Interdisciplinary Research Group on Complex Systems

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Interdisciplinary Research Group onComplex
Systems

• Indian Institute of Technology Madras,
• Chennai , India.

http//www.iitm.ac.in
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Broad Areas of Investigation
http//www.physics.iitm.ac.in/labs/dynamical http
//www.physics.iitm.ac.in/labs/cfl http//www.che
.iitm.ac.in/hpel

• Complex Fluids
• Complex Networks
• Dynamical Systems
• Quantum Computing and Information
• Also,
• Artificial Intelligence, Cognitive studies
• (Dept. of Comp. Sci.)
• Management Studies (Dept. of Mgmt. Stud.)

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Complex Fluids Background

• Complex media ranging from gels, suspensions to
  composite solids are the basis of much of
  state-of-the-art technology.
• Dynamical response is characterized in terms of
  generalized susceptibilities.
• Tools from equilibrium and non-equilibrium
  statistical mechanics, stochastic techniques.
• Technical problems randomness arising from
  disorder, inhomogeneity and anisotropy, multiple
  length scales and time scales.

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Complex fluids
Faculty students includes

• A. K. Mishra, P. B. Sunil Kumar, Susy
  Varughese, Abhijit P. Deshpande, Sanoop
  Ramachandran, Snigdha Thakur, K. Jayasree, N. G.
  Praveen, P. Ranjith, K. C. Lakshmi, S.
  Balakrishnan, S. Sriram

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Activities in Complex Fluids and Collaborating
Institutes

• Micellar Solutions
• Nucleation and growth in Liquid Crystal mixtures
  (Uni. Bayreuth - Germany)
• Elasticity of Cytoskeleton (Helsinki Uni. Of
  Tech. - Finland)
• Active Colloidal Suspensions (Uni. Barcelona -
  Spain)
• Statistical Mechanics of Lipid Membranes.
  Electrostatic effects in DNA-Protein interaction
  (Uni. Southern Denmark)
• Active membranes (RRI - Bangalore, Uni. Memphis -
  USA)

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Complex Networks
Faculty students include
Neelima Gupte, Zahera Jabeen, Satyam Mukherjee,
Nirmal Thyagu

• Spatially extended systems, coupled-map lattices
• Structure, function and optimization of networks
• Small world networks

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Networks Structure, function and optimisation

• The structure and connectivity properties of
  networks have
• important consequences for their function
  and efficiency. Useful
• to ask whether these properties can be
  exploited to enhance the
• performance and efficiency of networks.
• Question examined in two specific contexts
  the load-bearing
• properties of a branching hierarchical
  network, and jamming and
• congestion in a two-dimensional
  communication network.
• The capacity and performance of these networks
  can be
• enormously enhanced by the judicious
  manipulation of
• connectivity properties. Our results have
  relevance in the
• general context of information spread
  processes on networks.

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Spatio-temporal Intermittency and Scaling laws in
Coupled-Sine Circle Maps

• The phase diagram of the system shows parameter
  regimes where the
• STI lies in the directed percolation class,
  as well as those which show
• pure spatial intermittency (where the
  temporal behaviour is regular) which
• do not belong to the DP class.
• Signatures of DP and non-DP behaviour can be
  seen in the spectrum of
• eigenvalues of the linear stability matrix
  of the evolution equation,
• as well as in the multifractal spectrum of
  the eigenvalue distribution.
• Spectrum in the DP regimes is continuous,
  whereas it shows
• evidence of level repulsion in the form of
  gaps in the non-DP regime.
• These results have implications for the manner
  in which correlations build
• up in extended systems.

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Mixing and De-mixing Behaviour in
Area-preserving Maps

• A variety of problems, where the mixing and
  demixing behaviour of
• chaotic Lagrangian flows has practical
  implications, have been studied
• in recent years. The transport of impurities
  in flows depends on the flow
• characteristics, and has practical
  implications in a variety of contexts.
• Lagrangian flows, and the behaviour of
  impurities suspended in such
• flows can be studied via area and volume
  preserving maps and flows.
• We study the mixing and de-mixing properties of
  such systems, analyse
• their behaviour under parameter
  perturbations, and also set up
• characterisers for their analysis.

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Dynamical Systems
Faculty students includes
S. Lakshmibala, A. Lakshminarayan, V.
Balakrishnan, C. Sudheesh, N. Meenakshisundaram,
S. Sree Ranjani, S. Seshadri

• Randomness and entropy in classical and quantum
  systems ergodicity, mixing, dynamical chaos
• Recurrences in chaotic dynamics
• Stochastic processes, random walks and
  applications transport in amorphous media,
  threshold crossing and extreme value statistics
• Quantum wave packet revival phenomena wave
  packet propagation in nonlinear media geometric
  phases entanglement dynamics
• Quantum chaos

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Threshold-crossing statistics in non-stationary
stochastic flows

• Driven stochastic processes with time-dependent
• control parameters or time-varying external
  forcings
• occur very frequently applications (driven
  chemical,
• biological and atmospheric processes, as well
  as
• stochastic processes in economics and related
  fields of
• application).
• Information regarding a random process is
  usually
• obtained is via moments. This is of a
  global' character,
• as it involves averaging over the distribution
  of the
• variate.

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• Much more local probe provided by the statistics
  of the level-crossings of such processes across a
  prescribed threshold, and by related aspects such
  as extreme value statistics and order statistics.
  
• The threshold-crossing statistics of stochastic
  flows driven by white noise and by coloured
  noise, and with time-dependent control
  parameters, has been
• analyzed.
• G. Nicolis, V.Balakrishnan C. Nicolis, Phys.
  Rev. E 65, 051109(2002)
• V.Balakrishnan, G. Nicolis C. Nicolis,
  Proc. of. Sci. (2005)
• Extreme value distributions in chaotic
  dynamics.
• V. Balakrishnan, G. Nicolis C. Nicolis, J.
  Stat. Phys. 80, 307 (1995)

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Wavepacket Dynamics, Non-Classical Effects
Entanglement in Single-Mode Propagation Through a
Nonlinear Medium

• Wavepacket revivals and fractional revivals in
  the propagation of a radiation field through a
  kerr medium signatures of a revival phenomena
  in expectation values and higher moments of
  observables.
• C. Sudheesh, S. Lakshmibala and V.
  Balakrishnan,
• Phys. Lett. A, 329, 14 (2004).
• Effects of departure from coherence of the
  initial wavepacket propagating in a nonlinear
  medium dynamics of a photon added coherent
  states.
• C . Sudheesh, S. Lakshmibala and V.
  Balakrishnan,
• Europhys. Lett., 71, 744 (2005)

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• Squeezing and higher-order squeezing properties
  of wavepackets propagating in a Kerr medium
  signatures of departure from coherence of the
  initial radiation field.
• C. Sudheesh, S. Lakshmibala and V.
  Balakrishnan,
• J. Opt. B Quant. Semiclass. Opt., 7, 5728
  (2005)
• Entangled two-mode states and entropy of
  entanglement in wavepacket dynamics, analogues of
  revivals and near-revivals and signatures.
  Effects of departure from coherence of an
  electromagnetic field mode interacting with the
  modes of the atoms in a nonlinear medium through
  it propagates.
• C. Sudheesh, S. Lakshmibala and V.
  Balakrishnan,
• arXivequant-ph/060320

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Eigenfunctions of Quantum Chaos

• Background
• Quantum Chaos The analysis of quantum systems
  whose classical limit corresponds to a chaotic
  Hamiltonian system. (eg. atoms in strong fields,
  quantum dots, quantum optics, nuclear physics
  etc..)
• Eigenfunctions of quantum chaos Analytical
  structure little known. Most are ergodic", many
  are localized on classical chaotic orbits,
  scarring". Statistical modelling via Random
  Matrix Theory successful. However no exactly
  solvable simple generic models exist (like the
  left -shift of classical chaos).

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• Relavant Highlight
• Nearly exact expressions for eigenstates of a
  paradigmatic model, the quantum bakers map, are
  found.
• These eigenstates are found to be dominated by
  Automatic Sequences, such as the Thue-Morse
  sequence. Simplest Model of deterministic
  disorder appears naturally in these quantum
  chaotic states.
• Eigenstates are generally multifractals, with
  peaks dominated by periodic orbits and their
  homoclinic excursions. Best examples of these
  states named "Thue-Morse states".

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The Thue-Morse state

• References
• N. Meenakshisundaram Arul Lakshminarayan Phys.
  Rev. E. 71 065303(R) (2005),
• Arul Lakshminarayan J. Phys. A 38 L597-L605
  (2005)

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Complexity and Quantum Information

• Background
• Entanglement has been recently studied to
  characterize complex quantum systems, for example
  at quantum phase transitions. We are studying
  the nature of entanglement across
  integrable-chaotic transitions, using various
  spin models and random matrix theory (RMT).
• Relevant Highlights
• If a bipartite system is completely chaotic then
  the eigenvalues of the reduced density matrix of
  typical eigenstates or time-evolving states have
  an universal distribution. This implies that the
  entanglement is nearly maximal for such states.
  Thus chaos encourages bipartite entanglement in
  bipartite systems.
• If subsystems are chaotic and coupling is weak to
  moderate perturbation theories combined with RMT
  describe entanglement production completely.
• One particle state of nonintegrable spin chains
  have universally distributed concurrence
  distributions. Time-reversal violating states
  share entanglement better.
• Multipartite entanglement can be enhanced with
  increasing nonitegrability often it seems at the
  expense of bipartite entanglement.

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Quantum Computation and Information
Faculty students includes
Arvind, Kavita Dorai, Arul Lakshminarayan,
Gurpreet Kaur, S. Begam Elavarasi

• Ensemble Quantum Computing
• Quantum Channels
• NMR Quantum Computing
• Spin Relaxation in Macro /Bio Molecules
• Complexity and quantum information
• Entanglement in spin chains
• Quantum random walks

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Interests

• Quantum cryptography, the physical implementation
  of quantum computers, and quantum channels.
• Theoretical and experimental investigations of
  ensemble quantum computers (nuclear spins in
  liquid).
• Study of quantum channels, which play an
  important role in quantum cryptography, in the
  storage and processing of quantum information,
  and help model the effects of decoherence.
• Linear optical implementations of quantum
  information processors where only optically
  passive (compact canonical transformations) are
  used to implement universal quantum gates.
• Study of decoherence in quantum systems and
  modeling of environment using master equations
  where we study the evolution of quantum phase
  space distributions for multi-mode systems.

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• NMR quantum computing Developing novel pulse
  schemes to experimentally implement quantum
  algorithms, initialisation methods to prepare the
  system in a known quantum state, and readout
  methods based on density matrix reconstruction.
• Constructed NMR schemes for multiqubit quantum
  gates that implement several unitary transforms
  simultaneously. We have also developed an
  initialisation method based on logical labelling
  of qubits, using selective pulse cascades and
  multiple quantum excitation.
• More recently, we experimentally implemented the
  Quantum Fourier Transform using selective pulse
  cascades. We found the most efficient
  decomposition to be the product of a
  non-selective Hadamard transformation on all the
  qubits followed by multiqubit gates corresponding
  to square - and higher-roots of controlled-NOT
  gates.

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Flow structures in lid driven cavity
Sinusoidal lid motion

• Dynamics of
• flow
• mixing

Newtonian fluid
Plate position 2
Plate position 1
Elastic fluid (polymer solution)
Vortical structures of interest
Viscosity 25 cP Frequency 1 s-1
Amplitude 0.05 m
Micellar solution (CTAB)
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Natural surfactants Saponin from Soapnut tree
(Sapindus mukurossi)
Critical micelle concentration

• Micellar characterization
• Applications
• Environmental remediation
• Solubilization
• Personal care
• Rheology

High concentration
Pouring
Applying
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Emission Spectra
Thermoreversible gels Poly n-isopropylacrylamide
(PNIPAM)
1-anilinonaphthalene-8-sulphonate (ANS)

• Fluorescence techniques
• steady state fluorescence spectroscopy
• life time measurements
• steady state and transient anisotropy
  measurements

Nile Blue (NB)
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Phase separation dynamics - mixtures of
isotropic liquid and liquid crystals.Snigdha
Thakur, P B Sunil KumarPramod Pullarkat,
University of Bayreuth - Germany

• Nematic Liquid Crystal Isotropic Liquid
• Only miscible in isotropic phase.
• Focus is on off-symmetric mixture case.
• Polarization and fluorescence microscopy
• is used for the studies.

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Phase separation dynamics - mixture cooled below
the isotropic-nematic transition temperature.

• Nematic phase nucleate and
• coalesce.
• Directed motion of smaller
• drops towards bigger.
• Drop velocity depends on
• cooling rate.
• Fluorescence microscopy
• confirms the expulsion of the
• isotropic component from the
• nematic liquid crystal.

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Origin of the attractive interaction

• Expulsion of the isotropic component makes
  concentration gradient around the nematic drops.
• Gradient of tension around the drop surface which
  propels the drops.
• Figure shows the asymmetric drop resulting from
  the impurity concentration dependent surface
  tension.

Other Possible Mechanisms

• Dipolar interaction? But the drop velocity
  depends on the cooling rate.
• Hydrodynamic flow ? But dust particle are
  not moving unless pushed
• by the big drops.
• Director filed distortions in the drop? But
  the interaction is mediated
• through an isotropic medium.

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Active colloids Lattice-Boltzmann(LB) model
Sanoop Ramchandran,P B Sunil Kumar and Ignacio
Pagonabaraga (University of Barcelona)

• Simulation of self-propelled
• particles, in two-dimensions.
• Low Reynolds number
• motion.
• Role of hydrodynamic
• interaction in the onset of
• collective behavior.

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• We use Lattice Boltzmann technique
• to simulate the fluid (Ladd- 1994)
• The particle exerts a force on the
• surrounding fluid in such a way that
• the total force exerted is zero.

Mover fluid profile
Shaker fluid profile
Model two types of particles Movers (asymmetric
force distribution) and Shakers (symmetric force
distribution).
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Typical fluid velocity distribution

• We investigate
• Changes in Temperature and Viscosity
• due to particle motion .
• Fluid mediated interaction between
• movers and Shakers
• Collective Motion

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Strain hardening in a dynamic elastic network a
model for cytoskeleton
P. B. Sunil Kumar Jan Astrom, Mikko Karttunen,
Ilpo Vattulainen, Helsinki University of
Technology - Finland
Electron Micrograph of actin (rods) and other
proteins in cell cytoskeleton (400 nm x 400
nm) Medallia et.al. Science 298 , 1210 (2002)
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Setup for single cell stretching experiments
Nonlinear response Stiffness as a function of
force
P. Fernadez, P. Pullarkat and A. Ott - Bayreuth
University, Germany- Private communication
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Side and Top view of cytoskeleton modeled as
random network of elastic beams. The model allows
for geometry change as a function of time.
Nonlinear response of the network.

Differential stiffness For an oscillating
strain of
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Activities

• Weekly Complex Systems Seminars.
• International conference, 12-15 July 2004,
• ("Perspectives in Nonlinear Dynamics").
• Active involvement in national conference series
  on Nonlinear Systems and Dynamics
• On-going collaborations with groups at Univ. of
  Barcelona, Univ. of Southern Denmark, Helsinki
  Univ. of Technology, Univ. Bayreuth, ULB
  Brussels, Hasselt Univ., IIT Kanpur, PRL
  Ahmedabad, JNU New Delhi, IMSc Chennai, RRI
  Bangalore, CMU Pittsburgh, IISc Bangalore, ICTP
  Trieste and others.
• Publications research papers, reports,
  dissertations, books.

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Some Relevant Courses Introduced at IIT Madras

• Dynamical Systems
• Dynamics of Chemical and Biological Systems
• Advanced Statistical Physics
• Advanced Dynamical Systems
• Simple and Complex Fluids
• Quantum Computation and Information
• Rheology of Polymers