Balakrishnan Ashok

Complex Systems, Nonlinear dynamics, Biomechanics & Biology-motivated problems, Theoretical Soft Condensed Matter  & Polymer Physics

Know more: Centre for Complex Systems & Soft Matter Physics

• Eros M. Sunny, Balakrishnan Ashok, Janaki Balakrishnan & Juergen Kurths. The ocean carbon sinks & climate change. Chaos 33, 103134 (2023).
• B. Ashok. "Logistic Attractors", in: Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series, B. S. Daya Sagar, Q. Cheng,  J. McKinley, F. Agterberg (eds), Springer, Cham. (2022).
• Brijesh K. Mishra and Balakrishnan Ashok. "Modeling multiwalled carbon nanotubes: from quantum mechanical calculations to mechanical analogues". Invited book chapter, in "Organized networks of carbon nanotubes", K.R.V. Subramanian, R. George & A.C.L. Rao (Eds.), CRC Press (2020). (ISBN 9780367278205).
• B. Ashok.  Tubes and containers at the nano and microscales: statics and dynamics. Indian Academy of Sciences Conference Series 2, 19-24 (2019).
• Brijesh Kumar Mishra and Balakrishnan Ashok. Coaxial carbon nanotubes: from springs to ratchet wheels and nanobearings. Mater. Res. Express 5, 075023 (2018).
• B. Ashok, Thotreithem Hongray and Janaki Balakrishnan. The charged bubble oscillator: dynamics and thresholds. Indian Academy of Sciences Conference Series (from Pramana: Journal of Physics) 1, 109 (2017).
• Balakrishnan Ashok. "Dynamics and kinematics at small scales: from micro and nano bubbles to nanotubulation". Book chapter in "Unifying themes in Complex Systems IX", A. J. Morales et al. (Eds.): ICCS2018, Springer Proceedings in Complexity, pp 210-219, Springer Nature (2018).
• T. Hongray, B. Ashok and J. Balakrishnan. Oscillatory dynamics of a charged microbubble under ultrasound. Pramana: Journal of Physics 84, 517-541 (2015).
• B. Ashok and G. Ananthakrishna. Dynamics of intermittent force fluctuations in vesicular nanotubulation. J. Chem. Phys. 141, 174905-1--174905-13 (2014).​
• T. Hongray, B. Ashok and J. Balakrishnan. Effect of charge on the dynamics of an acoustically forced bubble. Nonlinearity 27, 1157-1179 (2014).
• B. Ashok. "On the importance of length scales in determining the physics of biological systems", Chapter 7, p.53-64, in Nature's longest threads: new frontiers in the mathematics & physics of information in biology, eds. J. Balakrishnan & B. V. Sreekantan, World Scientific Publishing Co., Singapore (2014). ​
• B. Ashok and Tarak K. Patra. Locating phase transitions in computationally hard problems. Pramana: Journal of Physics 75, 549-563 (2010).
• J. Balakrishnan and B. Ashok. The role of Hopf bifurcation dynamics in sensory processes. J. Theor. Biol. 265, 126-135 (2010).
• N. Malik, B. Ashok and J. Balakrishnan. Noise induced synchronization in bidirectionally coupled Type-I neurons. Eur. Phys. J. B 74, 177-193 (2010).
• N. Malik, B. Ashok and J. Balakrishnan. Complete synchronization in coupled Type-I neurons. Pramana: Journal of Physics 74, 189-205 (2010).
• B. Ashok and M. Muthukumar. Crossover behavior of viscosity of dilute and semidilute polyelectrolyte solutions. J. Phys. Chem. B 113, 5736-5745 (2009).
• B. Ashok, M. Muthukumar and T.P. Russell. Confined thin film diblock copolymer in the presence of an electric field. J. Chem. Phys. 115, 1559-1564 (2001).

Teaching Experience in the recent past:
Core courses:

• Advanced mathematical physics-1 (including linear algebra and  vector spaces & tensor analysis, introduction to stochastic processes, etc) for the Physics Ph.D. programme
• Advanced mathematical physics-2 (including fluid mechanics and other topics) for the Physics Ph.D. programme
• Research & Publication Ethics for the Ph.D. programme
• Physics-1 (classical physics theory: including classical mechanics, E&M, thermodynamics, waves, etc.) for the Integrated M.Tech programme
• Physics-2 (modern physics theory: including statistical mechanics, quantum mechanics, special relativity, nuclear physics, etc.) for the Integrated M.Tech programme
• Physics Laboratory-1 for the Integrated M.Tech programme
• Physics Laboratory-2 for the Integrated M.Tech programme

Elective courses:

• Intoduction to nonlinear dynamical systems
• Elements of statistical physics
• Fundamentals of theoretical neuroscience

Research Guidance:

M. Tech. & M.Sc. Theses supervised:

At IIIT Bangalore:

• Mr. Amogh Johri, "Dynamical behaviour and learning algorithms for theta neuron coupled models & networks", integrated M. Tech. thesis, International Institute of Information Technology Bangalore (2022).

At the University of Hyderabad:

• Mr. G. Naresh Raghava, "Aspects of General Relativity & Astrophysics", M. Sc. Physics project, School of Physics, University of Hyderabad (2012).
• Mr. Tarak K. Patra, "Statistical Physics of Computationally Hard Problems",  M.Tech (Computational Techniques) Thesis, School of Physics, University of Hyderabad, (2008).

Courses taught earlier:
At the University of Hyderabad, Hyderabad (April, 2007 - May, 2012):

• Mathematical Physics (IP 452 / PY 204) for 6th Semester Integrated Masters programme, School of Physics, University of Hyderabad.

1. December 2010 - April 2011,
2. December 2009 - April 2010. 

• Classical Mechanics (PY 402) (core course), M.Sc. Physics, University of Hyderabad, July- November 2007 session. 
• Designed the syllabus & course material for the core course on Combustion & Related Phenomena (HEMPH 901) for Ph.D. & Research Students at ACRHEM, University of Hyderabad. 
• Taught the course for the semesters:

1. July - November, 2010,
2. July - November, 2008,
3. January - May, 2008.  

• Delivered some guest lectures as an introduction to polymers and polymer physics as part of a course on Concepts of Materials introduced at the School of Engineering, University of Hyderabad, in September, 2008.

Research interests:
Our research interests focus on the study of complex systems and soft matter physics. This involves the modelling of various physical & biological systems, using dynamical systems theory and methods. These include biomechanics (the dynamics and control of vesicular nanotubulation), diverse complex systems, instabilities in nonlinear systems, the dynamics of macromolecular & micellar solutions and their behaviour in flows, the control of block copolymer morphology using electric fields, bubble dynamics & cavitation and the related phenomenon of single-bubble sonoluminiscence, instabilities in combustion phenomena, and aspects of climate modelling using a dynamical systems approach. Other research interests include certain aspects of quantum computation.

Brief summaries of some of the topics of our research are given below.

Know more: Centre for Complex Systems & Soft Matter Physics, https://www.iiitb.ac.in/cssmp/

Locating phase transitions in computationally hard problems 

We discuss how phase-transitions may be detected in computationally hard problems in the context of Anytime Algorithms. Treating the computational time, value and utility functions involved in the search results in analogy with quantities in statistical physics, we indicate how the onset of a computationally hard regime can be detected and the transit to higher quality solutions be quantified by an appropriate response function. The existence of a dynamical critical exponent is shown, enabling one to predict the onset of critical slowing down, in the specific case of a Travelling Salesman Problem. This can be used as a means of improving efficiency and speed in searches, and avoiding needless computation.

Dynamics of vesicular nanotubulation

An interesting problem, one motivated by nanotubulation  experiments concerns the dynamics of vesicle-pulling. This phenomenon of nanotube formation has practical applications – e.g., the formation of networks of nanotubes and containers that can be formed through mechanical excitation of vesicles, useful in making nanofluid devices & drug delivery systems. We have theoretically investigated the dynamical  behaviour of a vesicle attached to a substrate and pulled with a constant velocity. We have considered the effects of change in vesicular geometry and various dissipative  effects that come into play as the lipid layers are pulled out to form a nanotube. Our theoretical model is in substantial qualitative agreement with experimental observations.

Bubble dynamics and cavitation 

Another problem under study is that of bubble dynamics and cavitation in fluids.  This occurs in various situations and is associated with various phenomena, ranging from the   cavitation damage to propellers of ships, single and multi-bubble sonoluminescence,    forced bubble oscillations in living tissue, shock-wave generation and cavitation by living organisms such as shrimps, the sound associated with running water -- the list goes on and on.  A forced oscillating bubble in a fluid is a very rich nonlinear system  which can show very surprising and interesting behaviour. We study the dynamics of  such a system, under acoustic forcing, using a modified Rayleigh- Plesset equation, investigating the effect of various physical parameters.

Dynamical instabilities, noise & sensory detection 

Living things depend upon their various senses for their survival. Sensory cells detecting  different modalities have developed sophisticated mechanisms to convey the various features of the external environment to the living system in the shortest possible time. The essential nonlinearities inherent in the signal transduction mechanism can take advantage of the noise from the environment the system is subject to, to display a highly amplified response to stimuli in a frequency-selective manner. We study the role of the Hopf bifurcation in detection of stimuli in sensory processes.

Synchronization in nonlinear systems 

We are also interested in the synchronization behaviour of nonlinear systems. Addition of weak noise may cause synchronization to occur in some systems.  We have studied noise-induced synchronization in a system of coupled nonlinear oscillators which exhibit self-sustained oscillations through global bifurcations.

Dynamics of coupled neurons

Studies of neuronal firing behaviour include investigations of neuron models as flows & maps, constructing models that replicate observed bursting behaviour, and understanding the dynamics of neuronal firing from a dynamical systems theory point of view.

Instabilities in combustion

We are also investigating, theoretically, the behaviour of combustion growth fronts under various conditions. Phenomena like fingering instabilities & effect of geometry on the combustion dynamics are sought to be understood. Another aspect being investigated focuses on issues of partial combustion.

Polyelectrolyte solutions, micelles, block copolymers

Other topics include studies of the viscosity of polymer and polyelectrolyte solutions and of micellar systems, the control of the orientational morphology of block copolymers at  small length scales by means of electric fields, the effect of flows on rheological and configurational properties of a polymer, etc.​

Other work

Other work includes modelling climate phenomena, modelling of ecological systems, etc., and aspects of quantum computing.