Suresh, Vettoor V; Nandakumaran, V M(Physica C,Elsevier Science, 1992)
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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.
Saratchandran, P P; Nandakumaran, V M; Ambika, G(Springer, November , 1996)
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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.
Thomas, Kuruvilla; Nandakumaran, V M(Indian Academy of Sciences, March , 2000)
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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.
Manu P, John; Jijo, P U; Nandakumaran, V M(Indian Academy of Sciences, March , 2009)
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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 Ф 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.
Suresh, Vettoor V; Nandakumaran, V M(World Scientific Publishing Company, 1990)
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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 tbe possible quasiparticle excitations' are
determined. The quantity 2delta k(O)/ kB Tc is calculated for Tc= 40 K. The calculated values
are in good agreement with the experimental results.
Harikrishnan, K P; Nandakumaran, V M(Elsevier, November 21, 1988)
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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.
Krishnan Nair, P R; Nandakumaran, V M(Springer, October , 1998)
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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 > 1) 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.
Ambika, G; Nandakumaran, V M(Current Science, January 25, 1990)
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Abstract:
We discuss how the presence of frustration brings about
irregular behaviour in a pendulum with nonlinear
dissipation. Here frustration arises owing to
particular choice of the dissipation. A preliminary
numerical analysis is presented which indicates the transition
to chaos at low frequencies of the driving force.
Parvathi, M R; Bindu M, Krishna; Rajesh, S; Manu P, John; Nandakumaran, V M(Elsevier, October , 2009)
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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.
For the discrete-time quadratic map xt+1=4xt(1-xt) 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.
Ambika, G; Nandakumaran, V M; Babu Joseph,K(World Scientific Publishing Company, 1991)
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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.
Bindu M, Krishna; Manu P, John; Nandakumaran, V M(Elsevier, April , 2010)
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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.
Bindu, V; Nandakumaran, V M(Elsevier, December 11, 2000)
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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.
Thomas, Kuruvilla; Nandakumaran, V M(American Institute of Physics, March , 1999)
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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.
The role of acoustic plasmons in the recently discovered high Tc superconductors
is discussed. It is shown that the exchange of acoustic plasmons together with the
usual phonon exchange between electrons can give rise to a Tc - 100 K.
Bindhu M, Krishna; Manu P, John; Nandakumaran, V M(Indian Academy of Sciences, December , 2008)
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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.
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.
Kriashnan Nair, P R; Nandakumaran, V M; Ambika, G(Pramana, December , 1994)
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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.
Sreekumar, J; Nandakumaran, V M(Physics Letters, October 21, 1985)
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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.
Sreekumar, J; Nandakumaran, V M(Springer, December , 1989)
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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.