Image Credit: Prof. Janaki Balakrishnan.
We are surrounded by complex systems, the dynamical evolution of each governed by the nonlinearities in them. Ranging from cellular processes at the macroscopic scale to everyday situations in our life, complex systems show their presence everywhere. While we would all like to believe in the innate simplicity in the way Nature functions and expresses herself, one in fact comes to realise that complexity is an integral part of Nature and that often, simple explanations may not suffice to explain various phenomena observed.
The flourishing Complex Systems Research Programme at the National Institute of Advanced Studies (NIAS), Bangalore, headed by Prof. Janaki Balakrishnan aims to understand and explain the dynamical behaviour of complex systems of diverse kinds by constructing appropriate predictive mathematical models. The work done by Prof. Balakrishnan and her collaborators deals with a variety of disciplines and hence is highly interdisciplinary and trans-disciplinary in nature. Some of her recent works on ecological modelling and impact of climate change on ecological population dynamics have met with considerable success.
One ecological system they considered in a recent study was of the budmoth insect pest, the larch trees they infest, and parasitoids which parasitize upon the budmoth larvae – a system having 3 trophic levels. For centuries, regular cyclic outbreaks of budmoth infestations have caused widespread defoliation of entire larch forests around the world. These pose an ecological problem while also being a cause of concern for logging and tourism industries.
In their work published in the June, 2016 issue of the prestigious Scientific Reports, a Nature Publishing Group journal, Prof. Balakrishnan, her Ph.D. student Ms. Sudharsana V. Iyengar and their collaborator Prof. Dr. Juergen Kurths of the Potsdam Institute of Climate Impact Research, Germany, resolved the long-standing puzzle of the occurrence, absence & collapse of the budmoth outbreak cycles by incorporating climate parameters for the first time in a mathematical model.
They demonstrated that results of their model match observational and dendrochronological data recorded over 1200 years. Their work explains the sudden collapse of the cycles after 1981 due to a climatic tipping point reached in the 1980s, the absence of cycles in certain places and accounts for variations in the 8-9 year periodicity observed elsewhere. Their model predicts future budmoth infestation outbreaks with a changed periodicity of 40 and 100 years in the Swiss Alps – the next outbreak can be expected in the year 2021. In a more recent work published in the journal Chaos (September, 2016 issue) they showed that the mere presence of additional non-interacting parasitoid species in the system can also produce cessation of periodicity of population cycles or variations in their time periods.
An important unexpected finding of their work is that in a population dynamics system, the choice of initial conditions could decide whether a population could go extinct or whether it would survive exhibiting regular bursts of cyclicity of the population – one could have very different scenarios if the initial conditions varied by very little.
Another recent area of work in Prof. Balakrishnan’s lab is on the acoustic cavitation and dynamics of electrically charged bubbles in fluids subjected to ultrasound. Micron and nano-sized bubbles in fluids under ultrasonic forcing are forced to oscillate violently because of extremely rapid pressure variations and tend to implode. Bubble implosion is a highly energetic process and can cause enormous damage to nearby surfaces. In their work co-authored by Prof. B. Ashok at IIIT-Bangalore, Prof. Balakrishnan and her former Ph.D. student, Dr. Thotreithem Hongray also at IIIT-Bangalore, detailed results were obtained over two different papers giving pressure and charge thresholds for the implosion and collapse of micron and nano-sized gas bubbles in fluids when subjected to ultrasound at different driving frequencies and bubble radii. These are the first studies of charge and pressure thresholds and have very significant applications in medical diagnostics where one wants to avoid damage to living tissues in the body. Though rare, when bubbles are formed in body fluids, ultrasound may cause these bubbles to oscillate and implode violently. This could be averted or its impact reduced by such studies. Also, the wear and tear of vibrating machine parts, like in a propellor, could be drastically reduced.
Some of Prof. Balakrishnan's previous works in the last decade include correction of Fick's law to describe lateral diffusion on surfaces of arbitrary curvature. The standard laws that are used to describe a diffusion process give incorrect results for highly curved surfaces like the cell surface and cell organelles. Use of the corrected law would be useful not only in the study of cellular processes but also has practical applications in nano-scale engineering.
Prof. Balakrishnan's work also includes studies with a generic model related to hearing at the cellular scale and of neuronal firing and bursting activities. In these studies, generic mathematical models were worked with which mimic the behaviour of the inner hair cells in the cochlea, the part of the ear that is responsible for detecting sound. They also constructed mathematical models mimicking the spiking and bursting behaviour of neurons using tools and techniques of dynamical sytems theory to understand the mechanisms governing their activity. It is believed that such studies would contribute to addressing issues related to treatment of hearing and neural disorders.
One could hardly have ever imagined that such a wonderful world of possibilities lay unexplored when one heard the term ‘Complex nonlinear systems’. The Complex Systems Research Programme at NIAS, Bangalore, is a converging point for all disciplines of science and engineering. Today, it is essential that scientists work together, across traditional domains, so as to successfully address the open questions troubling the world for past decades. People like Prof. Janaki Balakrishnan have stepped up and accepted the challenge. We can hope that more scientists and researchers too join hands across disciplines to make this world a better place.
Contact Information:
Prof. Janaki Balakrishnan, Professor & Head, Complex Systems Programme School of Natural Sciences and Engineering, National Institute of Advanced Studies, Indian Institute of Science, Bangalore-560012. Email - janaki05@gmail.com