K S Viswanathan
Articles written in Pramana – Journal of Physics
Volume 8 Issue 4 April 1977 pp 348-362 Solids
The paper deals with a detailed numerical study of the sections of the inverse and ray velocity surfaces for cubic crystals. The figures for the sections of the inverse and ray surfaces by the (001) and (110) planes have been plotted for over 65 crystals and from these, the nature of the cuspidal edges has been discussed. Typical graphs of the inverse and ray surfaces have been given. The parameters characterising the dimensions of the cusps have been tabulated. It is shown that the A-15 compounds exhibit very unusual and interesting wave surfaces at temperatures below superconducting critical temperatures.
Volume 8 Issue 5 May 1977 pp 417-419 Solids
It is suggested that anomalous neutron scattering could prove a powerful experimental tool in studying ferroelectric phase transition, the sublattice displacements of the soft modes as well as their symmetry characteristics.
Volume 12 Issue 6 June 1979 pp 679-697 Crystallography
A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the type
Volume 14 Issue 1 January 1980 pp 1-10 Solid State Physics
The dispersion equation for oblique propagation of the wave in the
Volume 17 Issue 2 August 1981 pp 135-142 Solid State Physics
The nature of inverse velocity surfaces as well as energy surfaces for elastic wave propagation in the (111) plane have been studied for a number of cubic crystals. The sections of inverse velocity surfaces by the (111) plane exhibit six-fold symmetry in all cases. Cuspidal edges are exhibited with a six-fold symmetry by both the slow transverse and fast transverse shear modes in the (111) plane, unlike the case of the (100) and (110) planes for which only the slow transverse shear mode exhibits cuspidal edges. The slow transverse mode energy surface exhibits cuspidal edges along$$(\bar 1\bar 12)$$ direction or an equivalent symmetry direction. The inverse velocity surfaces of the A-15 compounds exhibit unusually large inflexions for the slow transverse mode, whereas their energy surfaces have large cuspidal edges which intersect each other resulting in common regions of cusps.
Volume 20 Issue 5 May 1983 pp 415-427 Mathematical Physics
Solitons are generated in an anharmonic linear lattice in which neighbouring atoms interact through a Morse potential by giving either a strong initial impulse or a large displacement to an end atom. Studies on the variation of the characteristic properties of the soliton with the strength of the initial pulse show that the velocity and the amplitude of the soliton increase with the strength of the initial impulse, but below a certain critical value for the initial impulse, only an oscillatory tail is generated. It is shown that when a defect is present in the lattice, a localised mode appears at the site of the defect and additional solitons travelling forward or even backwards, are generated. When two solitons collide at a defect region, they reemerge but leave a localised mode at the site of the defect. If an initial velocity is imparted to a particular particle, synchronously with the crossing of the particle by the soliton, a localised mode emerges at the site of the particle and additional solitons are also generated. When a soliton moves from a denser to a rarer medium, a strong localised pulse is created near the region of the density discontinuity and additional solitons appear; and further a weak oscillatory tail is left behind in the denser medium. On the other hand, if a soliton moves from a rarer to a denser medium, it is reflected back and a small localised mode is generated at the site of the density discontinuity. The variation of amplitude of the soliton with the velocity of propagation is also studied.
Volume 24 Issue 3 March 1985 pp 513-519 Solid State Physics
Solitons are simulated in an anharmonic linear lattice that is susceptible to a soft mode instability. The soft mode characteristic is introduced in the system by the addition of a term (−
Volume 24 Issue 6 June 1985 pp 875-886 Solid State Physics
The ballistic propagation of phonons in diamond and Nb3Sn at 40 and at 4.2 K is examined. The nature of variation of the phonon magnification factor has been analysed both in the wave vector as well as group velocity spaces. Using the Polar Schmidt-net with Pole at (
Volume 26 Issue 6 June 1986 pp 543-554
Dispersion equations for the ordinary and extraordinary cyclotron waves propagating perpendicular to the magnetic field in metals in the critical region where the wavelength is comparable to the electron Larmor radius are derived as an infinite but rapidly converging power series expansion in δ( = Ω/Ω-
Volume 27 Issue 1-2 July 1986 pp 307-320 Solid State Physics
An expression has been derived for the collision operator for phonons in a solid, which is valid at very low temperatures. The set of coupled equations for the elastic deformation and the phonon density or second sound has been reduced to a simple tractable form and the dispersion equation for the coupled waves consisting of the acoustic modes and second sound has been derived. It is shown that only the longitudinal mode interacts with the second sound. It is also shown that as a result of the interaction with the second sound, the longitudinal velocity along the principal axis acquires a correction term that is proportional to both
Volume 41 Issue 1 July 1993 pp 31-39
The anomalies of the second order elastic constants have been derived for barium titanate for the phase transition from cubic to tetragonal. The equilibrium values of the components of the order parameter and the strain variables have been obtained from the stability conditions. The fluctuations in the order parameter have been derived from the Landau-Khalatnikov equations. Expression for the shift in the zero point energy in the tetragonal phase is obtained and is shown to be proportional to (
Volume 41 Issue 3 September 1993 pp 203-208 Research Articles
The anomalies in second order elastic constants and gyrotropic constants have been considered for the phase transition of triglycine sulphate. Expressions have been derived for the equilibrium values of order parameter and strain variables in both phases. Using Landau-Khalatnikov equation the fluctuation in order parameter is expressed in terms of fluctuations in strain variables. Substitution of these in free energy gives anomalies arising from Landau and coupling energies in second order elastic constants. The real part of the anomalies decreases steeply across the transition temperature and thereafter flatly tend to ferroelectric values. The anomalies in the components of the gyrotropic tensor have been derived and their temperature variation discussed.
Volume 42 Issue 3 March 1994 pp 175-185
The anomalies of the second and third-order elastic constants have been considered for the phase transition of strontium titanate within the framework of Landau’s theory. All the anomalies of the second-order elastic constants have been obtained in a single formula using Kronecker delta functions and relations among them have been established. The real parts of
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