V. Sridhar

Molecular dynamics simulations of oxygen ion diffusion in yttria-stabilized zirconia

Oxygen ion diffusion in yttria-stabilized zirconia (YSZ) is studied employing molecular dynamics simulation. Oxygen ions migrate mainly by nearest neighbour hopping amongst the tetrahedral lattice sites of zirconium ions. A linear relation between the mean square displacement and time is found, after the oxygen ions have moved over distances much larger than the characteristic distances of the underlying crystal structure. In this diffusive region, the bulk oxygen tracer diffusion coefficient is 2.21×10−6cm2s−1 at 1759K and 3.53×10−6cm2s−1 at 2057K. The ionic conductivity, calculated from the bulk oxygen tracer diffusion coefficient, matches well with the experimental values. For all the ion pairs in YSZ, we have calculated the radial distribution function. We find that the peak height is smaller at higher temperature, due to the volume expansion of the YSZ crystal.

Signature of chaos in power spectrum

We investigate the nature of the numerically computed power spectral densityP(f, N, τ) of a discrete (sampling time interval,τ) and finite (length,N) scalar time series extracted from a continuous time chaotic dynamical system. We highlight howP(f, N, τ) differs from the true power spectrum and from the power spectrum of a general stochastic process. Non-zeroτ leads to aliasing;P(f, N, τ) decays at high frequencies as [πτ/sinπτf]2, which is an aliased form of the 1/f2 decay. This power law tail seems to be a characteristic feature of all continuous time dynamical systems, chaotic or otherwise. Also the tail vanishes in the limit ofN → ∞, implying that the true power spectral density must be band width limited. In striking contrast the power spectrum of a stochastic process is dominated by a term independent of the length of the time series at all frequencies.

Interacting growth walk on a honeycomb lattice

The interacting growth walk (IGW) is a kinetic algorithm proposed recently for generating long, lattice polymer configurations. The growth process in IGW is tuned by a parameter called the growth temperature TG=1/(kBβG). In this paper we consider IGW on a honeycomb lattice. We take the non-bonded nearest neighbour contact energy as e=−1. We show that at βG=0, IGW algorithm generates a canonical ensemble of interacting self-avoiding walks at β=β(βG=0)=ln(2). However for βG>0, IGW generates an ensemble of polymer configurations most of which are in equilibrium at β=β(βG). The remaining ones are frozen in ‘non-equilibrium’ configurations.

flatIGW — An inverse algorithm to compute the density of states of lattice self avoiding walks

We show that the Density of States (DoS) for lattice Self Avoiding Walks can be estimated by using an inverse algorithm, called flatIGW, whose step-growth rules are dynamically adjusted by requiring the energy histogram to be locally flat. Here, the (attractive) energy associated with a configuration is taken to be proportional to the number of non-bonded nearest neighbor pairs (contacts). The energy histogram is able to explicitly direct the growth of a walk because the step-growth rule of the Interacting Growth Walk (Narasimhan et al. (2003) [5]) samples the available nearest neighbor sites according to the number of contacts they would make. We have obtained the complex Fisher zeros corresponding to the DoS, estimated for square lattice walks of various lengths, and located the θ temperature by extrapolating the finite size values of the real zeros to their asymptotic value, ∼1.49 (reasonably close to the known value, ∼1.50 (Barkema et al. (1998) [14]).

Characterization of chaos in a serrated plastic flow model

We report new results on a dynamical model of serrated yielding. These essentially pertain to the full spectrum of Lyapunov exponents of the non-linear (chaotic) model and fractal characterization of the associated strange attractor. The power spectrum of scalar time series extracted from the phase space trajectories decays exponentially with increase of frequency and the decay constant is found proportional to the Kolmogorov-Sinai entropy.

First passage time on a multifurcating hierarchical structure

Asymptotic behaviour of the moments of the first passage time (FPT) on a one-dimensional lattice holding a multifurcating hierarchy of teeth is studied. There is a transition from ordinary to anomalous diffusion when the parameter controlling the relative sizes of the teeth, is varied with respect to the furcating number of the hierarchy. The scaling behaviour of the moments of FPT with the linear dimensions of the lattice segment indicates that in the anomalcus phase the probability density of the FPT is multifractal.

Persistence and life time distribution in coarsening phenomena

We investigate the lifetime distribution P(τ,t) in one and two dimensional coarsening processes modelled by Ising–Glauber dynamics at zero temperature. The lifetime τ is defined as the time that elapses between two successive flips in the time interval (0,t) or between the last flip and the observation time t. We calculate P(τ,t) averaged over all the spins in the system and over several initial disorder configurations. We find that asymptotically the lifetime distribution obeys a scaling ansatz: P(τ,t)=t−1φ(ξ), where ξ=τ/t. The scaling function φ(ξ) is singular at ξ=0 and 1, mainly due to slow dynamics and persistence. An independent lifetime model where the lifetimes are sampled from a distribution with power law tail is presented, which predicts analytically the qualitative features of the scaling function. The need for going beyond the independent lifetime models for predicting the scaling function for the Ising–Glauber systems is indicated.

Multiscaling in Normal Grain Growth: A Monte Carlo Study

We describe Monte Carlo simulation of the phenomenon of normal grain growth employing q state Potts model. We find that at long times after quench the grain size distribution is multiscaling.

Fractal measures of first passage time of a simple random walk

We consider random walks, starting at the site i = 1, on a one-dimensional lattice segment with an absorbing boundary at i = 0 and a reflecting boundary at i = L. We find that the typical value of first passage time (FPT) is independent of system size L, while the mean value diverges linearly with L. The qth moment of the FPT diverges with system size as L2q−1, for q >12. For a finite but large L, the FPT distribution has an 1/t tail cut off by an exponential of the form exp(-t/L2). However, if L is set equal to infinity, the distribution has an algebraic tail given by t-12. We find that the generalised dimensions D(q) have a nontrivial dependence on q. This shows that the FPT distribution is a multifractal. We also calculate the singularity spectrum f(α).