T. R. Ramamohan

Chaotic rheological parameters of periodically forced suspensions of slender rods in simple shear flow

We demonstrate for the first time that the rheological parameters like the apparent viscosities and the first and second normal stress differences of suspensions of orientable particles can show chaotic behavior when the orientation vector evolves chaotically. We also demonstrate that the range of the values of the rheological parameters is about 10 000 times greater when the parameters evolve chaotically. This suggests that a wide range of properties may be obtained by small variations in controllable parameters. When coupled with suitable control of chaos algorithms, a wide range of suspension behavior is thus possible since a chaotic solution can be considered as an unlimited reservoir of periodic solutions of arbitrary period.

Chaotic dynamics of a periodically forced slender body in a simple shear flow

Abstract The dynamics of a periodically forced slender body in a simple shear flow is analysed. This represents the simplest case of a class of problems that have not attracted attention in the literature. The system undergoes a quasiperiodic transition to chaos in the range of parameters investigated. It also exhibits chaotic transients obtained by the apparent collision of a stable nonchaotic attractor and a chaotic attractor with the transients scaling in a manner similar to that analysed by Grebogi et al. [Ergodic Theory Dynamical Systems 5 (1985) 341] with the exponent of scaling approximately equal to -0.5. The class of problems to which this paper is an introduction is technologically important and can lead to new methods of processing composites, electrorheological fluids and polymer solutions.

Controlling chaotic dynamics of periodically forced spheroids in simple shear flow: Results for an example of a potential application

Recently, we studied the technologically important problem of periodically forced spheroids in simple shear flow and demonstrated the existence of chaotic parametric regimes. Our results indicated a strong dependence of the solutions obtained on the aspect ratio of the spheroids, which can be used to separate particles from a suspension. In this paper we demonstrate that controlling the chaotic dynamics of periodically forced particles by a suitably engineered novel control technique, which needs little information about the system and is easy to implement, leads to the possibility of better separation. Utilizing the flexibility of controlling chaotic dynamics in a desired orbit irrespective of initial state, we show that it is theoretically possible to separate particles much more efficiently than otherwise from a suspension of particles having different shapes but similar sizes especially for particles of aspect ratiore>1.0. The strong dependence of the controlled orbit on the aspect ratio of the particles may have many applications such as in the development of computer-controlled intelligent rheology. The results suggest that control of chaos as discussed in this work may also have many applications.

Mathematical Modelling of the Liquid-Liquid Extraction Separation of Rare Earths

Abstract An empirical mathematical model has been developed for the simulation of an integrated solvent extraction circuit consisting of an extractor, scrubber and a stripper. This model is designed to simulate the separation of any lanthanide from a mixed lanthanide feed. The Kremser equation is used to calculate the separation occurring in each section of the circuit. The inputs required for the simulation are the feed composition, separation factors, equilibrium data of the key element under a wide range of conditions, the number of stages and flow rates of the aqueous and organic streams in the circuit. This model has been validated with the experimental data for the separation of Nd from a mixed lanthanide chloride feed with 2-ethylhexyl phosphonic acid mono 2-ethyl-hexyl ester (EHPNA) as an extractant.

COMPARATIVE ANALYSIS OF A HEURISTIC CONTROL OF CHAOS ALGORITHM IN SOME MODEL SYSTEMS

In this work we propose a Heuristic algorithm based on parametric perturbation for control of chaos in systems of ODEs. This method appears to be the first to apply a perturbation to a parameter in a system of ODEs that is active over a finite length of time only. The method proposed is comparatively easy to implement and needs almost no information about the system beyond the existence of a system-wide controllable parameter. We demonstrate certain advantages of this technique over two well-known algorithms, namely, control by periodic parametric perturbation and control by addition of a second weak periodic force, such as the possibility of switching behavior, pretargetting the period of the controlled orbit, stabilizing high period orbits etc. We also demonstrate the applicability of the technique in certain numerical models of physical systems and also in a rather difficult model problem, viz. the control of the rheological parameters of periodically forced suspensions of slender rods in simple shear flow.

Chaotic Dynamics and Rheology of Suspensions of Periodically Forced Slender Rods in Simple Shear Flow

In an earlier paper, we had outlined a procedure for calculating the rheological parameters for periodically forced suspensions of slender rods in simple shear flow in the chaotic regime. In this work, we examine the consequences of the above procedure on the dynamics and rheology of similar suspensions starting off with uniform initial orientation distributions as well as aligned initial distributions. We provide numerical evidence for existence of riddled and intermingled basins of attractions in the system. We discuss the limitations of the diffusion equation approach in the chaotic regime. We also demonstrate that small changes in the preparation of aligned suspensions can lead to dramatically different rheological behaviour in some parametric regimes. In other parametric regimes differences in the dynamical behaviour do not translate into differences in the rheological behaviour of aligned suspensions.

Application of chaotic noise reduction techniques to chaotic data trained by ANN

We propose a novel method of combining artificial neural networks (ANNs) with chaotic noise reduction techniques that captures the metric and dynamic invariants of a chaotic time series, e.g. a time series obtained by iterating the logistic map in chaotic regimes. Our results indicate that while the feedforward neural network is capable of capturing the dynamical and metric invariants of chaotic time series within an error of about 25%, ANNs along with chaotic noise reduction techniques, such as Hammel’s method or the local projective method, can significantly improve these results. This further suggests that the effort on the ANN to train data corresponding to complex structures can be significantly reduced. This technique can be applied in areas like signal processing, data communication, image processing etc.

New Class I intermittency in the dynamics of periodically forced spheroids in simple shear flow

Abstract We report a physically realisable system in which the possibility of an interesting and novel type of Class I intermittency is demonstrated. Price and Mullin [Physica D 48 (1991) 29] have observed experimentally a similar type of phenomenon in which a hysteretic form of intermittency with extreme regularity of the bursting is observed. The system described in this work appears to be one of the very few ODE systems describing a physically realisable system showing a nonhysteretic form of Class I intermittency with nearly regular reinjection period. The regularity of the bursting is unaffected by variation in the control parameter. The maximum Lyapunov exponents of the bursts and laminar phase are estimated separately and indicate existence of chaos. The length of the laminar phase shows scaling behaviour typical of Class I intermittency near the tangent bifurcation and also shows new scaling behaviour. Return maps of the dynamical system are presented to explain the behaviour observed.