# Dibyendu Das

# Associate Professor

##### Contact Information

Address : Physics Department, IIT Bombay, Powai, Mumbai 400076, India.

E-mail: dibyendu@phy.iitb.ac.in

Telephone : 25767555 (Office), 25768555 (Residence)

Fax : 25767552

# Academic Qualifications

I.S.C. (10+2, St. Pauls Mission School, Calcutta, in 1990.)

B.Sc. (Presidency College, University of Calcutta, in 1993.)

M.Sc. (IIT Kanpur, in 1995.) **Ph.d.** * (Tata Institute of Fundamental Research, Mumbai, India, in 2000.)*

Post-doctoral fellow (Brandeis University, USA, 2000-2002.)

Post-doctoral fellow (Laboratoire LPTMS, Universite Paris Sud, Orsay, France, 2002-2003.)

Faculty (IIT Bombay, India, 2003 - now.)

# Research Interests

The research in our group deals with theoretical analysis of simple models aimed to understand soft matter and biological phenomena. Statistical mechanics, theory of stochastic processes, and non-linear dynamics, provide theoretical tools to study them. Below, I highlight some of my published and ongoing works.

1. *Stochastic processes in biological systems*

*I) Collective motion of cells:*

Experiments on collectively moving cells exhibit large scale velocity ordering, pattern formation, and large traction force fluctuations in wound healing assays. We study dynamics of simple statistical mechanical models of visco-elastic sheets with heterogeneity to see if some of these features can be understood.

(i) ``Broad-tailed force distributions and velocity ordering in a heterogeneous membrane model for collective cell migration’‘, *Europhys. Lett.* **99**, 18004 (2012).

*II) Stochastic population dynamics of microbes:*

It is well-known from the old works of Luria and Delbruck that growth phases of microbial populations undergoing birth and spontaneous mutations exhibit “giant fluctuations” violating central limit theorem. Recently we have shown that models of more complicated ecological scenarios like viral infection of bacteria (undergoing Lysis-lysogeny), and horizontal gene transfer among bacterial species, may exhibit very similar fluctuations in certain limits.

(i) “Giant number fluctuations in microbial ecologies”, *Jr. Theo. Bio.* **308**, 96 (2012).

2. *Active biological and driven granular matter*

Study of spatio-temporal pattern formation in flocks of animals (birds, fishes, insects, bacteria), in motile actin and microtubule assays, and in driven granular disks and rods have been an active area of research over the past decade. Theoretically these systems are studied using rule based models of discrete objects, as well as coarse-grained continuum approaches. We study general properties of density structure formation in several of these theoretical models.

(i) “Spatial structures and Giant number fluctuations in models of active Matter”, *Phys. Rev. Lett.* **108**, 238001 (2012).

3. *Polymer motion in laminar flow fields.*

In recent years, flourescent microscopic studies of single polymers in various laminar flows have revealed very accurate measures of static and dynamic properties of polymers. Flow patterns can be elongational, rotational, *shear*, or random. In particular, in shear flow, the polymer exhibits an interesting tumbling motion. We have studied the latter phenomenon recently for a flexible polymer (see (i) and (ii)). Other first passage problems related to polymer motion have been studied in (iii) and (iv) below.

(i) “Dynamics of a flexible polymer in planar mixed flow”, *J. Phys.: conf. ser.* **297**, 012007 (2011).

(ii) “Accurate statistics of a flexible polymer chain in shear flow” *Phys. Rev. Lett.* **101**, 188301 (2008).

(iii) “Persistence of a Rouse polymer chain under transverse shear flow”, *Phys. Rev. E* **75**, 061122 (2007).

(iv) “Persistence of Randomly Coupled Fluctuating Interfaces”, *Phys. Rev. E* **71**, 036129 (2005).

4. *Freely cooling granular gases.*

Granular systems (like sand or marbles) can be forced to flow (by shaking, or applying shear), but otherwise they freely cool. We have studied freely cooling granular gases using molecular dynamics, to understand universal properties of these systems. It turns out that as they cool and order, the ordering becomes spatially inhomogeneous. For a long time it has been speculated that this inhomogeneous clustering state is identical to that of a completely inelastic (sticky) gas, and its dynamics is governed by inviscid Burgers equation. We have shown (see (ii) and (iii) below) that this connection to sticky gas is *not true* at asymptotically large times for any realistic granular gas (in which inter-particle collision cease to be inelastic as very low relative velocities). We have also shown (in (i) below) that in 3-d, the system is different from the Burgers prediction in its energy decay.

(i) “Energy decay in Three-dimensional freely cooling granular gas”, *Phys. Rev. Lett.* **112**, 038001 (2014).

(ii) “Coarse grained dynamics of the freely cooling granular gas in one dimension”, *Phys. Rev. E* **84**, 031310 (2011).

(iii) “Lattice models for ballistic aggregation in one dimension”, *Europhys. Lett.* **93**, 44001 (2011).

(iv) “Equivalence of the freely cooling granular gas and the sticky gas”, *Phys. Rev. E* **79**, 021303 (2009).

(v) “Violation of Porod law in a freely cooling granular gas in one dimension”, *Phys. Rev. Lett.* **99**, 234505 (2007).

5. *Critical properties of statistical models*

The *Loop model* (related to the O(n) model) is an extensively studied model in equilibrium statistical mechanics literature. The model maps to models of self-avoiding polymers, magnets (Ising and XY), and dimers, for different values of its parameters. Recently we have solved this model, and some generalizations of it, on a fractal lattice, using exact real space renormalization group (see (i) below). We had shown earlier that this model on 2d hexagonal lattice, subjected to a *staggered field*, maps to critical Potts model (see (ii) below).

(i) “Critical behavior of loops and biconnected clusters on fractals of dimension d < 2”, *J. Phys. A: Math. Theor.* **41**, 485001 (2008).

(ii) “Two-dimensional O(n) model in a staggered field”, *J. Phys. A: Math. Gen.* **37**, 1-35 (2004).

# Awards

**American Physical Society (APS-IUSSTF) Professorship** award (2011) – delivered a lecture series at Colorado State University.

**Satyamurthy** award, from Indian Physics Association (2009).

**Excellence in teaching** award, from IIT Bombay (2008).

# Courses taught

1. Spring ‘10, ‘11, ‘12, ‘13: Statistical Mechanics (PH 304).

2. Autumn ‘07, ‘08: Advanced Statistical Mechanics (EP 403).

3. Spring ‘07, ‘08, ‘09, ‘14: Mathematical Methods II – Complex analysis and ODEs (PH 408).

4. Autumn ‘04, ‘05, ‘06, ‘09, ‘10, ‘11, ‘12: Classical Mechanics (PH 401, EP 222).

5. Spring ‘04, ‘05, ‘06: Electricity and Magnetism (PH 102).

# Ph.d. Students

1. *Mahendra Shinde*

Thesis: * Spatio-temporal pattern formation in freely cooling granular gases * (submitted – 2009; defended – June 2010).

Currently: Post-doctoral fellow (in JNCASR)

2. *Supravat Dey*

Thesis: Pattern formation in models of active matter, Dissipative gases on lattice, and intrinsic noise in chemical systems. (submitted – July 2012; defended – October 2012)

Currently: Post-doctoral fellow (in Rome, Italy)

3. *Dipjyoti Das*

Thesis: Collective cell migration, Statistical aspects of microbial evolution.

Currently: 5th year

4. *Aparna J.S.*

(In collaboration with Prof. Ranjith P. of Bio-Sc and Bio-Engg, IITBombay)

Thesis: Dynamics of bio-filaments, and amyloid aggregation.

Currently: 1st year

# Projects

1. Sponsored project (completed): Indo-French Center – **IFCPAR/CEFIPRA** (project no. 3404-2).

Period: 01.05.2006 – 30.04.2009.

Jointly with J.L. Jacobsen, Alain Comtet and S.N. Majumdar (of Laboratoire LPTMS., Orsay,France) and Deepak Dhar and Mustansir Barma (of TIFR Mumbai).

# Publications

29. “Energy decay in Three-dimensional freely cooling granular gas”,

Sudhir N. Pathak, Zahera Jabeen, *Dibyendu Das* and R. Rajesh, *Phys. Rev. Lett.***112**, 038001 (2014).

28. “Broad-tailed force distributions and velocity ordering in a heterogeneous membrane model for collective cell migration”,

Tripti Bameta, Dipjyoti Das, Sumantra Sarkar, *Dibyendu Das*, and Mandar Inamdar, *Europhys. Lett.***99**, 18004 (2012).

27. “Giant number fluctuations in microbial ecologies”,

Dipjyoti Das, *Dibyendu Das*, and Ashok Prasad, *Jr. Theo. Bio.***308**, 96 (2012).

26. “Spatial structures and Giant number fluctuations in models of active Matter”,

Supravat Dey, *Dibyendu Das*, and R. Rajesh, *Phys. Rev. Lett.***108**, 238001 (2012).

25. “Coarse grained dynamics of the freely cooling granular gas in one dimension”,

Mahendra Shinde, *Dibyendu Das*, and R. Rajesh, *Phys. Rev. E* **84**, 031310 (2011).

24. “Dynamics of a flexible polymer in planar mixed flow”,

Dipjyoti Das, Sanjib Sabhapandit, and *Dibyendu Das*, *J. Phys.: conf. ser.* **297**, 012007 (2011).

23. “Lattice models for ballistic aggregation in one dimension”,

Supravat Dey, *Dibyendu Das*, and R. Rajesh, *Europhys. Lett.***93**, 44001 (2011).

22. “Intrinsic noise induced resonance in presence of sub-threshold signal in Brusselator”,

Supravat Dey, *Dibyendu Das*, and P. Parmananda, *Chaos* **21**, 033124 (2011).

21. “Predicting the coherence resonance curve using a semianalytical treatment”,

Santidan Biswas, *Dibyendu Das*, P. Parmananda, and Anirban Sain,

*Phys. Rev. E***80**, 046220 (2009).

20. “Equivalence of the freely cooling granular gas to the sticky gas”,

Mahendra Shinde, *Dibyendu Das*, and R. Rajesh, *Phys. Rev. E***79**, 021303 (2009).

19. “Accurate statistics of a flexible polymer chain in shear flow”,

*Dibyendu Das* and Sanjib Sabhapandit, *Phys. Rev. Lett.***101**, 188301 (2008).

18. “Critical behavior of loops and biconnected clusters on fractals of dimension d < 2”, *Dibyendu Das* , Supravat Dey, Jesper Lykke Jacobsen, and Deepak Dhar, *J. Phys. A: Math. Theor.***41**, 485001 (2008).

17. “Violation of Porod law in a freely cooling granular gas in one dimension”,

Mahendra Shinde, *Dibyendu Das*, and R. Rajesh, *Phys. Rev. Lett.***99**, 234505 (2007).

16. “Persistence of a Rouse polymer chain under transverse shear flow”,

Somnath Bhattacharya, *Dibyendu Das*, and Satya N. Majumdar, *Phys. Rev. E* **75**, 061122 (2007).

15. “Motion of a random walker in a quenched power law correlated velocity field”,

Soumen Roy and *Dibyendu Das*, *Phys. Rev. E***73**, 026106 (2006).

14. “Critical Dynamics of Dimers: Implications for the Glass Transition”, *Dibyendu Das*, Greg Farrell, Jane’ Kondev and Bulbul Chakraborty,

*J. Phys. Chem. B* **109**, 21413 (2005).

13. “Persistence of Randomly Coupled Fluctuating Interfaces”,

Satya N. Majumdar and *Dibyendu Das*, *Phys. Rev. E***71**, 036129 (2005).

12. “Landau-like theory of glassy dynamics”,

Satya N. Majumdar, *Dibyendu Das*, Jane’ Kondev, and Bulbul Chakraborty, *Phys. Rev. E***70**, 060501 (Rapid communications) (2004).

11. “Two-dimensional O(n) model in a staggered field”, *Dibyendu Das* and Jesper Lykke Jacobsen, *J. Phys. A: Math. Gen.***37**, 1-35 (2004).

10. “Activated dynamics at a non-disordered critical point”, *Dibyendu Das*, Jane’ Kondev and Bulbul Chakraborty, *Europhys. Lett.***61** (4), 506 (2003).

9. “Topological jamming and the glass transition in a frustrated system”,

Bulbul Chakraborty, *Dibyendu Das*, and Jane’ Kondev, *Eur. Phys. J. E* **9**, 227 (2002).

8. “Jamming in a model glass: Interplay of dynamics and thermodynamics”,

Bulbul Chakraborty, *Dibyendu Das*, and Jane’ Kondev, *Physica A* **318**, 23 (2003).

7. “Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates”,

R. Rajesh, *Dibyendu Das*, Bulbul Chakraborty, and Mustansir Barma, *Phys. Rev. E***66**, 056104 (2002).

6. “Phase diagram of a two-species lattice model with a linear instability”,

Sriram Ramaswamy, Mustansir Barma, *Dibyendu Das* and Abhik Basu,

*Phase Transitions* **75** (Nos. 4 & 5), 363 (2002).

5. “Fluctuation dominated phase ordering driven by stochastically evolving surfaces: depth models and sliding particles”, *Dibyendu Das*, Mustansir Barma and Satya N. Majumdar, *Phys. Rev. E***64**, 046126 (2001).

4. “Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: effects of kinematic waves”, *Dibyendu Das*, Abhik Basu, Mustansir Barma and Sriram Ramaswamy, *Phys. Rev. E* **64**, 021402 (2001).

3. “Particles sliding on a fluctuating surface: phase separation and power laws”, *Dibyendu Das* and Mustansir Barma, *Phys. Rev. Lett.***85**, 1602 (2000).

2. “Arrested states formed on quenching spin chains with competing interactions and conserved dynamics”, *Dibyendu Das* and Mustansir Barma, *Phys. Rev. E* **60**, 2577 (1999).

1. “Polytype kinetics and quenching of spin chains with competing interactions using trimer-flip dynamics”, *Dibyendu Das* and Mustansir Barma, *Physica A* **270**, 245 (1999).