Qualification: 
Ph.D, MSc, BSc
nandakumaran@am.amrita.edu

Dr. V. M. Nandakumaran received his Ph. D. from Indian Institute of Science in the area of theoretical condensed matter physics. Prior to that he did his M. Sc. in Physics from Indian Institute of Technology, Madras. His current areas of research are Nonlinear Dynamics and Chaos and Synchronization of Coupled Chaotic Systems. He has published 2 books and about 42 papers in top journals.

Dr V. M. Nandakumaran has taught at University of Calicut and at CUSAT, Kochi for the past 32 years. He also played a leading role in the development of the School of Photonics at CUSAT, heading it as its Director for four years. He was also the Principal Co-ordinator of ISP-MHO Project (NUFFIC) of the Netherlands "To develop the infrastructure facilites of the International School of Photonics".

He has successfully guided 12 Ph. D. s and has also supervised the project works of several MPhil, MSc and MTech students over the last several years.

Dr V. M. Nandakumaran has considerable international experience also. He was Visiting Scientist at Technical University of Eindhoven, The Netherlands from 1999 to 2003, Associate at the Inter University Centre for Astronomy & Astrophysics, Visitor at International Centre for Theoretical Physics (ICTP), Trieste, Italy etc.

Education

YEAR DEGREE/PROGRAM INSTITUTION
1979 PhD in Theoretical condensed matter Physics Indian Institute of Science, Bangalore
1971 MSc in Physics Indian Institute of Technology Madras
1969 BSc (special) Kerala University, Kerala

Professional Appointments

Year Affiliation
June 2016 - Present Principal, Amrita School of Arts & Sciences Amritapuri Campus
July 2010 - Present Professor, Dept. of Physics, Amrita School of Arts & Sciences Amritapuri Campus
August 2009 - April 2010 Professor, International School of Photonics, Cochin University of Science & Technology
August 2008 - July 2009 Professor, IISER-TVM (on deputation from CUSAT)
May 2000 - August 2003 Director, International School of Photonics.
March 1995 - May 2000 Professor, International School of Photonics, Cochin University of Science & Technology
July 1987 - July 1993 Reader, Department of Physics, Cochin University of Science & Technology
July 1979 - July 1987 Lecturer, Department of Physics, Cochin University of Science & Technology
July 1978 - July 1979 Lecturer, Department of Physics, University of Calicut

Research Project

Principal Co-ordinator, ISP-MHO Project (NUFFIC) of the Netherlands “To develop the infrastructure facilites of the International School of Photonics” Amount: Approx Rs 40 Million 1999-2003.

Publications

Publication Type: Journal Article

Year of Publication Publication Type Title

2010

Journal Article

B. M. Krishna, John, M. P., and Dr. V . M. Nandakumaran, “Multi-user bidirectional communication using isochronal synchronisation of array of chaotic directly modulated semiconductor lasers”, Physics Letters A, vol. 374, pp. 1835–1842, 2010.[Abstract]


Isochronal synchronisation between the elements of an array of three mutually coupled directly modulated semiconductor lasers is utilized for the purpose of simultaneous bidirectional secure communication. Chaotic synchronisation is achieved by adding the coupling signal to the self feedback signal provided to each element of the array. A symmetric coupling is effective in inducing synchronisation between the elements of the array. This coupling scheme provides a direct link between every pair of elements thus making the method suitable for simultaneous bidirectional communication between them. Both analog and digital messages are successfully encrypted and decrypted simultaneously by each element of the array

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PDF iconmulti-user-bidirectional-communication-using-isochronal-synchronisation-of-array-of-chaotic-directly-modulated-semiconduc-or-lasers.pdf

2010

Journal Article

B. M. Krishna, John, M. P., and Dr. V . M. Nandakumaran, “Bidirectional communication using delay coupled chaotic directly modulated semiconductor lasers”, Pramana, vol. 74, pp. 177–188, 2010.[Abstract]


Chaotic synchronization of two directly modulated semiconductor lasers with negative delayed optoelectronic feedback is investigated and this scheme is found to be useful for efficient bidirectional communication between the lasers. A symmetric bidirectional coupling is identified as a suitable method for isochronal synchronization of such lasers. The optimum values of coupling and feedback strength that can provide maximum quality of synchronization are identified. This method is successfully employed for encoding/decoding both analog and digital messages. The importance of a symmetric coupling is demonstrated by studying the variation of decoding efficiency with respect to asymmetric coupling.

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PDF iconbidirectional-communication-using-delay-coupled-chaotic-directly-modulated-semiconduc-or-lasers.pdf

2009

Journal Article

M. P. John, Jijo, P. U., and Dr. V . M. Nandakumaran, “Effect of a fluctuating parameter mismatch and the associated time-scales on coupled Rossler oscillators”, Pramana, vol. 72, pp. 495–503, 2009.[Abstract]


We study the effect of parameter fluctuations and the resultant multiplicative noise on the synchronization of coupled chaotic systems. We introduce a new quantity, the fluctuation rate ϕ as the number of perturbations occurring to the parameter in unit time. It is shown that ϕ is the most significant quantity that determines the quality of synchronization. It is found that parameter fluctuations with high fluctuation rates do not destroy synchronization, irrespective of the statistical features of the fluctuations. We also present a quasi-analytic explanation to the relation between ϕ and the error in synchrony.

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PDF iconeffect-of-a-fluctuating-parameter-mismatch-and-the-associated-time-scales-on-coupled-rossler-oscillators.pdf

2009

Journal Article

M. R. Parvathi, Krishna, B. M., Rajesh, S., John, M. P., and Dr. V . M. Nandakumaran, “Hopf bifurcation in parallel polarized Nd: YAG laser”, Chaos, Solitons & Fractals, vol. 42, pp. 515–521, 2009.[Abstract]


Dynamics of Nd:YAG laser with intracavity KTP crystal operating in two parallel polarized modes is investigated analytically and numerically. System equilibrium points were found out and the stability of each of them was checked using Routh–Hurwitz criteria and also by calculating the eigen values of the Jacobian. It is found that the system possesses three equilibrium points for (Ij, Gj), where j = 1, 2. One of these equilibrium points undergoes Hopf bifurcation in output dynamics as the control parameter is increased. The other two remain unstable throughout the entire region of the parameter space. Our numerical analysis of the Hopf bifurcation phenomena is found to be in good agreement with the analytical results. Nature of energy transfer between the two modes is also studied numerically.

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PDF iconhopf-bifurcation-in-parallel-polarized-nd-yag-laser.pdf

2009

Journal Article

Dr. V . M. Nandakumaran, Parvathy, M. R., Krishna, B. M., and John, M. P., “Antiphase to Inphase Transition in Coupled Nd:YAG Lasers”, Nonlinear Dynamics, 2009.

2009

Journal Article

Dr. V . M. Nandakumaran, Parvathy, M. R., Krishna, B. M., and John, M. P., “Antiphase to Inphase Transition in Coupled Nd:YAG Lasers”, Nonlinear Dynamics, 2009.

2008

Journal Article

B. M. Krishna, John, M. P., and Dr. V . M. Nandakumaran, “Performance characteristics of positive and negative delayed feedback on chaotic dynamics of directly modulated InGaAsP semiconductor lasers”, Pramana, vol. 71, pp. 1259–1269, 2008.[Abstract]


The chaotic dynamics of directly modulated semiconductor lasers with delayed optoelectronic feedback is studied numerically. The effects of positive and negative delayed optoelectronic feedback in producing chaotic outputs from such lasers with nonlinear gain reduction in its optimum value range is investigated using bifurcation diagrams. The results are confirmed by calculating the Lyapunov exponents. A negative delayed optoelectronic feedback configuration is found to be more effective in inducing chaotic dynamics to such systems with nonlinear gain reduction factor in the practical value range.

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PDF iconperformance-characteristics-of-positive-and-negative-delayed-feedback-on-chaotic-dynamics-of-directly-modulated-ingaasp-semiconductor-lasers.pdf

2008

Journal Article

M. R. Parvathi, Krishna, B. M., Rajesh, S., John, M. P., and Dr. V . M. Nandakumaran, “Synchronization and control of chaos in coupled chaotic multimode Nd: YAG lasers”, Physics Letters A, vol. 373, pp. 96–101, 2008.[Abstract]


In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.

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PDF iconsynchronization-and-control-of-chaos-in-coupled-chaotic-multimode-nd-yag-lasers.pdf

2006

Journal Article

S. Rajesh and Dr. V . M. Nandakumaran, “Control of bistability in a directly modulated semiconductor laser using delayed optoelectronic feedback”, Physica D: Nonlinear Phenomena, vol. 213, pp. 113–120, 2006.[Abstract]


We show numerically that direct delayed optoelectronic feedback can suppress hysteresis and bistability in a directly modulated semiconductor laser. The simulation of a laser with feedback is performed for a considerable range of feedback strengths and delays and the corresponding values for the areas of the hysteresis loops are calculated. It is shown that the hysteresis loop completely vanishes for certain combinations of these parameters. The regimes for the disappearance of bistability are classified globally. Different dynamical states of the laser are characterized using bifurcation diagrams and time series plots.

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PDF iconcontrol-of-bistability-in-a-directly -modulated-semiconductor-laser-using-delayed-optoelectronic-feedback.pdf

2004

Journal Article

Dr. V . M. Nandakumaran, M, K. Bindu, P, J. Manu, and , “Chaotic Dynamics of Semiconductor Laser with Current Modulation and optoelectronic feedback”, 2004.[Abstract]


Chaotic dynamics of directly modulated semiconductor lasers have been studied extensively over the last two decades because of their application in secure optical communication. However, chaos is generally suppressed in such systems when the nonlinear gain reduction factor is above 0.01 which is very much smaller than the reported values in semiconductors like InGaAsP. In this paper we show that by giving an optoelectronic feedback with appropriate delay one can increase the range of the values of the gain reduction factor for which chaos can be observed. Numerical studies show that negative feedback is more efficient in producing chaotic dynamics.

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PDF iconchaotic-dynamics-of-semiconductor-laser-with-current-modulation-and-optoelectronic-feedback.pdf

2003

Journal Article

S. Rajesh and Dr. V . M. Nandakumaran, “Suppression of chaos in a directly modulated semiconductor laser with delayed optoelectronic feedback”, Physics Letters A, vol. 319, pp. 340–347, 2003.[Abstract]


The effect of delayed optoelectronic feedback on a directly modulated InGaAsP laser diode is numerically studied. It is found that a complete elimination of the previously observed period doubling, chaos and formation of pulses with double peak structure is possible by the feedback with small delays. Bifurcation diagrams and time series plots are used to characterize the chaotic and periodic states of the laser.

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2002

Journal Article

V. Bindu and Dr. V . M. Nandakumaran, “Chaotic encryption using long-wavelength directly modulated semiconductor lasers”, Journal of Optics A: Pure and Applied Optics, vol. 4, p. 115, 2002.[Abstract]


A new feedback function to synchronize two diode lasers is introduced. This function is then applied to a secure communication system for decoding a message. Chaotic outputs of a direct-current-modulated long-wavelength semiconductor laser are used for encoding the message by direct amplitude modulation at the output of the transmitter. Numerical results show that the method of chaotic encoding is successfully employed in the cases of analogue and digital messages. Since long-wavelength semiconductor lasers are widely used for optical communication, this demonstration may prove to be useful for secure communication using chaotic optical systems. The message is decoded at the receiver by synchronizing it with the transmitter by the use of a proportional-integral feedback function, optimized for the case of semiconductor lasers.

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2000

Journal Article

V. Bindu and Dr. V . M. Nandakumaran, “Numerical studies on bi-directionally coupled directly modulated semiconductor lasers”, Physics Letters A, vol. 277, pp. 345–351, 2000.[Abstract]


Results of a numerical study of synchronisation of two directly modulated semiconductor lasers, using bi-directional coupling, are presented. The effect of stepwise increase in the coupling strength (C) on the synchronisation of the chaotic outputs of two such lasers is studied, with the help of parameter space plots, synchronisation error plots, phase diagrams and time series outputs. Numerical results indicate that as C increases, the system achieves synchronisation as well as stability together with an increase in the output power. The stability of the synchronised states is checked by applying a perturbation to the system after it becomes synchronised and then noting the time it takes to regain synchronisation. For lower values of C the system does not regain synchronisation. But, with higher values synchronisation is regained within a very short time.

More »»
PDF iconnumerical-studies-on-bi-directionally-coupled-directly-modulated-semiconductor-lasers.pdf

2000

Journal Article

T. Kuruvilla and Dr. V . M. Nandakumaran, “Dynamics of two coupled chaotic multimode Nd: YAG lasers with intracavity frequency doubling crystal”, Pramana, vol. 54, pp. 393–402, 2000.[Abstract]


The effect of coupling two chaotic Nd:YAG lasers with intracavity KTP crystal for frequency doubling is numerically studied for the case of the laser operating in three longitudinal modes. It is seen that the system goes from chaotic to periodic and then to steady state as the coupling constant is increased. The intensity time series and phase diagrams are drawn and the Lyapunov characteristic exponent is calculated to characterize the chaotic and periodic regions.

More »»
PDF icondynamics-of-two-coupled-chaotic-multimode-nd-yag-lasers-with-intracavity-frequency-doubling-crystal.pdf

1999

Journal Article

T. Kuruvilla and Dr. V . M. Nandakumaran, “Suppression of chaos through reverse period doubling in coupled directly modulated semiconductor lasers”, Physics Letters A, vol. 254, pp. 59–64, 1999.[Abstract]


The effect of coupling on two high frequency modulated semiconductor lasers is numerically studied. The phase diagrams and bifurcatio.n diagrams are drawn. As the coupling constant is increased the system goes from chaotic to periodic behavior through a reverse period doubling sequence. The Lyapunov exponent is calculated to characterize chaotic and periodic regions.

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PDF iconsuppression-of-chaos-through-reverse-period-doubling-in-coupled-directly-modulated-semiconductor-lasers.pdf

1999

Journal Article

T. Kuruvilla and Dr. V . M. Nandakumaran, “Numerical study of reverse period doubling route from chaos to stability in a two-mode intracavity doubled Nd-YAG laser”, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 9, pp. 208–212, 1999.[Abstract]


We have numerically studied the behavior of a two-mode Nd-YAG laser with an intracavity KTP crystal. It is found that when the parameter, which is a measure of the relative orientations of the KTP crystal with respect to the Nd-YAG crystal, is varied continuously, the output intensity fluctuations change from chaotic to stable behavior through a sequence of reverse period doubling bifurcations. The graph of the intensity in the X-polarized mode against that in the Y-polarized mode shows a complex pattern in the chaotic regime. The Lyapunov exponent is calculated for the chaotic and periodic regions.

More »»
PDF iconnumerical-study-of-reverse-period-doubling-route-from-chaos-to-stability-in-a-two-mode.pdf

1998

Journal Article

P. R. Krishnan Nair and Dr. V . M. Nandakumaran, “Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map”, Pramana, vol. 51, pp. 377–385, 1998.[Abstract]


We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We establish that whenever the elements of an n~cycle (n > I) approach the discontinuities of the nth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors. Our results are verified by numerical experiments as well.

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PDF iconexistence-of-multiple-attractors-and-the-nature-of-bifurcations-in-a-discontinuous-logistic-map.pdf

1997

Journal Article

Dr. V . M. Nandakumaran, “Chaos in modulated logistic systems”, Pramana, vol. 48, pp. 99–108, 1997.[Abstract]


This paper is a review of the work done on the dynamics of modulated logistic systems. Three different problems are treated, viz, the modulated logistic map, the parametrically perturbed logistic map and the combination map obtained by combining two maps of the quadratic family. Many of the interesting features displayed by these systems are discussed.

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PDF iconchaos-in-modulated-logistic-systems.pdf

1996

Journal Article

P. P. Saratchandran, Dr. V . M. Nandakumaran, and Ambika, G., “Dynamics of the logistic map under discrete parametric perturbation”, Pramana, vol. 47, pp. 339–345, 1996.[Abstract]


By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.

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PDF icondynamics-of-the-logistic-map-under-discrete-parametric-perturbation.pdf

1994

Journal Article

G. Ambika and Dr. V . M. Nandakumaran, “The quantum effects in quadratically damped systems”, Physics Letters A, vol. 192, pp. 331–336, 1994.[Abstract]


A dynamical system with a damping that is quadratic in velocity is converted into the Hamiltonian format using a nonlinear transformation. Its quantum mechanical behaviour is then analysed by invoking the Gaussian effective potential technique. The method is worked out explicitly for the Duffing oscillator potential.

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PDF iconthe-quantum-effects-in-quadratically-damped-systems.pdf

1994

Journal Article

P. R. Krishnan Nair, Dr. V . M. Nandakumaran, and Ambika, G., “Scaling relations in the Lyapunov exponents of one dimensional maps”, Pramana, vol. 43, pp. 421–429, 1994.[Abstract]


We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map, where the scaling index is found to be different.

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PDF iconscaling-relations-in-the-lyapunov-exponents-of-one-dimensional-maps.pdf

1994

Journal Article

Dr. V . M. Nandakumaran, Nair, P. R. Krishnan, and Ambika, G., “Dynamics of a Combination Map”, Computational Aspects in Chaos and Nonlinear Dynamics Eds, 1994.

1994

Journal Article

Dr. V . M. Nandakumaran and Ambika, G., “Non-MSS sequences in the dynamics of a parametrically perturbed logistic map”, ibid, 1994.

1992

Journal Article

S. V. Vettoor and Dr. V . M. Nandakumaran, “Density of states in high - Tc superconductors”, Physica C: Superconductivity, vol. 191, pp. 277–281, 1992.[Abstract]


The density of states and the low temperature specific heat of higb-Tc superconductors are calculated in a functional integral formalism using the slave boson technique. The manybody calculation in a saddle point approximation shows that the Iow energy sector is dominated by 3 single band. The calculated values of density of states are in good agreement with experimental results.

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PDF icondensity-of-states-in-high-tc-superconductors.pdf

1991

Journal Article

G. Ambika, K Joseph, B., and Dr. V . M. Nandakumaran, “Metastable States and Irregular Behaviour in a Josephson Junction with Nonlinear Resistance”, Modern Physics Letters B, vol. 5, pp. 519–529, 1991.[Abstract]


We consider a resistively shunted Josephson junction with a resistance that depends inversely on voltage. It is shown that such a junction in the underdamped case can give rise to extremely long-lived metastable states even in the absence of external noise. We investigate numerically this metastable state and its transition to a chaotic state. The junction voltages corresponding to these states are studied.

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PDF iconmetastable-states-and-irregular-behaviour-in-a-josephson-junction-with-nonlinear-resistance.pdf

1991

Journal Article

R. E. Amritkar, Gade, P. M., Gangal, A. D., and Dr. V . M. Nandakumaran, “Stability of periodic orbits of coupled-map lattices”, Physical Review A, vol. 44, pp. R3407–R3410, 1991.[Abstract]


We consider the stability properties of spatial and temporal periodic orbits of one-dimensional coupled-map lattices. The stability matrices for them are of the block-circulant form. This helps us to reduce the problem of stability of spatially periodic orbits to the smaller orbits corresponding to the building blocks of spatial periodicity, enabling us to obtain the conditions for stability in terms of those for smaller orbits.

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PDF iconstability-of-periodic-orbits-of-coupled-map-lattices.pdf

1990

Journal Article

S. V. Vettoor and Dr. V . M. Nandakumaran, “ELECTRON-PHONON INTERACTION WITHIN THE FRAMEWORK OF THE FLUCTUATING VALENCE OF COPPER ATOMS—A THEORETICAL MODEL FOR HIGH TEMPERATURE SUPERCONDUCTIVITY”, Modern Physics Letters B, vol. 4, pp. 325–331, 1990.[Abstract]


Electron-phonon interaction is considered within the framework of the fluctuating valence of Cu atoms. Anderson's lattice Hamiltonian is suitably modified to take this into account. Using Green's function technique the possible quasiparticle excitations are determined. The quantity 2∆k(0)/kBTc is calculated for Tc = 40 K. The calculated values are in good agreement with the experimental results.

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PDF iconelectron-phonon-interaction-within-the-framework-of-the-fluctuating-valence-of-copper-atoms.pdf

1990

Journal Article

G. Ambika and Dr. V . M. Nandakumaran, “Frustrated limit cycle and irregular behaviour in a nonlinear pendulum”, 1990.[Abstract]


We discuss how the presence of frustration brings about irregular behaviour in a pendulum with nonlinear dissipation. Here frustration arises owing to the particular choice of the dissipation. A preliminary numerical analysis is presented which indicates the transition to chaos at low frequencies of the driving force.

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PDF iconfrustrated-limit-cycle-and-irregular-behaviour-in-a-nonlinear-pendulum.pdf

1990

Journal Article

J. Sreekumar and Dr. V . M. Nandakumaran, “Two dimensional large amplitude quasi solitons in thin helium films”, Modern Physics Letters B, vol. 4, pp. 47–51, 1990.[Abstract]


Large amplitude local density fluctuations in a thin superfluid 4He film is considered. It is shown that these large amplitude fluctuations travel and behave like "quasi-solitons" under collision, even when the full nonlinearity arising from the Van der Waals potential is taken into account.

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PDF icontwo-dimensional-large-amplitude-quasi-solitons-in-thin-helium-films.pdf

1989

Journal Article

K. P. Harikrishnan and Dr. V . M. Nandakumaran, “An analogue of the logistic map in two dimensions”, Physics Letters A, vol. 142, pp. 483–489, 1989.[Abstract]


This is a sequel to our earlier work on the modulated logistic map. Here, we first show that the map comes under the universality class of Feigenbaum. We then give evidence for the fact that our model can generate strange attractors in the unit square for an uncountable number of parameter values in the range μ∞<μ<1. Numerical plots of the attractor for several values of μ are given and the self-similar structure is explicity shown in one case. The fractal and information dimensions of the attractors for many values of μ are shown to be greater than one and the variation in their structure is analysed using the two Lyapunov exponents of the system. Our results suggest that the map can be considered as an analogue of the logistic map in two dimensions and may be useful in describing certain higher dimensional chaotic phenomena.

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PDF iconan-analogue-of-the-logistic-map-in-two-dimensions.pdf

1989

Journal Article

J. Sreekumar and Dr. V . M. Nandakumaran, “Solitons and their resonances on two-dimensional superfluid films”, Pramana, vol. 33, pp. 697–704, 1989.[Abstract]


The dynamics of saturated two-dimensional superfluid4He films is shown to be governed by the Kadomtsev-Petviashvili equation with negative dispersion. It is established that the phenomena of soliton resonance could be observed in such films. Under the lowest order nonlinearity, such resonance would happen only if two dimensional effects are taken into account. The amplitude and velocity of the resonant soliton are obtained.

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PDF iconsolitons-and-their-resonances-on-two-dimensional-superfluid-films.pdf

1988

Journal Article

K. P. Harikrishnan and Dr. V . M. Nandakumaran, “Evidence for the existence of Sarkovskii ordering in a two-dimensional map”, Physics Letters A, vol. 133, pp. 305–308, 1988.[Abstract]


We analyse numerically the bifurcation structure of a two-dimensional noninvertible map and show that different periodic cycles are arranged in it exactly in the same order as in the case of the logistic map. We also show that this map satisfies the general criteria for the existence of Sarkovskii ordering, which supports our numerical result. Incidently, this is the first report of the existence of Sarkovskii ordering in a two-dimensional map.

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PDF iconevidence-for-the-existence-of-sarkovskii-ordering-in-a-two-dimensional-map.pdf

1987

Journal Article

K. P. Harikrishnan and Dr. V . M. Nandakumaran, “Universal behaviour in a “modulated” logistic map”, Physics Letters A, vol. 125, pp. 465–468, 1987.[Abstract]


We study the period-doubling bifurcations to chaos in a logistic map with a nonlinearly modulated parameter and show that the bifurcation structure is modified significantly. Using the renormalisation method due to Derrida et al. we establish the universal behaviour of the system at the onset of chaos.

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PDF iconuniversal-behaviour-in-a-modulated-logistic-map.pdf

1987

Journal Article

K. P. Harikrishnan and Dr. V . M. Nandakumaran, “Bifurcation structure and Lyapunov exponents of a modulated logistic map”, Pramana, vol. 29, pp. 533–542, 1987.[Abstract]


We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated logistic map is less chaotic compared to the logistic map.

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PDF iconbifurcation-structure-and-lyapunov-exponents-of-a-modulated-logistic-map.pdf

1987

Journal Article

Dr. V . M. Nandakumaran, “On the role of acoustic plasmons in highT c superconductors”, Pramana, vol. 29, pp. L113–L115, 1987.[Abstract]


The role of acoustic plasmons in the recently discovered highTc superconductors is discussed. It is shown that the exchange of acoustic plasmons together with the usual phonon exchange between electrons can give rise to aTc ∼ 100 K.

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PDF iconon-the-role-of-acoustic-plasmons-in-high-tc-superconductors.pdf

1987

Journal Article

Dr. V . M. Nandakumaran, “Characterisation of Deterministic Chaos in Nonlinear Dissipative Systems”, Recent Developments in Theoretical Physics Ed, 1987.

1985

Journal Article

Dr. V . M. Nandakumaran, “Invariant density for a class of initial distributions under quadratic mapping”, Journal of Physics A: Mathematical and General, vol. 18, p. L1021, 1985.[Abstract]


For the discrete-time quadratic map x t+1 =4x t (1-x t ) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.

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PDF iconinvariant-density-for-a-class-of-initial-distributions-under-quadratic-mapping.pdf

1985

Journal Article

J. Sreekumar and Dr. V . M. Nandakumaran, “Soliton resonances in helium films”, Physics Letters A, vol. 112, pp. 168–170, 1985.[Abstract]


The phenomenon of two-soliton resonances of the Kadomtsev-Petviashvilli equation for the superfluid surface density fluctuation in He films is studied. The velocity of the resonant soliton is obtained.

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PDF iconsoliton-resonances-in-helium-films.pdf

1975

Journal Article

Dr. V . M. Nandakumaran and Sinha, K. P., “Possibility of a condensed phase of excitons because of phonon induced exciton-exciton pairing”, Zeitschrift für Physik B Condensed Matter, vol. 22, pp. 173–176, 1975.[Abstract]


In this paper we study the phonon-induced exciton-exciton interaction. It is found that the interaction can be attractive under certain conditions. Taking into account this attractive interaction, the pairing of excitons with opposite momenta is studied and the excitation spectrum determined. The results are similar to a system of bosons. There appears to be some possibility of superfluid behaviour.

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0

Journal Article

Dr. V . M. Nandakumaran, Thomas, J., and Sinha, K. P., “Absence of Goldstone Modes in Excitonic Insulators”, ibid.

Publication Type: Book Chapter

Year of Publication Publication Type Title

2004

Book Chapter

Dr. V . M. Nandakumaran, Nair, K. R. Suresh, Radhakrishnan, P., and Nampoori, V. P. N., “Harnessing Light”, in Photonics, 2004.

1990

Book Chapter

Dr. V . M. Nandakumaran and Sreekumar, J., “Dynamics of Solitons on 4He Films”, in Symmetries and Singularity Structures, Springer, 1990, pp. 183–195.

Publication Type: Conference Paper

Year of Publication Publication Type Title

1989

Conference Paper

Dr. V . M. Nandakumaran, “ROLE OF ACOUSTIC PLASMONS IN CERAMIC SUPERCONDUCTORS”, in Proceedings of the International Symposium on High Temperature Superconductivity, 6-8 July 1988, Department of Physics, University of Rajasthan, Jaipur, India, 1989.

1989

Conference Paper

Dr. V . M. Nandakumaran and Harikrishnan, K. P., “Universal Properties in a Modulated Logistic Map”, in Proc.Int.Conf.on Mathematical Modelling in Science and Technology, 1989.

Publication Type: Conference Proceedings

Year of Publication Publication Type Title

1975

Conference Proceedings

Dr. V . M. Nandakumaran and Sinha, K. P., “Ground State Energy of a New Exciton Condensate”, Proceedings of Nuclear Physics and Solid State Physics Symposium, vol. 18. 1975.

1973

Conference Proceedings

Dr. V . M. Nandakumaran and .P.Sinha, K., “Exciton Tunnelling”, Proceedings of Nuclear Physics ande Solid State Physics Symposium, vol. 16. 1973.

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    Amrita Vishwa Vidyapeetham,
    Amritanagar,
    Coimbatore - 641 112,
    Tamil Nadu, India.
    • Fax                 : +91 (422) 268 6274
    • Coimbatore   : +91 (422) 268 5000
    • Amritapuri    : +91 (476) 280 1280
    • Bengaluru     : +91 (080) 251 83700
    • Kochi              : +91 (484) 280 1234
    • Mysuru          : +91 (821) 234 3479
    • Chennai         : +91 (44 ) 276 02165
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