Seminar iitkgp

Particle and field based methods in Computational Science
Funding:
December 6, 2018
Department of Physics
Asutosh College
University of Calcutta
CCDS IIT Kgp
Dr. Amit Kumar Bhattacharjee
IMSc Chennai DLR-IMP Köln University of
Konstanz
Courant Institute
New York
IISc Bangalore
Prof. Gautam Menon (Chennai)
Prof. Ronojoy Adhikari (Cambridge)
Prof. Thomas Voigtmann (Köln)
Prof. Jürgen Horbach (Düsseldorf)
Prof. Matthias Fuchs (Konstanz)
Prof. Aleksandar Donev (NewYork)
Prof. Chandan Dasgupta (Bangalore)
Collaborator(s):
C0u(r)an(t)

Overview
 Field theoretic and particulate methods in nematic liquid crystals (2007-2009, 2015 - ).
 Particulate methods in dense isotropic liquid glass-formers (2010-2012).
 Multiscale methods in multispecies reactive & non-reactive fluids (2013-2014).
 Complex Fluids / Soft Matter.
 Non-equilibrium Thermodynamics.
 Stochastic Processes.
 Deterministic & stochastic time-dependent PDE solver in quasi-2D, 3D for scalar & tensor field.
 Dissipative Particle Dynamics (momentum-conserving), Kinetic Monte-Carlo for particulate
simulation.
Theoretical expertise
Numerical expertise
CCDS IIT KgpAmit Bhattacharjee 1

Prologue
CCDS IIT KgpAmit Bhattacharjee
States of matter
 Solid, liquid, gas, plasma.
 ; Hard matter (crystals) = E dominated phases (minimize E);
Soft matter (fluids) = S dominated phases (maximize S).
 Changes of phase – order of transition (e.g. liquid to solid, paramagnet to
ferromagnet).
 Soft to touch, easily malleable, can't withhold shear.
 Examples: milk, paint (colloid), rubber, tissues (polymer), toothpaste
(gels), LCD devices (liquid crystal), ….
Complex fluids
2
ℱ =E−TS

Prologue
Atomistic description:
i) Ignore electronic d.o.f. classical N-particle Newton's equation.
ii) Approximation: 2-body interactions in central forcefield (e.g. L-J, Yukawa,
WCA potentials).
Mesoscopic description:
i) Identify order parameter, broken symmetry, conservation laws, type of
phase transition.
ii) Construct a free energy functional and spatially coarse-grain.
iii) Temporal coarse graining.
●
Measurement of the equilibrium and nearly-equilibrium properties.
Theoretical methods
3

Prologue
Numerical methods
mm
μm
nm
fs−ps μ s ms−s
CFD
TDGL
LLNS
DPD/SPH
LBM, BD,
SRD
DFT
MD
KMC
Mesoscale
Macroscale
Microscale
4

Work at Courant Inst. (2013-2014)
 Soret effect induced large-scale non-equilibrium concentration fluctuations in
microgravity[1,2]
.
 We formulated complete theory to study quantitatively multicomponent liquid
diffusion with thermal fluctuations and flow from first principles of non-eq TIP.
1mmthick
5mm side
∂t (ρi)+∇⋅(ρi v) = ∇⋅
{ρW
[χ
(Γ ∇ x+(ϕ−w)
∇ P
nkBT
+ζ
∇ T
T )]+√2kB L1
2
Ζ
}
∂t(ρv)+∇ π =−∇⋅(ρv v
T
)+∇⋅(η(∇ +∇
T
)v+Σ)+ρg
[2] GRADFLEX Experiment: https://spaceflightsystems.grc.nasa.gov/sopo/ihho/psrp/expendable/gradflex/
[1] Vailati et al, Nature Comm. (2011).
5
Finite Volume Method
Staggered Grid
7 million d.o.f. on 64 node cluster
HPC: Fortran code developed on
BoxLib Library (LBNL)

Work at Courant Inst. (2013-2014)
 We formulated[1]
complete theory to study quantitatively multicomponent reactive
gas diffusion with thermal fluctuations and flow from first principles of non-eq TIP.
∂t ρs =−∇⋅(ρs v)−∇⋅Fs +ms Ωs , (s=1,2,..., Ns)
∂t (ρ v) =−∇⋅Π−∇⋅(ρv v
T
+ p I )+ρ g,
∂t (ρ E) =−∇⋅[(ρ E+ p)v]−∇⋅[ϑ+Π⋅v]+ρ v⋅g
16 monomer
+ 8 dimer
6
[1] Bhattacharjee et al, J. Chem. Phys. (2015).
Finite Volume Method
Collocative Grid
HPC: Fortran code developed on
BoxLib Library (LBNL)
7 million d.o.f. on 64 node cluster

Publications

Work at DLR & Uni-Kon (2010-2012): Vitrification
(a) Alloy of linear size 4.3nm, (b)
colloidal systems, (c) a beer foam
with sub-millimeter size, (d) granular
materials of millimeter size grains
[Berthier & Biroli, RMP (2011)]
 Glass transition – a non-thermodynamic transition:
a) no consumption/expulsion of latent heat.
b) no changes in structural properties.
c) (almost) no change in thermodynamic properties.
d) drastic change in transport properties (viscosity,
diffusion-constant etc).
8
0 ˙−1
(a) (b)
(c) (d)

Technological applications:
Casting, cooling and solidification[1,2]
, Dutch tears,
Body armour (STF enabled Kevlar)[3]
, Pitch-drop
experiment[4]
(how do glasses flow?)
Images [1] Vinayak Industries, Mumbai,©
[2] Schott AG, Mainz, [3] Norm Wagner Lab
(Delaware), [4] Prof.J.Mainstone, Univ. of
Queensland.
9

=
˙
˙
˙γ
˙
+ = ?
˙
˙
=
mi
˙⃗ri= ⃗pi ; ˙⃗pi=−∑i≠ j
⃗∇ Uij(⃗r)−∑i≠ j
ζω2
( ⃗rij)( ^rij⋅⃗vij) ^rij+√2kB T ζω( ⃗rij)Nij ^rij .
Uij
WCA
(r)=
{4 ϵij [(
σij
r
)
12
−(
σij
r
)
6
+
1
4
]S , r<2
1/6
σij
0, r≥21/6
σij
We gave the complete structure and kinetics of
a sheared supercooled glass-forming liquid
using NEMD and MCT methods and gave the
microscopic foundation of the Bauschinger
effect which is lower yield for a sheared non-
Newtonian fluid when reversed the flow direction.
10
˙
˙
+ = ?
==
DPD for WCA + LE
104
d.o.f. on103
cores in BW-grid
Serial Fortran77 Code / LAMMPS

Publications
11
σ=
ρ
2
2
∫
0
∞
dr ∑α,β
cα cβ
rr
r
∂V
αβ
∂r
g
αβ
(r)

Present Work: Controlling thermal and motile disclinations
using an electric field.
Ψb
Ψt
ε = ? =
Ψt
Ψb
ε

Point defects in nematics
Amit Bhattacharjee
Prologue GLdG model Electrokinetics UN Electrokinetics BN Conclusion
 Mesophases consist of anisotropic molecules (e.g. rods, discs, V-shape) with long range
orientational order without translational order. uniaxial (UN), biaxial (BN) phase rotational
symmetry about direction of order described by headless vector n (director) and m (secondary
director).
 Orientational order
12CCDS IIT Kgp
n
ℚ=
3
2
S(n⊗n−
1
3
δ)+B2(l⊗l−m⊗m). S=Uniaxial degree of ordering.
B2=Biaxial degree of ordering .

Amit Bhattacharjee
 In a continuous symmetry breaking phase transition by (a) rapid quench, rigidity and topological
defects are inevitable during solidification, (b) shallow quench, anisotropic droplets nucleation
kinetics[1]
.
[1] Bhattacharjee, Scientific Reports (2017).
13CCDS IIT Kgp

Amit Bhattacharjee 14
 Under crossed polarizers, charged point defects in UN & BN display 2 or 4 brushes
texture with core structure of enhanced/reduced degree of ordering.
sin
2
[2θ]spatial extentS and n
±1,±
1
2
Cz
CCDS IIT Kgp
1
0
C y
0
1
UN
BN

Amit Bhattacharjee
 Topological classification[1]
: (a) UN phase (b) BN phase From
Homotopy theory, UN phase have one class and BN phase have five class of defects.
π1(P2)=Z2 , π1(P3)=Q8 .
±
1
2
[1] Mermin, Rev.Mod.Phys (1979), Kleman-Lavrentovich, Soft Mat (2002).
[2] Kobdaj et al, Nucl.Phys.B (1994), Zapotoky et al, PRE (1996).
15CCDS IIT Kgp

Amit Bhattacharjee
 However, energetics and direct numerical simulation[2]
showed (a) dissociation of integer defect
into a pair of defects, (b) existence of 2 class of defects in BN.
Energy of single point defect:
π1(P2)=Z2 , π1(P3)=Q8 .
±
1
2
±
1
2
±
1
2
ℱ discl=π K k2
ln(
R
rc
)+ℱ discl
c
.
CCDS IIT Kgp 15

Amit Bhattacharjee
 However, energetics and direct numerical simulation[2]
showed (a) dissociation of integer defect
into a pair of defects, (b) existence of 2 class of defects in BN.
Energy of single point defect:
 Identify and classify defects using Burger’s circuit[2]
:
(a) in UN, traversing contour rotates by
(b) in BN defect class rotates by no rotation.
rotates by no rotation.
both rotates by
π1(P2)=Z2 , π1(P3)=Q8 .
±
1
2
±
1
2
±
1
2
ℱ discl=π K k2
ln(
R
rc
)+ℱ discl
c
.
γ, n ±π.
Cx , n ±π, l
Cy , l ±π, n
Cz ,{n ,l } ±π.
CCDS IIT Kgp 15

Line disclinations in nematics
Amit Bhattacharjee
±
1
2
 Points in 2D correspond to strings in 3D.
 Tensor field visualization: (i) evaluate singularity using Burger’s circuit in
the vector field, (ii) glyph based techniques like Muller and Westin matrices[1]
,
(iii) hyperstreamline seeding method[2]
, (iv) streamtubes formed in the
singularity of easy identification and classification scheme[3]
.
S ,B2
[1] McLoughlin et al, Comput.Graph.Forum, (2010).
[2] Abukhdeir et al, IEEE Visual.Comp.Graph, (2015).
[3] Bhattacharjee, Ph.D. Thesis, HBNI (2010).
ℚ=
3
2
S(n⊗n−
1
3
δ).
CCDS IIT Kgp 16

Line disclinations in nematics
Amit Bhattacharjee
S
±
1
2
 Points in 2D correspond to strings in 3D.
 Kinetics : (i) formation of reduced nematic domains,
(ii) domain coarsening generating to disclinations,
(iii) line extinction kinetics through intercommutation and ring formation.
 Three subsequent stage in kinetics:
Initial diffusive regime : for 5CB, T*
= 34.20o
C
Porod’s law scaling regime : Tc
= 34.44o
C
String diffusion regime : [Reference T = 33.65o
C] B2
C y
Cz
L(t)t
0.5
,
L(t)t
0.4
,
L(t)t
0.5
.
UN
±
1
2
BN
C y
Cz
CCDS IIT Kgp 17

Importance in Science and Technology
Cosmic strings,
Turok et al, Science, '91
Amit Bhattacharjee
Abrikosov Lines in
Superconductor,
Smørgrav et al, PRL, '05
Vortex Lines in
BoseEinstein Condensate,
Henn et al, PRL, '09
Flux line Vortex in He3
,
Grzybowsk et al,
PNAS, '02
String networks in
Ecology,
Avelino et al, PLA, '14
Trefoil knot particle,
Martinez et al,
Nat. Mat. '14
Cholesteric colloidal Knot,
Musevic et al, Science '11
Self-assembly Amphiphiles
Wang et al, Nat. Mat. '15 Nematic Caps, Uchida et al,
Soft Matter '15
CCDS IIT Kgp 18

Central question to ponder
Amit Bhattacharjee
 How to control disclinations using external forces such as thermal fluctuations,
electro-magnetic field, shear forces and so on …
 Electric field driven alignment of the director : Fréedericksz transition.
[1] Yeomans et al, PRE (2001), PRL (2002), Vella et al, PRE (2005),
Tanaka et al, PRL (2006), Avelino SoftMat. (2011).
[2] Nikkhou et al, Nat.Phy. (2015).
CCDS IIT Kgp 19

Amit Bhattacharjee
 Disclinations under intense electric field[1,2]
: key-components are (i) backflow, (ii) uniform
electric field, (iii) elastic anisotropy and (iv) nematic tensor. Both for point and line defects,
it is shown that defect merging speed are different.
±
1
2
[1] Yeomans et al, PRE (2001), PRL (2002), Vella et al, PRE (2005),
Tanaka et al, PRL (2006), Avelino SoftMat. (2011).
CCDS IIT Kgp 19

Amit Bhattacharjee
 Disclinations under intense electric field : key-components are (i) backflow, (ii) uniform
 Disclinations under low to moderate electric field ? In this limit, backflow probably neglected.
Important questions are: (i) role of thermal fluctuations, (ii) nonuniformity in the electric field,
(iii) elastic anisotropy and (iii) nematic tensor.
±
1
2
CCDS IIT Kgp 19

Amit Bhattacharjee
 Disclinations under intense electric field : key-components are (i) backflow, (ii) uniform
 Disclinations under low to moderate electric field ? In this limit, backflow probably neglected.
Important questions are: (i) role of thermal fluctuations, (ii) nonuniformity in the electric field,
(iii) elastic anisotropy and (iii) nematic tensor.
 Progress were limited[1,2]
, as it is not easy to solve the Poisson equation with an inhomogeneous
dielectric constant to calculate the local electric field. Central claims were nematic caps form
on colloidal surface due to nonuniform electric field intensity distribution.
±
1
2
[1] Onuki et al, PRE (2006), EPJE (2009), Soft Matter (2015).
[2] Cummings et al, PRE (2014).
CCDS IIT Kgp 19

Amit Bhattacharjee
 In previous example, is the nonuniformity is
manifest due to the colloidal inclusion or
inherently the field structure is nonuniform in
pure sample?
 Whether long-lived loops are due to nonuniform
electric field or symmetry-breaking boundaries?
±
1
2
CCDS IIT Kgp 20

Amit Bhattacharjee
Outline
 Ginzburg-Landau-de Gennes theory and “Fluctuating Electronematics” method.
 Effect of thermal fluctuations on disclination kinetics.
 Effect of nonuniform electric field on disclination kinetics of uniaxial nematics.
 Effect of nonuniform electric field on disclination kinetics of biaxial nematics.
 Conclusions.
CCDS IIT Kgp

ℱ bulk=[1
2
ATr ℚ2
+
1
3
BTr ℚ3
+
1
4
C Tr (ℚ2
)2
+E ' Tr(ℚ3
)2
],
Amit Bhattacharjee
ℚ . Ground state free energy[1]
as a polynomial expansion of
Landau – de Gennes formalism
ℱ total=∫d
3
x( ℱ bulk+ ℱ elastic +ℱ dielec).
A=A0 (1−
T
T *
) ,
B= size disparity .
uniaxial biaxial
[1] Gramsbergen etal, Phys.Rep. (1986).
CCDS IIT Kgp 21

ℱ bulk=[1
2
ATr ℚ2
+
1
3
BTr ℚ3
+
1
4
C Tr (ℚ2
)2
+E ' Tr(ℚ3
)2
],
Amit Bhattacharjee
ℱ elastic= L1[1
2
(∂ ℚ)2
+
1
2
κ(∂⋅ℚ)2
+
1
2
Θℚ⋅(∂ℚ)2
],
 Ground state free energy[1]
at 25o
C[2]
.
ℱ total=∫d
3
x( ℱ bulk+ ℱ elastic +ℱ dielec). A=A0 (1−
T
T
*
) ,
B= size disparity .
uniaxial biaxial
{κ=L2/L1, Θ=L3/ L1}.
κ=Θ=1 for MBBA, κ=40,Θ=1for 5CB
[2] Blinov & Chigrinov, Electrooptic displays (1994).
CCDS IIT Kgp
ℚ .
21

ℱ bulk=[1
2
ATr ℚ2
+
1
3
BTr ℚ3
+
1
4
C Tr (ℚ2
)2
+E ' Tr(ℚ3
)2
],
Amit Bhattacharjee
ℱ elastic= L1[1
2
(∂ ℚ)2
+
1
2
κ(∂⋅ℚ)2
+
1
2
Θℚ⋅(∂ℚ)2
],
 Ground state free energy[1]
at 25o
C[2]
.
ℱ total=∫d
3
x( ℱ bulk+ ℱ elastic +ℱ dielec). A=A0 (1−
T
T
*
) ,
B= size disparity .
uniaxial biaxial
{κ=L2/L1, Θ=L3/ L1}.
ℱ dielec=−
ϵ0
8 π
D⋅∂ Ψ , where D=−ϵ⋅∂ Ψ=−(ϵs δ+ϵa ℚ)⋅∂ Ψ .
κ=Θ=1 for MBBA, κ=40,Θ=1for 5CB
[2] Blinov & Chigrinov, Electrooptic displays (1994).
CCDS IIT Kgp
ℚ .
21

ℱ bulk=[1
2
ATr ℚ2
+
1
3
BTr ℚ3
+
1
4
C Tr (ℚ2
)2
+E ' Tr(ℚ3
)2
],
Amit Bhattacharjee
ℱ dielec=−
ϵ0
8 π
D⋅∂ Ψ , where D=−ϵ⋅∂ Ψ=−(ϵs δ+ϵa ℚ)⋅∂ Ψ .
 Ground state free energy as a polynomial expansion of
 Fréedericksz threshold
EF= π
Lx
[9S2
L1 {1+2(L2+L3)/3 L1}
2ϵ0 ϵa
]
1/2
; ΨF=Lx EF .
ℱ total=∫d
3
x( ℱ bulk+ ℱ elastic +ℱ dielec).
uniaxial
ℱ elastic= L1[1
2
(∂ ℚ)
2
+
1
2
κ(∂⋅ℚ)
2
+
1
2
Θℚ⋅(∂ℚ)
2
],
{κ=L2/L1, Θ=L3/ L1}.
CCDS IIT Kgp
biaxial
ℚ .
21

Fluctuating Electronematics
[1] Stratonovich, Zh.Eksp.Teor.Fiz (1976).
[3] Onuki et al, Soft Matter (2015).
Amit Bhattacharjee
 Thermal kinetics[1-3]
as for moderate to low electric field,
∂t Ψ(x ,t)=∂⋅D ,
O(Ψ/ΨF )~O(ℚ).
∂t ℚαβ(x ,t)=−Γ
[δαμ δβν+δαν δβμ−
2
3
δαβ δμ ν]δ ℱ total
δℚμ ν
+ ζαβ(x ,t).
=ϵ0(ϵs ∂2
Ψ+ϵa ∂α ℚαβ ∂β Ψ)
=...− ϵ0 ϵa ∂α Ψ∂β Ψ/8 π
CCDS IIT Kgp 22

2
3
δℚμ ν
+ ζαβ(x ,t).
[3] Vella et al, PRE (2005).
Amit Bhattacharjee
 Thermal kinetics[1,2]
 For intense electric field,
Note that hydrodynamic flow must be accounted for in this limit, as electric drag can be
balanced by the backflow[3]
.
∂t Ψ(x ,t)=∂⋅D ,
O(Ψ/ΨF )~O(ℚ).
O(Ψ/ΨF )≫O(ℚ).
2
3
δℚμ ν
+ ζαβ(x ,t).
=ϵ0(ϵs ∂2
=...− ϵ0 ϵa ∂α Ψ∂β Ψ/8 π
CCDS IIT Kgp 22

2
3
δℚμ ν
+ ζαβ(x ,t).
⟨ζα β( x ,t)⟩ = 0 ,
⟨ζαβ( x ,t)ζμ ν(x ' ,t ')⟩ = 2kB T Γ[δαμ δβν +δαν δβμ−
2
3
δαβδμ ν]δ(x−x')δ(t−t').
Amit Bhattacharjee
.
 Thermal force sets the temperature scale via FDT
∂t Ψ(x ,t)=∂⋅D ,
O(Ψ/ΨF )~O(ℚ).
2
3
δℚμ ν
+ ζαβ(x ,t).
=ϵ0(ϵs ∂2
=...− ϵ0 ϵa ∂α Ψ∂β Ψ/8 π
CCDS IIT Kgp 22

2
3
δℚμ ν
+ ζαβ(x ,t).
⟨ζα β( x ,t)⟩ = 0 ,
⟨ζαβ( x ,t)ζμ ν(x ' ,t ')⟩ = 2kB T Γ[δαμ δβν +δαν δβμ−
2
3
δαβδμ ν]δ(x−x')δ(t−t').
Amit Bhattacharjee
.
 Thermal force sets the temperature scale via FDT
 In dry limit, Stokes-Einstein equation dictates the viscosity.
∂t Ψ(x ,t)=∂⋅D ,
O(Ψ/ΨF )~O(ℚ).
2
3
δℚμ ν
+ ζαβ(x ,t).
kB T
K η
= constant , K=Frank constant .
=ϵ0(ϵs ∂2
=...− ϵ0 ϵa ∂α Ψ∂β Ψ/8 π
CCDS IIT Kgp 22

2
3
δℚμ ν
+ ζαβ(x ,t).
Amit Bhattacharjee
.
 Stochastic MOL approach : change of basis.
∂t Ψ(x ,t)=∂⋅D ,
O(Ψ/ΨF )~O(ℚ).
∂t ℚαβ(x,t)=−Γ[δαμ δβν+δα ν δβμ−
2
3
δαβδμ ν]δ ℱ total
δℚμ ν
+ ζαβ(x,t).
=ϵ0(ϵs ∂2
=...− ϵ0 ϵa ∂α Ψ∂β Ψ/8 π
CCDS IIT Kgp 22
8 X 107
d .o. f on1024 nodes(Kabru)IMSc
Finite Difference Method Explicit/Implicit
GSL C code (serial) + HDF5
PETSc C code (parallel) + HDF5
108
d.o.f on256nodes(TUE−CMS)IISc

Amit Bhattacharjee
 Droplet morphology & nucleation kinetics in 5CB material.
Experimental reproducibility of SMOL
Experiment Theory
CCDS IIT Kgp 23
ℱ =−∫V
dV ℱ bulk(ℚ) + ∫∂ S
dS ℱ surf (∂ ℚ)

[1] Chen et al, Langmuir (2007),
Bhattacharjee, Sci.Rep. (2017).
[2] Turok etal, PRL(1991), Science(1994).
Amit Bhattacharjee
 Droplet morphology & nucleation kinetics[1]
in 5CB material.
 Intercommutation events and,
Kinetics of disclination surface density[2]
 Both thermal fluctuation and elastic anisotropy tend to
increase string density without affecting the physical laws.
ρ = t−1∓0.001
.
Experimental reproducibility of SMOL
CCDS IIT Kgp 24
TheoryExperiment

Amit Bhattacharjee
 Electric field is switched on at and switched off at
 Disclinations are long lived[1]
in the presence of electric field.
Electrokinetics in uniaxial nematic
ton toff .
ton toff
disclinationdensity(inμm−2
)
t(in ms)
10
0
10
1
10−2
10−1
10−2
EF
10−1
EF
100
EF
no field
10−2
EF
10−1
EF
100
EF
ϵa>0ϵa<0
CCDS IIT Kgp 25

 Electric field is switched on at and switched off at
 Disclinations are long lived[1]
in the presence of electric field.
Energy of a planar disclination:
elastic energy / unit length = drag force / unit area
equilibrium kinetics
electric field effect

= π K k2
ln(
ξ
ζ
)−
π ϵ0 ϵa
4k
E2
(ξ2
−ζ2
)+ ℱ discl
c
.
ℱ discl = ∬d2
x[K (∂ f )2
−ϵ0 ϵa E2
sin2
f ]/2 ,
ton toff .
ton toff
(with f =k ϕ+c ,0≤ϕ≤2 π , k=±
1
2
).
)
t(in ms)
10
0
10
1
10−2
10−1
10−2
EF
10−1
EF
100
EF
no field
10−2
EF
10−1
EF
100
EF
ϵa>0ϵa<0
ℱ discl
ξ
−η∂t ξ
ξ = t−1/ 2
.
ξ = e
νt
, ν=
π ϵ0 ϵa E2
8k η
.
Thus ,
ϵa
k
>0 holds for both sign of k and ϵa ,leading to a slowed down kinetics .
CCDS IIT Kgp

 Electric flux lines are inherently nonuniform for
 String cores remain with sufficiently-reduced nematic
order, such that they aren’t influenced much by
the electric forces, even if the director is aligned.
 The medium exhibits memory in between an
elastic response to the field.
[1] Vella et al, Phys.Rev.E (2005).
E≤EF for both ϵa<0and ϵa>0.
10
−1
EF10
−2
EF 10
0
EF
100μ m
S&∂Ψ(inVμm−1
)
 We qualitatively find BL lines[1]
connecting strings for that we
don’t quantify in devoid of backflow.
E≥2 EF
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Comparison between uniform/nonuniform scenario with/without one elastic approximation.
100μ m
S&∂Ψ(inVμm−1
)
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Application: electrokinetics in biaxial nematic
t=0.96ms t=1.5 ms t=4.5 ms t=7.5 ms
 In Biaxial nematic media also the flux
lines are highly nonuniform and electric
field dilates the disclination kinetics.
 Depending on the sign of , electric
field filters out strings of different
topology by inducing a kinetic
asymmetry.
ϵa>0ϵa<0
ϵa
Cz
C y
toff =∞
ton=1ms
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asymmetry.
 Recall that for a planar string,

ϵa>0ϵa<0
ϵa
Cz
C y
ξ = eνt
, ν=
π ϵ0 ϵa E
2
8k η
.
Thus,
ϵa
k
yields ± sign for different topological string, leading to a faster decay of either class.
)
t(in ms)
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Conclusions
Unlike droplet nucleation kinetics, thermal fluctuations do not play a dramatic role other than
slowing down the athermal kinetics and increasing the disclination density.
Electric field is inherently nonuniform in the pure sample [while ] and it’s not
the colloidal impurity that brings nonuniformity in the electric field structure.
Uniformity in the electric field is obtained as the Fréedericksz limit is reached, thus a term
proportional to “EQE” in the GLdG free energy is valid only in the intense electric field limit
where backflow plays a crucial role.
Combination of thermal fluctuation and nonuniform electric field results into a time dilated
disclination kinetics.
Electric field cannot influence the disclinations to orient along/perpendicular to the field
direction, even when the director is oriented.
The nonuniform electric field induces a memory to the system within the elastic response &
induces a kinetic asymmetry between the different class of disclinations in biaxial nematics.
O( Ψ
ΨF
)~ O(ℚ)
Results
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Conclusions
Amit Bhattacharjee
Methods
Conclusions
CCDS IIT Kgp 31
Without using traditional methods, we directly identify defect location from the structure of
Q tensor & classify them by computing a Burger’s circuit integral.
Fluctuating Electronematics is an efficient, 2nd
order accurate numerical scheme that
brings control over various key-components of this complex problem.
Without calculating the traditional correlators, a dynamic length scale is extracted from the
geometry of the disclinations using surface triangulation method.

 “Stochastic Electronematics” solver in 3D for Maxwell-GLdG integrator (explicit) using PETSc.
 Gay-Berne NEMD for anisotropic droplet nucleation using LAMMPS.
 Kinetic Monte Carlo (KMC), GENERIC formalism (LME) and Chemical Langevin Equation (CLE)
integrator for dimerization reaction, Schlögl reaction and Baras-Pearson-Mansour model.
 Compressible fluctuating hydrodyamics (CFHD) integrator with Law of mass action in 3D
collocative grid using BOXLIB.
 Low-Mach (incompressible) fluctuating hydrodyamics (IFHD) integrator on 3D staggered grid
using BOXLIB.
 Dissipative particle dynamics with Lees-Edwards boundaries for WCA/Yukawa forces in 3D.
 Stochastic Method of Lines (SMOL) integrator using GSL and PETSc.
 Method of Lines (MOL) serial integrator using GSL, Python & Spectral Collocation Method.
 Allen-Cahn explicit/implicit solver in 3D using PETSc.
Code Development/Data Handling
Experience handling of TB’s of data with HDF5.
Visuals: OpendX, Mathematica, Matlab, Ovito, BoxLib.

Research proposal
 Rare events under external forcing Next step is to combine Fluctuating Electronematics
with Nucleation Kinetics in liquid crystals.
The central idea is to manipulate the energetics and topology of a 3D nucleated droplet that
contains a hyperbolic hedgehog defect & to understand its kinetic pathway, structure &
response in free-standing film under non-uniform electric field.
∂t ℚαβ(x,t)=−Γ[δαμ δβν+δαν δβμ−
2
3
δαβ δμ ν ]δ ℱ total
δℚμ ν
+ ζαβ(x,t).
∂t Ψ=ϵ0(ϵs ∂2

Research proposal
 Rare events under external forcing
We also want to compare the GLdG field theory results with mesoscopic NEMD simulation
of Gay-Berne nematic system to gain control over the results whenever experiments are
unavailable. ( Work is done by a student at IISER-Bhopal). Also, flexoelectric switching
kinetics can be performed within the methodology.
Uij
GB
(r)=4 ϵ( ûi , û j , ^rij )
{[
σ0
rij−σ (ûi , ûj ,^rij)+σ0 ]
12
−
[
σ0
rij−σ( ûi , û j , ^rij)+σ0 ]
6
}
mi
¨⃗ri=−∑i≠j , j=0
N
⃗∇ Uij(⃗r ); Ii
¨⃗θi=−∑i≠j , j=0
N
(ûi×
∂Uij
∂ ûi
+Ti
E
)
∂t ℚαβ(x,t)=−Γ[δαμ δβν+δαν δβμ−
2
3
δαβ δμ ν ]δ ℱ total
δℚμ ν
+ ζαβ(x,t).

Research proposal
 Externally driven colloids in Here we want to combine Fluctuating Electronematics in liquid
anisotropic media crystals with Brownian dynamics for colloids.

Research proposal
 There are other simpler methods (Zumer et al, Onuki et al, Tasenkevych et al) to include
colloids in nematic. Electro-rheology of knotted colloids is yet to be understood.
ℱ total=∫V
dV (ℱ bulk+ ℱ elastic +ℱ dielec)+∫S
dSℚij ^ui ^uj .
Rapini-Papoular
Energy

Research proposal
There are other simpler methods (Zumer et al, Onuki et al, Tasenkevych et al) to include
colloids in nematic. Electro-rheology of knotted colloids is yet to be understood.
We could add chemical reaction / activity to the particles to understand much more complex
phenomena. Additionally, by solving three equations for , phase separation
dynamics of CNT/Polymer dispersed NLC phases can be studied within the model.
Φ
CNT
,Ψ
EF
,ℚ
UN

Research proposal
 Orientational Glassy Rheology
Vitrification in sheared-anisotropic systems is not well-understood, unlike simple-colloidal
system. I’ll create a supercooled dense melt of GB particles & explore the Geometry, e.g.
Couette, Poiseuille flow, Bauschinger effect & compare the structure-kinetics with previous.
I want to study in detail these responses as there can be fascinating phenomena attached
with rod-like systems, e.g. shear induced crystallization, lane-formation using LAMMPS. This
computation will not be too data-heavy as compared to previous, but will require sufficient
supercomputing time for equilibration of, even, 1000 GB particles.
mi
¨⃗ri=−∑i≠ j, j=0
N
⃗∇ Uij(⃗r ); Ii
¨⃗θi=−∑i≠ j, j=0
N
(ûi×
∂Uij
∂ ûi
+Ti
E
)
Uij
GB
(r)=4 ϵ( ûi , ûj , ^rij)
{[
σ0
rij−σ(ûi , ûj ,^rij)+σ0
]
12
−
[
σ0
rij−σ(ûi , ûj ,^rij)+σ0
]
6
}

Research proposal
 Understanding nemato-hydrodynamics in presense of external agents, e.g. Carbon Nanotube,
semi-flexible polymers etc.
Eventually I want to prepare a Landau-Lifshitz-Navier-Stokes velocity solver combined
with the Q-tensor dynamics and external scalar/ vector field. Nemato-hydrodynamics is
one of the hardest problems in liquid crystals due to incorporation of anisotropic stresses
and algorithm development, which is largely explored in lattice-Boltzmann method (LBM).
Collaboration with Prof. P.T. Sumesh, Chem.Engg. IIT
Madras to understand rheochaos and various states arising
in a sheared nematic system in 2D using LBM. Initial work
was done by a summer research student from IIT Bombay.
(a) To develop LLNS + Q-dynamics using staggered-grid,
finite-volume method, (b) Recently developed theoretical methods of coupling Q and
equation in PETSc / Numpy-Scipy.
 Long-term goal: understanding response in active system & compare with particle simulations.
ϕ

Teaching proposal
 Soft Condensed Matter Science Introductory course on materials science in the classical
physics domain. Knowledge of Thermodynamics and Statistical Mechanics is required.
 Classical field theory Thermodynamics of Irreversible Processes (TIP), Stochastic
Calculus, Elasticity theory, Stochastic Calculus.
 Numerical Analysis Computational basics, Linear solvers, Root finding, data-handling etc.
 Computational materials science MD/NEMD, coarse-grained methods, CFD.
I am conversant with UG/PG level introductory course in a Physics curricula, e.g. Math
Methods, Classical Mechanics, Electrodynamics, Heat & Thermodynamics, Solid State
Physics, Statistical Mechanics, Waves & Oscillations etc.
Thank You

asymmetry.
 Recall that for a planar string,

 This is attributed to an increase (decrease) of total free energy for positive (negative)
ϵa
ξ = eνt
, ν=
π ϵ0 ϵa E
2
8k η
.
Thus ,
ϵa
k
yields ± sign for different topological string, leading to a faster decay of either class .
ϵa .
no field
ϵa>0
ϵa<0
−1.86
−1.76
−1.66
0.05
0.10
0.15
−1.90
−1.89
−1.88
energydensity(inJcm
−3
)
bulkisotropictotal
t(in ms)
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