G Ananthakrishna
Articles written in Pramana – Journal of Physics
Volume 3 Issue 3 September 1974 pp 133-142 Solids
Phase transition in a class of Hamiltonians
G Ananthakrishna J Eduardo Suger
We consider a class of Hamiltonians for a system of one localized spin-1/2 particle per lattice site with the total spin as a good quantum number. We introduce a set of conditions in the form of a hypothesis relating the subpartition function, which is the partition function defined by the subset of energies with a specific value of spin. If the equality in the hypothesis is satisfied, then the system undergoes a phase transition as a consequence of Yang-Lee theorem. As an application, we estimate the bounds on the spectrum of the Heisenberg Hamiltonian.
Volume 12 Issue 5 May 1979 pp 527-541 Solids
Stochastic theory for clustering of quenched-in vacancies—1. General mathematical properties
The problem of clustering of quenched-in vacancies into various types of extended defects is considered. A master equation for the evolution of the concentration of clusters of various sizes is written down with general transition rates. It is shown that this model represents a continuous time non-stationary Markoff process. A particular choice of transition rates corresponding to the formation of vacancy loops and stacking fault tetrahedra is considered in some detail. It is shown that this choice of transition rates allows us to obtain the solution for the concentration of the single vacancy units, and hence yields some information on the nucleation time. Further, the transition matrix becomes stationary and doubly stochastic due to the short time constant of the concentration of single vacancy units. This in turn leads to an unphysical stationary state. Finally we show how the rate equations for the irradiated situation can be written down and derive the phenomenological rate equations that are conventionally used.
Volume 12 Issue 5 May 1979 pp 543-561 Solids
A stochastic theory for clustering of quenched-in vacancies—2. A solvable model
The model introduced for clustering of quenched-in vacancies in the first part of this series of papers is considered. Using a generating function, the rate equations are converted into a first order partial differential equation for the generating function coupled to a differential equation for the rate of change of the concentration of single vacancy units. A decoupling scheme is effected which gives an exponentially decaying solution with a very short time constant for the concentration of single vacancy units. The differential equation for the generating function is solved for times larger than the time required for the concentration of single vacancy units to reach its asymptotic value. The distribution for the size of the clusters is obtained by inverting the solution thus obtained. Several results that follow are shown to be in reasonably good agreement with the experimental results.
Volume 12 Issue 6 June 1979 pp 565-580 Solids
A stochastic theory for clustering of quenched-in vacancies—III. A continuum model
In continuation of our earlier investigation on the problem of clustering of quenched-in vacancies reported earlier, starting from the discrete model, we derive a second order partial differential equation for the growth of the clusters. The solution of this equation is shown to be in reasonable agreement with the solution of the discrete model proposed earlier. However, the total number of vacancies is not conserved under slightly less stringent conditions than the conditions dictated by the solution of the discrete model, suggesting a slightly modified differential equation for the concentration of the clusters. The solution of this modified differential equation has the required properties. The leading part of the distribution when transferred into the space designating the linear dimension of the cluster has a Gaussian form. This feature is shown to be consistent with writing a Langevin equation with the linear dimension of the cluster taking the role of the random variable. This permits the identification of the smallness of parameter. An alternate formulation is also given where the concentration of the vacancies stored in a cluster of a certain size is considered as the dynamical variable. The solution obtained in this alternate formulation is shown to be consistent with the other formulation.
Volume 12 Issue 6 June 1979 pp 581-591 Solids
The continuum model for the growth of clusters developed in the previous paper (paper III) is applied to the formation of stacking fault tetrahedra in quenched gold and the formation of faulted vacancy loops in quenched aluminium. The results of the theory namely the distribution of the clusters as a function of their size and time, and the average size and the total density of the clusters as a function of time and the ageing temperature are shown to be in good agreement with the experimental results.
Volume 19 Issue 6 December 1982 pp 633-643 Solid State Physics
It is known that the density of vacancy loops in quenched aluminium and stacking fault tetrahedra in quenched gold show a saturation for low ageing temperatures. The physical mechanism leading to this effect is not well understood. In this paper we consider a simple model which allows us to obtain the temperature dependence of total density. The analysis shows that the plateau region arises due to the fact that the number of absorption sites of a cluster is larger than the number of emission sites. The temperature dependence of the average number of vacancies in a cluster and the single vacancy concentration in equilibrium with the clusters are discussed.
Volume 36 Issue 3 March 1991 pp 335-346
A multifractal study of wave functions in 1-
Using multifractal analysis we study extended, self-similar and non-self-similar type of wave functions in the Fibonacci model. Extended states arising due to commutation of transfer matrices for certain blocks of atoms in quasiperiodic systems are shown to have the same signature as the Bloch states in terms of the singularity spectrum with
Volume 39 Issue 4 October 1992 pp 329-341
Rita Khanna T R Welberry G Ananthakrishna
We report the results of Monte Carlo simulation of the phase diagram and oxygen ordering in YBa_{2}Cu_{3}O_{6+x} for low intra-sublattice repulsion. At low temperatures, apart from tetragonal (
Volume 46 Issue 6 June 1996 pp 403-410
Optimal barrier subdivision for Kramers’ escape rate
Mulugeta Bekele G Ananthakrishna N Kumar
We examine the effect of subdividing the potential barrier along the reaction coordinate on Kramers’ escape rate for a model potential. Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate.
Volume 48 Issue 2 February 1997 pp 705-718 Applications
Chaos in jerky flow — Experimental verification of a theoretical prediction
S J Noronha G Ananthakrishna L Quaouire C Fressengeas
Sometime ago Ananthakrishna and coworkers had predicted the existence of chaos in jerky flow based on a nonlinear dynamical model consisting of the time evolution equations for three types of dislocations and an equation for the evolution of the stress. Our main focus here is to report the verification of this prediction by analysing the stress signals obtained from samples of AlCu alloys subjected to a constant strain rate test. The analysis of the stress signals is carried out by using several methods. The analysis shows the existence of a finite correlation dimension and a positive Lyapunov exponent. We also carry out a surrogate analysis of the time series to ascertain that the signals are not from a power law stochastic process. From the analysis we find that the minimum number of variables required for a dynamical description of the jerky flow appears to be four or five, consistent with the number of degrees of freedom envisaged in the model.
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