Dynamics of Stick-Slip: Some Universal and Not So Universal Features

Stick-slip is usually observed in driven dissipative threshold systems. In these set of lectures, we discuss, some generic and system specific features of stickslip systems by considering a few examples wherein there has been some progress in understanding the associated dynamics. In most stick slip systems, both at low and high drive rates, the system slides smoothly, but within a window of drive rates, the motion becomes intermittent; the system alternately “sticks” till the stress builds up to a threshold value, and then “slips” when the stress is rapidly released. This intermittent motion can be traced to the existence of an unstable branch separating the two resistive branches in the force-drive-rate relation. While the two resistive branches are experimentally measurable, the unstable branch is usually not measurable and is only inferred.

Universal SU(2) gadget for polarization optics

We present a design of a universal gadget, consisting of two half-wave plates and two quarter-wave plates coaxially mounted, which can realize every SU (2) polarization optical transformation; to realize a given SU (2) element one simply has to rotate these plates about the common axis to angular positions characteristic of the element. The design is also geometrically interpreted in terms of Hamilton's theory of turns for the group SU (2).

Critical age-dependent branching Markov processes and their scaling limits

This paper studies:(i)the long-time behaviour of the empirical distribution of age and normalized position of an age-dependent critical branching Markov process conditioned on non-extinction;and (ii) the super-process limit of a sequence of age-dependent critical branching Brownian motions.

Scaling behavior of plasmon coupling in Au and ReO3 nanoparticles incorporated in polymer matrices

Polymer nanocomposites containing different concentrations of Au nanoparticles have been investigated by small angle X-ray scattering and electronic absorption spectroscopy. The variation in the surface plasmon resonance (SPR) band of Au nanoparticles with concentration is described by a scaling law. The variation in the plasmon band of ReO3 nanoparticles embedded in polymers also follows a similar scaling law. Sistance dependence of plasmon coupling in polymer composites f metal nanoparticles. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Scaling theory of quantum resistance distributions in disordered systems

We have derived explicitly, the large scale distribution of quantum Ohmic resistance of a disordered one-dimensional conductor. We show that in the thermodynamic limit this distribution is characterized by two independent parameters for strong disorder, leading to a two-parameter scaling theory of localization. Only in the limit of weak disorder we recover single parameter scaling, consistent with existing theoretical treatments.

Critical phenomena in polymer solutions: Scaling of the free energy

The thermodynamics of monodisperse solutions of polymers in the neighborhood of the phase separation temperature is studied by means of Wilson’s recursion relation approach, starting from an effective ϕ4 Hamiltonian derived from a continuum model of a many‐chain system in poor solvents. Details of the chain statistics are contained in the coefficients of the field variables ϕ, so that the parameter space of the Hamiltonian includes the temperature, coupling constant, molecular weight, and excluded volume interaction. The recursion relations are solved under a series of simplifying assumptions, providing the scaling forms of the relevant parameters, which are then used to determine the scaling form of the free energy. The free energy, in turn, is used to calculate the other singular thermodynamic properties of the solution. These are characteristically power laws in the reduced temperature and molecular weight, with the temperature exponents being the same as those of the 3d Ising model. The molecular weight exponents are unique to polymer solutions, and the calculated values compare well with the available experimental data.

Supercritical age-dependent branching Markov processes and their scaling limits

This paper studies the long-time behavior of the empirical distribution of age and normalized position of an age-dependent supercritical branching Markov process. The motion of each individual during its life is a random function of its age. It is shown that the empirical distribution of the age and the normalized position of all individuals alive at time t converges as t -> infinity to a deterministic product measure.

Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation

Atomic vibration in the Carbon Nanotubes (CNTs) gives rise to non-local interactions. In this paper, an expression for the non-local scaling parameter is derived as a function of the geometric and electronic properties of the rolled graphene sheet in single-walled CNTs. A self-consistent method is developed for the linearization of the problem of ultrasonic wave propagation in CNTs. We show that (i) the general three-dimensional elastic problem leads to a single non-local scaling parameter (e(0)), (ii) e(0) is almost constant irrespective of chirality of CNT in the case of longitudinal wave propagation, (iii) e(0) is a linear function of diameter of CNT for the case of torsional mode of wave propagation, (iv) e(0) in the case of coupled longitudinal-torsional modes of wave propagation, is a function which exponentially converges to that of axial mode at large diameters and to torsional mode at smaller diameters. These results are valid in the long-wavelength limit. (C) 2011 Elsevier Ltd. All rights reserved.

Universal Stability and Temperature Dependent Phase Transformation in Group VIIIB-IB Transition Metal FCC Nanowires

Atomistic simulation of Ag, Al, Au, Cu, Ni, Pd, and Pt FCC metallic nanowires show a universal FCC -> HCP phase transformation below a critical cross-sectional size, which is reported for the first time in this paper. The newly observed HCP structure is also confirmed from previous experimental results. Above the critical cross-sectional size, initial < 100 >/{100} FCC metallic nanowires are found to be metastable. External thermal heating shows the transformation of metastable < 100 >/{100} FCC nanowires into < 110 >/{111} stable configuration. Size dependent metastability/instability is also correlated with initial residual stresses of the nanowire by use of molecular static simulation using the conjugant gradient method at a temperature of 0 K. It is found that a smaller cross-sectional dimension of an initial FCC nanowire shows instability due to higher initial residual stresses, and the nanowire is transformed into the novel HCP structure. The initial residual stress shows reduction with an increase in the cross-sectional size of the nanowires. A size dependent critical temperature is also reported for metastable FCC nanowires using molecular dynamic, to capture the < 110 >/{111} to < 100 >/{100} shape memory and pseudoelasticity.

Some recent advances in the theory of homogeneous isotropic turbulence

We review some advances in the theory of homogeneous, isotropic turbulence. Our emphasis is on the new insights that have been gained from recent numerical studies of the three-dimensional Navier Stokes equation and simpler shell models for turbulence. In particular, we examine the status of multiscaling corrections to Kolmogorov scaling, extended self similarity, generalized extended self similarity, and non-Gaussian probability distributions for velocity differences and related quantities. We recount our recent proposal of a wave-vector-space version of generalized extended self similarity and show how it allows us to explore an intriguing and apparently universal crossover from inertial- to dissipation-range asymptotics.

Universal behaviour in erosive burning of solid propellants

This paper considers the extensive data and correlations on the erosive burning of solid propellants. A relatively simple nondimensional relationship between the ratio of the actual to nonerosive burn rate (eta) and a quantity g, which is the product of g(0)-the ratio of free stream mass flux to the mass flux from the surface for nonerosive condition-and Re-0(m), where Re-0 is the Reynolds number based on the nonerosive mass flux of the propellant and port diameter, is shown to correlate most data within the accuracies of the experiments with m = -0.125. This shows the above relationship to account for the effects of pressure, aluminum, even up to a proportion of 17%, burn rate catalysts, and motor size. It is concluded that the suggested correlation between eta and g may be adopted universally for most practical propellants. (C) 1997 by The Combustion Institute.

Performance and scaling of a 1.2 V/1.5 Ah nickel/metal hydride cell to a 6 V/1.5 Ah battery

A 1.2 V/1.5 Ah positive-limited nickel/metal hydride cell has been studied to determine its charge-discharge characteristics at different rates in conjunction with its AC impedance data. The faradaic efficiency of the cell is found to be maximum at similar to 70% charge input. The cell has been scaled to a 6 V/1.5 Ah battery. The cycle-life data on the battery suggest that it can sustain a prolonged charge-discharge schedule with little deterioration in its performance.