTe;

• Functionals:• free energy from non-zero temperature Thomas-Fermi and gradient correction

(Perrot, PRA 1979);• LDA exchange-correlation;

• Minimization of the electronic free energy: constrained conjugate gradientalgorithm;

• algorithm specially dedicated to orbital free methods (Jiang et al, JCP 2004):fake orbital;

n(r) = ψ(r)2

Outline








Challenges

The regularization procedure

• r−1 divergence of the electron-nucleus potential: regularization (not apseudo-potential);

• all-electron calculation!

• Numerical limitation: cut-off radius on the atomic scale, not on thenuclear one;

• Use of the of average atom model (Feynman, Metropolis & Teller) andnorm conserving pseudo-potential idea:

• charge conservation is mandatory!• pressure and forces correctly evaluated (Gauss theorem);

The regularization procedure

• Use of the of average atom model (Feynman, Metropolis & Teller) andnorm conserving pseudo-potential idea:

• charge conservation is mandatory!• pressure and forces correctly evaluated (Gauss theorem);

n(r) =

exp(a + br2 + cr4

)if r ⩽ rc

n(r) if r > rc= αI 1

2

[β(µ− VH(r)− V(r)

)]

0

1

2

3

0 0.2 0.4 0.6 0.8 1

4πr2n(r

)(a.u.)

r/a

Average atom: coulombRegularization

-30

-25

-20

-15

-10

-5

0

0 0.2 0.4 0.6 0.8 1V(r

)(a.u.)

r/a

Average atom: coulombRegularization

Outline








Challenges

The parallelization paradigm

• Spread to efficiently work;• energy calculation, i.e. computation of integrals;

• Functionals’ claim: “Let’s be local!”• local functionals through Perrot’s polynomial fit;

Ω =⊎ℓ

Ωℓ

∫Ω

dr F[n(r)

]=

Np∑ℓ=1

∫Ωℓ

dr F[n(r)

]




Fe[n] =∫

dr(

t[n(r)

]− β−1σ

[n(r)

])+

∫dr εxc

[n(r)

]+

∫dg |n(g)|2 4π

g2−

Na∑ℓ=1

Zℓ

∫dg n(g) 4π

g2e−ıg·Rℓ




Fe[n] =∫

dr(

t[n(r)

]− β−1σ

[n(r)

])+

∫dr εxc

[n(r)

]+

∫dg |n(g)|2 4π

g2−

Na∑ℓ=1

Zℓ

∫dg n(g) 4π

g2e−ıg·Rℓ

Number of processors ⟨∆t⟩ (s) ratio (real/linear)512 25.6 1/11024 13.5 1.9/22048 7.5 3.4/44096 5.6 4.6/88192 2.8 9.1/16

Average computation time per MD step, the electronic fluid being described ona 2563 grid (performed by C. Ticknor on the Cielo machine at LANL).

Contents








Challenges

From microphysics to macrophysics

..

quantum simulation

ABINIT code

.

orbital-free simulation

OFMD code

.

Big

com

pute

rs

.

stored in files

.

of coefficients: e.g eos

.

direct computation

.

validity of ugly (but fast)

.

models: e.g viscosity

.

analytic formulas

Outline








Challenges

Physics of the hot-spot

• Ignition: no bulk combustion but propagation of a combustion wave;• D and T burn for special ρ and kT, conditions reached with a specific

design of two zones:• a central very hot (kT ∼ keV) mixture - “the hot spot”: it’s a match to

launch a centrifugal combustion wave;• an outer very dense

(ρ ∼ 500 g cm−3) fuel: it releases most of the fusion

energy!

..

fuel

.

ablator

..

implosion

0

2

4

6

8

10

12

10 20 30 40 50 60 70 80

0

120

240

360

480

600

720

k×

Tem

per

atu

re(k

eV)

Den

sity

(

gcm

−3)

cell number

hot spot cold fuel



design of two zones:• a central very hot (kT ∼ keV) mixture - “the hot spot”: it’s a match to

launch a centrifugal combustion wave;• an outer very dense

(ρ ∼ 500 g cm−3) fuel: it releases most of the fusion

energy!

• Wide range of plasma behavior:• from kinetic to partially degenerate

and coupled;• conditions reached only in ICF!

θ =kTεF

∼ 1

Γ =⟨U⟩⟨K⟩

=Z⋆2

a kT∼ 1

0.1

1

10

10 20 30 40 50 60 70 80

0

0.2

0.4

0.6

0.8

1

1.2

deg

ener

acy

para

met

er

coupling

const

ant

cell number

hot spot cold fuel



design of two zones:• What are the physical processes involved in ignition?• energy balance: (+) fusion energy (alpha particle deposition) and mechanical

work, (-) radiative emission and electronic conduction;



design of two zones:• How confident are we in simulating such a process, e.g. thermal

conduction?• very crude approximations of thermal conductivity;

• need for the verification of microscopic models in extreme conditions;

• κ too low:• fusion energy confined in the center (no

loss through conduction), cold fuelinert;

• start but no propagation;

• κ too high:• too many energy loss, not enough

heating of the “hot-spot”;• no start at all.

0

5

10

15

20

0.1 0.2 0.3 0.4 0.5 0.6

k×

Tem

peratu

re

(keV

)Surface density

(

g cm−2)

κ

2 × κ

12× κ

0 × κ

Hot-spot average

thermodynamical path

Ignition



design of two zones:• How confident are we in simulating such a process, e.g. thermal

conduction?

• need for the verification of microscopic models in extreme conditions;

How can we compute thermal conductivity?

• Electronic transport coefficients: scattering, i.e. quantum states;• Linear response formalism, the Kubo-Greenwood/Chester-Thellung

formulation;

• We need orbitals…but at 500 eV!• computationally expensive!

κ =1

T

(L22 −

L12 × L21

L11

)

Lij = (−1)i+j+1

∫dε ∂f(ε, µ)

∂ε(ε− µ)i+j−2s(ε)

s(ε) = 1

Ω

∑ℓ,ℓ′

∑α

∣∣⟨ψℓ′ | vα |ψℓ⟩∣∣2δ(εℓ′ − ε)δ(εℓ − ε)

• How can we do that?

• perform the MD with the orbital free (orbitals useless) scheme: nuclearstructure;

• extract a few nuclear configurations;• compute the full quantum electronic structure on those configurations and

average!



formulation;• We need orbitals…but at 500 eV!• computationally expensive!

κ =1

T

(L22 −

L12 × L21

L11

)

Lij = (−1)i+j+1

∫dε ∂f(ε, µ)


s(ε) = 1

Ω

∑ℓ,ℓ′

∑α

∣∣⟨ψℓ′ | vα |ψℓ⟩∣∣2δ(εℓ′ − ε)δ(εℓ − ε)

• How can we do that?

• perform the MD with the orbital free (orbitals useless) scheme: nuclearstructure;


average!




κ =1

T

(L22 −

L12 × L21

L11

)

Lij = (−1)i+j+1

∫dε ∂f(ε, µ)


s(ε) = 1

Ω

∑ℓ,ℓ′

∑α

∣∣⟨ψℓ′ | vα |ψℓ⟩∣∣2δ(εℓ′ − ε)δ(εℓ − ε)

• How can we do that?• perform the MD with the orbital free (orbitals useless) scheme: nuclear

structure;


average!




κ =1

T

(L22 −

L12 × L21

L11

)

Lij = (−1)i+j+1

∫dε ∂f(ε, µ)


s(ε) = 1

Ω

∑ℓ,ℓ′

∑α

∣∣⟨ψℓ′ | vα |ψℓ⟩∣∣2δ(εℓ′ − ε)δ(εℓ − ε)


structure;• extract a few nuclear configurations;

• compute the full quantum electronic structure on those configurations andaverage!




κ =1

T

(L22 −

L12 × L21

L11

)

Lij = (−1)i+j+1

∫dε ∂f(ε, µ)


s(ε) = 1

Ω

∑ℓ,ℓ′

∑α

∣∣⟨ψℓ′ | vα |ψℓ⟩∣∣2δ(εℓ′ − ε)δ(εℓ − ε)


structure;• extract a few nuclear configurations;• compute the full quantum electronic structure on those configurations and

average!

Comparison with models

• Application to hydrogen at 10, 80 and 160 g cm−3 up to 800 eV!• True challenge in terms of numerical simulation;• no pseudo-potential: purely coulombian;• competition between density and temperature effects: kT ⩽ εf;• electronic states are nearly plane waves;• at low temperatures need for 2000 atoms: numerical discretisation of the

energy, sharp boundary of the Fermi distribution;

0

20

40

60

80

100

120

-500 -400 -300 -200 -100 0 100 200 300

Densi

tyofst

ate

s

ε − εf (eV)

2048 atoms1458 atoms1024 atoms256 atoms

dos(ε) =∑

ℓ δ(ε− εℓ) ∝√ε and ∆ε ∝ Ω−1 for a free fermion gas

Comparison with models

• Application to hydrogen at 10, 80 and 160 g cm−3 up to 800 eV!• Comparison with models used in ICF or astrophysics codes:• Hubbard-Spitzer: kinetic Boltzmann theory at high kT and quantum

perturbation theory at very low kT, interpolation inbetween;• Ichimaru: Ziman formulation plus a specific treatment of the dielectric

function;• Lee-More: quantum Boltzmann equation with approximations on phase

transitions;

104

105

106

107

1 10 100 1000

Thermalconductivity(

Wm

−1K

−1)

k × Temperature (eV)

160 g cm−3

80 g cm−3

10 g cm−3

qmd

IchimaruHubbard-SpitzerLee-More

Outline








Challenges

Why do we need mixing rules?

• Material composed of elements ℓ of atomic mass Aℓ and atomic fractionxℓ, e.g. C2H3;

• EOS building based on using different models: average atom calculation,i.e. one element (qeos, sesame);

• tabulated eos production;

• System involving a huge number of different materials: gravitationalsegregation in astrophysics;

• on-line eos calculation;

• Molecular dynamics: rule of thumb for mixing laws;• put the right number of atoms in the right box, let the system live its life:

direct calculation of mixture eos.

Isobaric-isothermal mixing rule

temperaturematching

Tℓ = T, ∀ℓ

additivity of partialvolumes

1

ρ

∑ℓ

xℓAℓ =∑ℓ

xℓAℓ

ρℓ≡ Ω =

∑ℓ

Ωℓ

pressure matching

pℓ(ρℓ,T) = pℓ′ (ρℓ′ ,T), ∀ℓ = ℓ′

⇔ F(ρ,T) =∑ℓ

xℓFℓ(ρℓ,T)

..Ω

.

S1 + S2

.p

.Ω = ΩS1 +ΩS2

.

S1

.

S2

.p1

.p2

.

≈

Isobaric-isothermal mixing rule. The pressure matching between constituentsprovides the pressure of the mixture.

Isobaric-isothermal mixing rule

temperaturematching

Tℓ = T, ∀ℓ

additivity of partialvolumes

1

ρ

∑ℓ

xℓAℓ =∑ℓ

xℓAℓ

ρℓ≡ Ω =

∑ℓ

Ωℓ

pressure matching

pℓ(ρℓ,T) = pℓ′ (ρℓ′ ,T), ∀ℓ = ℓ′ ⇔ F(ρ,T) =∑ℓ

xℓFℓ(ρℓ,T)

..Ω

.

S1 + S2

.p

.Ω = ΩS1 +ΩS2

.

S1

.

S2

.p

.p

.

≈

Isobaric-isothermal mixing rule. The pressure matching between constituentsprovides the pressure of the mixture.

He/Fe example

• Equimolar mixture of He and Fe at 10 g cm−3;• test of mixing law validity: agreement whatever the functional (Danel et al,

PRE 79, 066408 (2009));

-1.5

-1

-0.5

0

0.5

1 10 100 1000

pex

mr/p

ex

md

−1(%

)

kT (eV)

without gradient correction

with gradient correction

Outline








Challenges

Hydrodynamic instability: the picture

• Deleterious effects for ignition: hydrodynamic instabilities at materialinterfaces (fuel/ablator) or at the ablation front;

• e.g. Rayleigh-Taylor instability: driven by ∇p and ∇ρ;• precise knowledge of equation of state, thermal conductivity, viscosity or

molecular diffusion;

..

gaseous fuel

.

solid fuel

.

ablator

..

heavy material (ablator)

.

light material (fuel, ablator)

.p. e. r. t. u. r. b. e. d.. i. n. t. e. r. f. a. c. e.g

. or.∇p ·∇ρ < 0

Hydrodynamic instability: eos

• Hydrodynamic simulations: tabulated equation of state;• three contributions: cold curve, thermal electronic and thermal ionic

(arbitrary);• often composed of several different models: average atom, Debye, etc but

promising efforts (e.g. hydrogen by Kohn-Sham and PIMC for example);• approximations for mixtures: carbon and hydrogen for ablator;

• Need for comparisons with more fundamental calculations (quantum ororbital-free);

Hydrodynamic instability: eos

• Hydrodynamic simulations: tabulated equation of state;• Need for comparisons with more fundamental calculations (quantum or

orbital-free);• relevant conditions for instabilities: 7 and 9 g cm−3 isochores for C2H3;• ofmd features: 250 atoms propagated during 50000 time steps;

3.7

4.8

6.3

8.2

10.6

13.8

17.9

0 5 10 15 20 25 30 35 40 45

p(T

Pa)

kTe (eV)

9 g cm−3 isochore

7 g cm−3 isochore

qeos tableqmd

ofmd

ofmd gradient

Hydrodynamic instability: thermal conductivity

• Thermal conduction: smoothing of temperature gradients but eitherstabilizing or destabilizing;

• thermal conductivity: high impact on instability growth in hydrodynamicssimulations (Hammel et al, HEDP 2010);


• As for hot-spot: validity of approximate models but new questions;• models adapted for single element with a free parameter, the effective charge

state;• ablator: multi-specie, different scattering centers;• several strategies: mix elements and compute conductivity (done in

hydrodynamics code) or compute conductivities and mix them;


• As for hot-spot: validity of approximate models but new questions;• models adapted for single element with a free parameter, the effective charge

state;• ablator: multi-specie, different scattering centers;• several strategies: mix element and compute conductivity (done in hydrodynamics

code) or compute conductivities and mix them;• input parameters: average element (⟨Z⟩,⟨A⟩) or average ion (⟨Z⋆⟩,⟨A⟩);

104

0 5 10 15 20 25 30 35 40 45

Therm

alconducti

vity

(

Wm

−1K

−1)


qmd

Hubbard-SpitzerHubbard-Spitzer Z⋆

AAM

Ichimaru Z⋆

AAM

Ichimaru FZ mix

104

0 5 10 15 20 25 30 35 40 45

Therm

alconducti

vity

(

Wm

−1K

−1)


qmd

Hubbard-SpitzerIchimaru Z

⋆

AAM

Hydrodynamic instability: viscosity

• Determination of the flow behavior: laminar, turbulent, etc;• Reynolds number: relevant length scale;

• Limitation of RT growth for small length scale (high modes);• ofmd simulations: direct computation of viscosity for mixtures!• Need for a quick evaluation: approximate parametrized model, e.g One

component plasma with effective charge state;

η =1

3ΩkT∑ℓ>ℓ′

∫ ⟨σℓℓ′ (t)σℓℓ′ (0)

⟩dt

0

5

10

15

20

0 5 10 15 20 25 30 35 40 45

η(m

Pa

s)

kTe (eV)

ofmd, ρ = 9g cm−3

ocp, ρ = 9 g cm−3

ofmd, ρ = 7g cm−3

ocp, ρ = 7 g cm−3

Contents








Challenges

Challenges?

• Equation of state: improvement of the moderate temperature part;• new orbital-free functionals: not Exc[n] but Ts[n] and σs[n];

• “Ionic” transport coefficients: increase system size, catch atomic traces,e.g. Si in plastic;

• FFT, real space methods, minimization algorithms;

• “Electronic” transport coefficients:• semi-classical expansion of the Kubo-Greenwood formulation? Kubo?• time-dependent formulation of orbital-free DFT (Jérôme’s talk, quantum

hydrodynamics: Gao et al PRB 2008, Pittalis et al PRB 2011);• radiative coupling, out-of-equilibrium simulations (Cimarron project,

Graziani et al HEDP 2012);

Acknowledgments

V. Recoules (QMD), A. Decoster (Wisdom), G. Salin (QEOS),J. Clérouin, L. Kazandjian, J.-F. Danel

and L. Masse (Instabilities)Commissariat à l’Energie Atomique

C. Ticknor, J. Kress and L. CollinsLos Alamos National Laboratory

M. DesjarlaisSandia National Labortory

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