granular thermoelectrics · spillmann, teschner, “cosserat nets”, 2009 • twist buckling...

Andreas Glatz1, Igor Aronson1, George Crabtree1, Hanqi Guo2, Gregory Kimmel1, Alexei Koshelev1, Todd Munson2, Carolyn Phillips2, Ivan Sadovsky1, Jason Sarich2

1Materials Science Division, Argonne National Laboratory 2Mathematics and Computer Science Division, Argonne National Laboratory

http://www.oscon-scidac.org/






http://oscon-scidac.org

Outline

Optimizing SuperConductor Transport Properties Through Large-Scale Simulation

Critical Current by Design

Experimental validation

Non-additivity of defects

Prediction of critical currents

Intelligent optimization of Superconductors

Approach

Examples

Extracting, Tracking, and Visualizing of Vortices

Tracking methods

Tools

Next steps

2

SDAV

FASTMath & SUPER

see Poster A1 (18)


Model and Pinning


Time dependent GL equations:

In dimensionless units:

3

Inclusions and defects are modeled by critical temperature Tc(r) [ε(r)=Tc(r)/T-1] modulation


Examples: Order parameter ψ(r) follows Tc-

pattern


4

Ch

ecke

rbo

ard

Po

lycry

sta

llin

e

Re

cta

ng

ula

r

|ψ|2

Tc


Experimental motivation


5

Angular dependence of the critical current in commercial REBCO coated conductors

TEM image of heavy-

ion damage tracks

Irradiation

YBCO tape made by


Observation and scientific questions


6

• Disappearance of central peak

after irradiation Pinning

effects are non-additive.

Explanation?

• Overall increase of the critical

current. Can we increase it

more?

• Can we get a more

homogeneous critical current?

• What is the optimal irradiation

track concentration?

Here we use large-scale Ginzburg-Landau simulations to address these

questions

Simulation-assisted design of mixed-pinning landscapes with

predictable “critical-current-by-design”


Sample realization


7

Sample is realized as a cuboid, discretized using a regular mesh of 108 grid points with mesh size of x0/2

(quasi-)periodic boundary conditions Inclusions and irradiation tracks are modeled by a

different low-Tc component Anisotropy in c-direction is implemented by an

anisotropy factor g=5 For each field and pinning configuration an IV curve

is calculated from which the critical current is obtained


Comparison

Experiment &

Simulation


8


Validation of the simulation


9


Depinning in fixed field B (θ = 0°/45°)=0.08


10


Discovery of novel mechanism: Non-additivity of

defects


11

B (θ = 0°) FL

Columnar defects work like shortcuts for vortices


Predication of the critical current in irradiated samples


12

BΦ

[Hc2]

BΦ

[Hc2]

Jc

[Jd

p]

θ [°] Angle of field, θ [°]

Sa

me

cu

rre

nt, J

> J

c

nanorods + columns B || c

Sadovskyy et. al., submitted to Nature Materials (2015)



13





Intelligent Optimization of Superconductors

Approach

Example


Tracking methods

Tools

Next steps

SDAV

FASTMath & SUPER

see Poster A2 (19)


Optimization Challenge & Approach


14

Desired output

Optimal inclusion configurations for maximal critical current

Robustness of these configurations

Dependence on magnetic field and temperature

Challenge

We need to calculate the critical current for many configurations with small fluctuations (requires disorder averaging)

A typical pinning landscape has about 10 free parameters

Approach

Fully automated derivative-free optimizer: Define possible parameter ranges and the optimizer samples promising pinning configurations

Can handle arbitrary combination of different defect types


Example: 2 parameter optimization of random

spherical inclusions


15

System size: 100x100x50 x3 [256x256x128 mesh points] Simulation time=105 per current

Occupied volume fraction f npVp

Overlap: f f - f2/2

with diameter a and density np


Optimal particle density at fixed magnetic field


16

IVs for different numbers of particles (occupied volume fractions)

0.000 0.005 0.010 0.015 0.020 0.025 0.0300

5

10

15

20 300 (0.02) 4800 (0.27)

500 (0.033) 5600 (0.305)

800 (0.052) 6400 (0.337)

1200 (0.077)

1600 (0.1) flux flow

2400 (0.148) 0.02 ff J

3200 (0.191)

4000 (0.232)

a=4x, g=5,

Bz=0.1H

c2

E [

x1

04]

J

0.0 0.1 0.2 0.30.00

0.01

0.02

0.03

0.04

0.053 Jdp

0.076 Jdp

B=0.016

B=0.05

B=0.1 a=4

J c

Volume fraction

0.1 Jdp


Optimal parameters


17

Critical current vs particle density for different particle sizes

Dependences of optimal parameters on magnetic field

0.0 0.1 0.2 0.30.000

0.005

0.010

0.015

0.020

Jc

a = 3

a = 2

a = 6

B = 0.1

f

a = 4

0.00 0.05 0.10 0.15 0.200.00

0.01

0.02

0.03

0.04

B

J c,m

ax

0.00

0.02

0.04

0.06

0.08

0.10

J c,m

ax/J

dp

0

1

2

3

4

5

aopt/x

0.0

0.1

0.2

0.3

0.4

0.5

fopt

(b)

(a)

Contour plots of critical current

• Optimal particle diameter

decreases with field

• Optimal volume fraction = 18-

20% 0.10 0.15 0.20 0.25 0.302.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

f

a

0.0136

0.0140

0.0144

0.0148

0.0152

0.0156

0.0160

0.0164

0.0168

0.0172

0.0176

0.0180

0.0184

0.0188

0.0192

0.0196

0.0200

0.0204

0.0206

0.0208

B=0.1

0.10 0.15 0.20 0.253.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

f

a

0.0250

0.0252

0.0254

0.0256

0.0258

0.0260

0.0262

0.0264

0.0266

0.0268

0.0270

0.0272

0.0274

0.0276

0.0278

0.0280

0.0282

0.0284

0.0285

0.0286

B=0.05


Sampling in parameter space


18



19





Intelligent Optimization of Superconductors

Approach

Examples


Extraction & tracking methods

Tools

Next steps

SDAV

FASTMath & SUPER

see Poster B1 (19)


Vortices in superconductors


20

Vortices are defined as topological defects of the order parameter field ψ, which are a locus of points satisfy n is usually +/-1, indicating the chirality

Vortices are 1D curves in 3D space

The vortices are fundamentally different from vortices in fluid flow

Amplitude |ψ|

Phase θ


TDGL Data Visualization


21

Little research has been done in visualizing complex-field data

– Volume rendering/isosurface blur fine features

– Vortex extraction for single frames in regular grid data is proposed by Phillips et al. recently

Extracting, tracking, and visualizing vortices are the keys to understand the dissipative material behaviors and the impact of adding material inclusions.


Deliverables of a detection algorithm


22

A vortex extraction algorithm for both structured and unstructured mesh TDGL data

A vortex tracking algorithm, which is as accurate as the data discretization

Application of various visualization techniques


Overview of the Vortex Extraction Algorithm


23

• Vortex extraction locates vortex line at single time frames

By definition, singularities can be localized by checking phase jumps over mesh faces.

As there are always equal numbers of “ins” and “outs” for each cell, the punctured faces are further connected into vortex lines based on the mesh connectivity.


Overview of the Vortex Tracking Algorithm


24

• Vortex tracking algorithm relates vortex lines over adjacent frames, unless there are topological changes.

The movement of a vortex line is detected by checking each space-time edge to see whether it is intersected at an intermediate time between two adjacent frames.


Algorithm Pipeline


25

Load data

Extract punctured spatial faces

Extract intersected space-time edges

Graph-based vortex extraction and tracking


Algorithm Details –

Punctured Face/Intersected Edge Detection


26

Phase jump over faces

Phase jump over space-time edges

• Gauge transformation

*) Always use local transformations

to compute phase jumps


Event Detection and Visualization


27

Events are defined as topological changes of vortex graphs: merging, splitting, birth, death, recombination/crossing, etc.

Event visualization is based on storyline-like visual representations [Tanahashi and Ma 2012]


Results – 3D Structured Grid Data


28


Results – 3D Unstructured Data


29 Guo et. al., Proc. IEEE SciVis (2015)


Software Development and ParaView Plugins


30

A standalone visualization tool, as well as a ParaView plugin are developed for loading, analyzing, and visualizing TDGL simulation data.

The unstructured mesh data structures are based on libMesh, which is the finite element library used by the simulation. The framework can be integrated with the simulation for in-situ analysis in the future.


Next steps: Twist, Writhe, and Stabilizing Helical

Vortices


31

When electrostatic and magnetic fields aligned, phase field twists around the vortex.

Shielding supercurrents spirals around vortex rather than form planar loops.

Twisting phase field can be numerically extracted from GL simulations. Represented as ribbon.

No Twist

Twisting phase field Twisting phase field


Excess Twist leads to Writhe


32

Spillmann, Teschner, “Cosserat Nets”, 2009

• Twist Buckling Instability Writhe of Filament/Rod/Vortex

• Perpendicular Lorentz Forces on writhing vortex helical coils unstable. “Blows up” (Superconducting state lost): New criterion for upper limit of the critical current

• However, if vortex inside a cylindrical inclusion, cylinder can “traps” helical vortex state. (Superconducting state retained)

Twisted Rod Buckles and Writhes

Stable Helical Twisted Vortex

in Cylindrical Inclusion


Acknowledgements


Igor Aronson Alexei

Koshelev

Dmitry

Karpeev

Carolyn

Phillips

Ivan

Sadovskyy

33

George

Crabtree

Todd

Munson

Gregory

Kimmel

The Team

Jason

Sarich Stefan Wild Hanqi Guo

granular thermoelectrics · spillmann, teschner, “cosserat nets”, 2009 • twist buckling...

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