Hidden order in crackling noise during peeling of an adhesive tape

We address the longstanding problem of recovering dynamical information from noisy acoustic emission signals arising from peeling of an adhesive tape subject to constant traction velocity. Using the phase space reconstruction procedure we demonstrate the deterministic chaotic dynamics by establishing the existence of correlation dimension as also a positive Lyapunov exponent in a midrange of traction velocities. The results are explained on the basis of the model that also emphasizes the deterministic origin of acoustic emission by clarifying its connection to stick-slip dynamics.

Nonlinear ensemble prediction of chaotic daily rainfall

The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. Many of these approaches aim at only analyzing the chaotic nature and not its prediction. In the present study, an attempt is made to identify chaos using various techniques and prediction is also done by generating ensembles in order to quantify the uncertainty involved. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha, Mahanadi and All-India for the period 1955-2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series. Correlation dimension method is done on th phase randomized and first derivative of the data series to check whether the saturation of the dimension is due to the inherent linear correlation structure or due to low dimensional dynamics. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996-2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are done from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. (C) 2010 Elsevier Ltd. All rights reserved.

Dynamo onset as a first-order transition: Lessons from a shell model for magnetohydrodynamics

We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydro-dynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number Pr-M and the magnetic Reynolds number Re-M. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the (Pr-M(-1), Re-M) plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain a hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

On the study of a third-order mechanical oscillator

In this paper, the study of a third-order mechanical oscillator is presented by demonstrating its equivalence to the well-known R.C. multivibrator with two additional reactive elements. The conditions for the oscillator's possession of periodic solutions are presented. It is also shown that under certain conditions, the study of the given third-order autonomous system can be reduced to the study of an equivalent second-order, non-autonomous system.

Cubic and ultimate groups of complete symmetry

It is shown that the systems of definite actions described by polar and axial tensors of the second rank and their combinations during the superposition of their elements of complete symmetry with the elements of complete symmetry of the "grey" cube, result in 11 cubic crystallographical groups of complete symmetry. There are 35 ultimate groups (i.e., the groups having the axes of symmetry of infinite order) in complete symmetry of finite figures. 14 out of these groups are ultimate groups of symmetry of polar and axial tensors of the second rank and 24 are new groups. All these 24 ultimate groups are conventional groups since they cannot be presented by certain finite figures possessing the axes of symmetry {Mathematical expression}. Geometrical interpretation for some of the groups of complete symmetry is given. The connection between complete symmetry and physical properties of the crystals (electrical, magnetic and optical) is shown.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Design of first- and second-order sliding mode observers for induction motors using a stator-flux model

We extend current research in the area of 'sensorless' control of induction motors by presenting two observers based on first- and second-order sliding mode control theories for the simultaneous estimation of flux and speed. We base the observers on the stator-flux model of the motor instead of the usual rotor-flux model mainly because of the uncertain rotor resistance that plays a significant role in the latter. By designing the observers as if they are sliding mode controllers, we lend the properties of parameter insensitive closed-loop dynamics and finite time convergence to the stator flux and speed estimation schemes. We also present simulation and experimental results to validate the operation of the observers.

Charge-order driven multiferroic and magneto-dielectric properties of rare earth manganates

Charge-order driven magnetic ferroelectricity is shown to occur in several rare earth manganates of the general formula, Ln(1-x)A(x)MnO(3) (In = rare earth, A = alkaline earth). Charge-ordered manganates exhibit dielectric constant anomalies around the charge-ordering or the antiferromagnetic transition temperature. Magnetic fields have a marked effect on the dielectric properties of these compounds, indicating the presence of coupling between the magnetic and electrical order parameters. Magneto-dielectric properties are retained in small particles of the manganates. The observation of magneto-ferroelectricity in these manganates is in accordance with theoretical predictions.

Charge-order driven multiferroic and magneto-dielectric properties of rare earth manganates

Charge-order driven magnetic ferroelectricity is shown to occur in several rare earth manganates of the general formula, Ln(1-x)A(x)MnO(3) (In = rare earth, A = alkaline earth). Charge-ordered manganates exhibit dielectric constant anomalies around the charge-ordering or the antiferromagnetic transition temperature. Magnetic fields have a marked effect on the dielectric properties of these compounds, indicating the presence of coupling between the magnetic and electrical order parameters. Magneto-dielectric properties are retained in small particles of the manganates. The observation of magneto-ferroelectricity in these manganates is in accordance with theoretical predictions.