G. Ananthakrishna

Research:

• Theoretical Materials Science and Condensed Matter Physics.
• Modeling far from equilibrium physical phenomena
• Materials Science: Clustering of point defects into extended defects, dislocation dynamics and collective behavior of dislocations, Phase transformations – Martensites, magneto-martensites, Omega transformation etc, Dynamics of peeling of an adhesive tape, Dynamics friction, Nanoindentation, Radiation damage.
• Condensed Matter Physics: Critical point phenomenon, Quasicrystals,Phase transformation, Stochastic processes – diffusion in confined systems, Kramer escape rate under inhomogeneous conditions; dynamical systems, chaos, fractals, self organized criticality, stochastic resonance, Biophysics.Research Areas:

  Large body of work is related to applying techniques in the forefront of theoretical physics to problems in physics of materials and condensed matter. In particular, statistical mechanics, stochastic processes and dynamical systems have been used to model physical phenomenon cutting across disciplines. The emphasis has shifted from equilibrium systems to nonequilibrium systems, with particular emphasis on driven far-from equilibrium systems. Areas of materials science include physics of defects, both point defects and extended defects, plasticity, phase transformation, quasicrystals, and stick-slip dynamics. Contributions to condensed matter physics include critical point phenomenon, stochastic processes, physical properties of quasiperiodic systems, chaos, fractals and dynamical systems. Some of these techniques find applications in problems as varied as ‘identification of cancer cells’ to ‘low level computer vision’.

  Clustering of point defects:
  Initial work on materials physics was concerned with the problem of clustering of point defects (vacancies) to extended defects such as vacancy loops, stacking fault tetrahedra and voids under quenched conditions. These problems constituted the first stochastic approach to this area.

  Dislocation dynamics and Collective behavior of dislocations:
  Early work was focused on applying methods of stochastic processes to dislocation dynamics. Starting from a statistical description of dislocations (a kind of extended Fokker-Planck equation which is nonlinear and nonlocal), several features of creep in simple materials were recovered. While the mathematical structure is complicated, exact expressions for the several cumulants have been calculated. This equation also leads to quantitative expression for mobile dislocation density. The above approach forms the basis for deriving a model that explains most features of the Portevin-Le Chatelier (PLC) effect, an effect discovered more than a century ago that lacked a coherent model till early 80’s. The Ananthakrishna (AK) model explains the rich spatio-temporal dynamics of the PLC effect. The work extending over twenty years of concerted efforts explains a large number of generic features of the PLC effect. The basic idea is that the whole phenomenon is a consequence of nonlinear interaction of different populations of dislocations representing essentially, collective modes of dislocations. The model exhibits several experimentally observed features such as the existence of the PLC effect in a window of strain rates and temperature, a negative strain rate sensitivity normally assumed in many theories, and different types of bands observed in experiments. All these features are a direct consequence of Hopf bifurcation followed by a reverse Hopf bifurcation. The model also predicts chaotic behavior which has been since verified by analyzing the experimental signals. The number of degrees of freedom estimated from this analysis is the same as that used in the model, thus confirming the dynamical basis of the model. Further analysis of stress signal shows a crossover in the nature of the dynamics from chaotic to power law type of dynamics. This is only example of such a crossover in the physics or metallugical literature other than the well known example of hydrodynamics. Again the AK model explains this crossover. The model predicts type A, B and C bands found with decreasing strain rates. The dynamical approach provides a basis for understanding the negative strain rate behaviour as also the critical nature of type A serrations reflected in power law statistics of stress drops. This is the only model in the literature which has the ability to explain the entire range of dynamical and generic metallurgical features of the phenomenon. A similar dynamical approach to radiation induced effects on mechanical properties is under active investigation.

  Again, the AK model forms the basis for explaining a long standing problem of acoustic emission that accompanies plastic deformation. The main reason for lack of any theoretical basis for explaining acoustic emission during plastic deformation is the necessity for describing simultaneously widely separated time scales and length scale corresponding to speed of sound and the imposed deformation rate. Since the nature of acoustic emission spectrum is characteristic of the PLC band type, the Ananthakrishna model for the PLC effect provides a basis for understanding the nature of acoustic emission spectrum observed during type C to type A dislocation bands.

  Acoustic Emission:
  One common theme connecting several topics in materials science is the generation of acoustic emission during widely different deformation processes such as, fracture, plastic deformation, peeling of an adhesive tape, martensitic transformation etc. However there is a lack of clarity in attempting to model what constitutes the dissipation in the form of acoustic energy. Our approach has been to use Rayleigh dissipation function that depends on local strain rate. Using this functional form acoustic emission during the varied process mentioned above has been explained.

  Dynamical systems:
  Work in this area is largely a result of the need to use dynamical systems approach to understand the PLC effect. Time series analysis of the stress-time charts from the PLC experiments has been carried out for a large number of samples, strain rates and initial conditions. As experimental time series are usually short and noisy, a new method was developed that is appropriate for this situation. This has has been applied to several stress – time series. Several analytical studies on the AK model have been carried out. For example the model equations have been reduced to Ginzburg-Landau form with a view to extract order parameter equations and also to map theoretical parameters with the experimental ones. One major spin off arising from detailed theoretical studies of the model is its connection to an unsolved problem in global bifurcation theory, namely incomplete approach to homoclinicity. It turns out that the AK model helps to resolve this long standing problem. The model has also thrown up several possible solutions to other areas, like the connection to turbulence, characterization of critical state in terms of slow manifold approach. One feature displayed by the model is the generic feature of many mixed mode oscillatory systems that exhibit period doubling and their reversal, and crossover to period adding sequences. Yet they have an unimodal one dimensional map with a long tail. This crossover has been explained by imposing a few generic constraints on the map period doubling and their reversal, and crossover to period adding sequences have been recovered. Some interesting non-typical scaling relations for certain types of periodic states have been derived. Recently, we have investigated the possibility of projecting low dimensional chaos out of a spatio-temporal chaotic system.

  Stochastic processes:
  This is another area where substantial contribution has been made. Indeed, stochastic approach has been used to understand clustering of point defects as also dislocation dynamics. Langevin dynamics has been used to understand the nature of enhanced fluctuation in the neighborhood of an yield drop. Other topics studied specific to stochastic processes include solution of nonlinear Langevin equation, subdiffusive behavior, application of stochastic processes to transport of neutrons through shield material, and Kramer’s escape rate for the case of subdivided barrier. In the last example, there is an optimal barrier subdivision which maximizes the escape rate. This problem has also been cast as a biased random walk to obtain closed form solutions which permits a better understanding of the effects of barrier subdivision. Recently, the Landauers `blow torch’ conjecture has been studied with emphasis on the calculation of escape rate. Diffusion in confined systems such as zeolites is one area where these techniques have been applied. In particular, separation of mixtures has been shown to be much more effective by coupling the blow torch effect with levitation effect. Recently some of these techniques have been applied to model biological systems. One area that combines stochastic processes, soft condensed matter and friction is the recent work on sheared colloidal liquids where it has been shown that sheared colloidal liquids show all features of stochastic resonance.

  Quasicrystals:
  Substantial amount of work has been carried out on electronic structure of quasicrystals. Other properties such as critical magnetic properties and diffusion in quasicrystals have also been analyzed.

  Fractal and multifractals:
  Application of concept of fractals and multifractals to understand the influence of self similar structure on physical properties has been a theme followed over the years. To name a few examples, multifractal characterization of wave functions, mechanical properties of polymer blends and detection of cancer cells, and characterization of plume structure in hydrodynamic turbulence. Some work on fractal growth of surface fracture has also been carried out. Multifractal measures has been used to describe the transition from the type B bands in the PLC effect to type A propagating bands. Increased levels of multifractality is reflected in this region of strain rates.

  Phase transformations:
  Martensites are athermal transformations. They are unusual as they exhibit features of second order transition such as the precursor effect observed well above the transformation temperature and power law statistics of acoustic emission (AE) signals during thermal cycling. Another unusual feature is the correlated, repetitive AE signals found during thermal cycling in a restricted temperature domain. The latter has been shown to be related to the growth and shrinkage of plates and hence related directly to the shape memory effect. A model that includes hydrodynamic nature of sound, long range interaction of the transformed martensite phases, nucleation at defect sites and an additional dissipation that mimics acoustic emission has been designed. Morphological patterns resemble patterns observed in experiments. The model reproduces well known features such as jerky motion of the front and thermal hysteresis. The energy released during cooling runs show a power law distribution of acoustic emission signals as seen in experiments. The same model also explains the correlated nearly repetitive acoustic emission signals under thermal cycling in a small temperature interval as seen in experiments. The associated martensite platelets grow and shrink under thermal cycling and thus the model also explains the shape memory effect for the first time from a microscopic angle. The model also shows precursor effect. The model has also been extended to understand several features of magneto-martensites. Finally, dynamics of magneto-martensites has also been studied. Another transformation that is generally believed to be athermal is the beta to omega transformation. But this has never been established. Recently, we have designed a phase field model that demonstrates the beta to omega transformation occurs at nearly the speed of sound. The model also predicts several other features such as the existence of the omega phase in a certain domain of alloying element etc.

  Precursors, predictability of failure in earthquake models:
  Predicting time of failure is very important question both conceptually as well as technologically, in particular, in the context of earthquake predictability. As the magnitudes of earthquakes follow Gutenberg-Richters law which is a power law, the system exhibits all length scales and time scales. Hence predicting an individual earthquake event is considered impossible. This statement clearly applies to model systems. This paradox has been resolved by considering the well known Burridge-Knopoff model for earthquakes by including a term that mimics acoustic emission. The model predicts individual earthquake events within one percent of time for the onset of the event. The increased precursor activity, which in this case is acoustic emission, itself follows a power law behavior in its approach to the failure point. This universal approach could be applicable to other failure systems. The model also explains many experimental features of AE signals observed in rock samples in laboratory that has not been explained so far.

  Peeling of an Adhesive Tape:
  Peeling is a kind of fracture that is important in the context of adhesion and falls into stick-slip systems like the PLC effect, i.e., measured force-velocity curve shows an unstable branch. The problem of peeling of an adhesive tape has been experimentally well studied for a long time but the equations of motion are beset with controversy as these do not produce stick-slip jumps. This has been resolved by showing that the equations of motion fall into the category of differential-algebraic set of equations and hence are singular requiring a special algorithm meant to solve differential algebraic equations. Once this method is used, the dynamical jumps follow naturally. Several experimental features are also explained. It turns out that the kinetic energy of stretched tape is missing and when it is included, the singular nature is lifted and natural stick-slip jumps follow. By including additional dissipative energy that mimics acoustic emission, the contact line dynamics is studied. Many features of acoustic emission automatically follow as also other experimental features such as the stuck-peeled configuration of the peel front. The model predicts chaotic dynamics in the mid range of pull velocities. The existence of chaotic dynamics has been verified though time series analysis of the acoustic emission signals.

  Friction:
  Dynamics of sliding friction has remained a difficult phenomenon to understand. A model had been developed that involves viscoelastic contribution, plastic deformation of asperities to explain the origin of stick-slip in dynamical condition. The model also provides a frame work for the velocity weakening friction law proposed in the literature. The approach is very general to the extent it can be extended to the nano-indentation, scratching tools etc.

  Biophysics:
  Biological systems exhibit rich dynamical and statistical features. Stochastic methods have been used to explain some unusual statistical features in gene expression. Langevin dynamical approach has been used to explain unusual statistics of motile particles. One of the areas of interest is nature of mechanical response of cells.

  Thin film Growth:
  As our laboratory has several experts in the area of thin film growth and characterization, some modeling efforts have been devoted to interpretation of several experimental findings.

Recent Publications:

1. Jayanta Dutta, G. Ananthakrishna and S. Banerjee, On the athermal nature of the β to ω transformation, Acta Mater., 556, 60 (2012)
2. Ritupan Sarmah and G. Ananthakrishna, Dynamics of strain bifurcations in magentostrictive ribbon, Phys. Rev. E, 016204, 86 (2012)
3. Ritupan Sarmah and G. Ananthakrishna, Projecting low dimensional and extensive chaos from spatio-temporal dynamics, Phys. Rev. E, 056208, 86 (2012)
4. Ritupan Sarmah and G. Ananthakrishna, Influence of system size on spatiotemporal dynamics of a model for plastic instability: Projecting low-dimensional and extensive chaos, Phys. Rev. E, 052907, 87 (2013)
5. Ritupan Sarmah and G. Ananthakrishna, A unified model for the dynamics of driven ribbon with strain and magnetic order parameters, CHAOS, 013116, 23 (2013)
6. G. Ananthakrishna and Ritupan Sarmah, Projecting low and extensive dimensional chaos from spatio-temporal dynamics, EPJ ST, 799, 222 (2013)
7. Ritupan Sarmah and G. Ananthakrishna, Dynamics of a driven magneto-martensitic ribbon, Comm. Nonlinear Sci. and Numer. Simul., in press, (2014)

Select Career Publications:

1. Moumita Das, S. Ramaswamy, A. K. Sood and G. Ananthakrishna, Brownian-drag induced particle current in a model colloidal system, Phys. Rev. E, 061409, 73 (2006)
2. Rumi De and G. Ananthakrishna, Dynamics of the Peel Front and the Nature of Acoustic Emission during Peeling of an Adhesive Tape, Phys. Rev. Lett., 165503, 97 (2006)
3. G. Ananthakrishna, Statistical and dynamical approaches to the collective behaviour of dislocations, Dislocations in Solids, 81, 13(73) (2007)
4. G. Ananthakrishna, Current theoretical approaches to collective behavior of dislocations, Physics Reports, 113, 440 (2007)
5. G. Ananthakrishna, Negative strain rate sensitivity and the critical nature of type A bands in the Portevin-Le Chatelier effect, J. Computer-Aided Mater. Des., 5, 14 (2007)
6. Rumi De and G. Ananthakrishna, Lifting the singular nature of a model for peeling of an adhesive tape, Euro. Phys. J. B, 475, 61 (2008)
7. Jagadish Kumar, M. Ciccotti and G. Ananthakrishna, Hidden order in crackling noise during peeling of an adhesive tape, Phys. Rev. E, 045202(R), 77 (2008)
8. Jagadish Kumar, Rumi De and G. Ananthakrishna, Intermittent peel front dynamics and the crackling noise in an adhesive tape, Phys. Rev. E, 066119, 78 (2008)
9. Jagdish Kumar and G. Ananthakrishna, Influence of visco-elastic nature of the adhesive on dynamics of the peel front, Phys. Rev. E, 016211, 82 (2010)
10. G. Ananthakrishna and Jagdish Kumar, Correlation between stick-slip frictional sliding and charge transfer, Phys. Rev. B, 075414, 82 (2010)
11. Jagadish Kumar and G. Ananthakrishna, Multiscale Modeling Approach to Acoustic Emission during Plastic Deformation, Phys. Rev. Let., 106001, 106 (2011)
12. Ritupan Sarmah, G. Ananthakrishna, B. A. Sun and W. H. Wang, Hidden order in serrated flow of metallic glasses, Acta Meter., 4482, 59 (2011)
13. Jayanta Dutta, G. Ananthakrishna and S. Banerjee, On the athermal nature of the β to ω transformation, Acta Mater., 556, 60 (2012)
14. Ritupan Sarmah and G. Ananthakrishna, Dynamics of strain bifurcations in magentostrictive ribbon, Phys. Rev. E, 016204, 86 (2012)
15. Ritupan Sarmah and G. Ananthakrishna, Projecting low dimensional and extensive chaos from spatio-temporal dynamics, Phys. Rev. E, 056208, 86 (2012)
16. Ritupan Sarmah and G. Ananthakrishna, Influence of system size on spatiotemporal dynamics of a model for plastic instability: Projecting low-dimensional and extensive chaos, Phys. Rev. E, 052907, 87 (2013)
17. Ritupan Sarmah and G. Ananthakrishna, A unified model for the dynamics of driven ribbon with strain and magnetic order parameters, CHAOS, 013116, 23 (2013)
18. G. Ananthakrishna and Ritupan Sarmah, Projecting low and extensive dimensional chaos from spatio-temporal dynamics, EPJ ST, 799, 222 (2013)
19. Ritupan Sarmah and G. Ananthakrishna, Dynamics of a driven magneto-martensitic ribbon, Comm. Nonlinear Sci. and Numer. Simul., in press, (2014)