Possibility of chaos in interval friction experiments of martensites

Wuttig and Suzuki's model on anelastic nonlinearities in solids in the vicinity of martensite transformations is analysed numerically. This model shows chaos even in the absence of applied forcing field as a function of a temperature dependent parameter. Even though the model exhibits sustained oscillations as a function of the amplitude of the forcing term, it does not exactly capture the features of the experimental time series. We have improved the model by adding a symmetry breaking term. The improved model shows period doubling bifurcation as a function of the amplitude of the forcing term. The solutions of our improved model shows good resemblance with the nonsymmetric period four oscillation seen in the experiment. (C) 1999 Elsevier Science B.V. All rights reserved.

Singularity structure and chaotic behavior of the homopolar disk dynamo

We study in great detail a system of three first-order ordinary differential equations describing a homopolar disk dynamo (HDD). This system displays a large variety of behaviors, both regular and chaotic. Existence of periodic solutions is proved for certain ranges of parameters. Stability criteria for periodic solutions are given. The nonintegrability aspects of the HDD system are studied by investigating analytically the singularity structure of the system in the complex domain. Coexisting attractors (including period-doubling sequence) and coexisting strange attractors appear in some parametric regimes. The gluing of strange attractors and the ungluing of a strange attractor are also shown to occur. A period of bifurcation leading to chaos, not observed for other chaotic systems, is shown to characterize the chaotic behavior in some parametric ranges. The limiting case of the Lorenz system is also studied and is related to HDD.

Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper we analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. We first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zero or positive, then the robot equations cannot exhibit chaos. We show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, we analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, we resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and we show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.

Dynamics of strain bifurcations in a magnetostrictive ribbon

We develop a coupled nonlinear oscillator model involving magnetization and strain to explain several experimentally observed dynamical features exhibited by forced magnetostrictive ribbon. Here we show that the model recovers the observed period-doubling route to chaos as function of the dc field for a fixed ac field and quasiperiodic route to chaos as a function of the ac field, keeping the dc field constant. The model also predicts induced and suppressed chaos under the influence of an additional small-amplitude near-resonant ac field. Our analysis suggests rich dynamics in coupled order-parameter systems such as magnetomartensitic and magnetoelectric materials.

A unified model for the dynamics of driven ribbon with strain and magnetic order parameters

We develop a unified model to explain the dynamics of driven one dimensional ribbon for materials with strain and magnetic order parameters. We show that the model equations in their most general form explain several results on driven magnetostrictive metallic glass ribbons such as the period doubling route to chaos as a function of a dc magnetic field in the presence of a sinusoidal field, the quasiperiodic route to chaos as a function of the sinusoidal field for a fixed dc field, and induced and suppressed chaos in the presence of an additional low amplitude near resonant sinusoidal field. We also investigate the influence of a low amplitude near resonant field on the period doubling route. The model equations also exhibit symmetry restoring crisis with an exponent close to unity. The model can be adopted to explain certain results on magnetoelastic beam and martensitic ribbon under sinusoidal driving conditions. In the latter case, we find interesting dynamics of a periodic one orbit switching between two equivalent wells as a function of an ac magnetic field that eventually makes a direct transition to chaos under resonant driving condition. The model is also applicable to magnetomartensites and materials with two order parameters. (C) 2013 American Institute of Physics. http://dx.doi.org/10.1063/1.4790845]

Synchronization of globally coupled two-state stochastic oscillators with a state-dependent refractory period

We present a model of identical coupled two-state stochastic units, each of which in isolation is governed by a fixed refractory period. The nonlinear coupling between units directly affects the refractory period, which now depends on the global state of the system and can therefore itself become time dependent. At weak coupling the array settles into a quiescent stationary state. Increasing coupling strength leads to a saddle node bifurcation, beyond which the quiescent state coexists with a stable limit cycle of nonlinear coherent oscillations. We explicitly determine the critical coupling constant for this transition.

Experimental and Analytical Investigations of the actions taking place in a Synchronous machine during the starting period when the starting Is effected by means of alternating current

The literature on the subject of the present investigation is somewhat meagre. A rotary converter or synchronous motor no! provided with any special starting devices forms, when started from the alternating current side, a type of induction motor whoso Htator is provided with a polyphase winding, and whoso rotor has a single-phase (or single magnetic axis) winding.

Influence of validation schemes in a laser Doppler anemometer period timing device for frequency measurement

The short duration of the Doppler signal and noise content in it necessitate a validation scheme to be incorporated in the electronic processor used for frequency measurement, There are several different validation schemes that can be employed in period timing devices. A detailed study of the influence of these validation schemes on the measured frequency has been reported here. These studies were carried out by using a combination of a fast A/D converter and computer. Doppler bursts obtained from an air flow were digitised and stored on magnetic discs. Suitable computer programs were then used to simulate the performance of period timing devices with different validation schemes and the frequency of the stored bursts were evaluated. It is found that best results are obtained when the validation scheme enables frequency measurement to be made over a large number of cycles within the burst.

Continuation of limit cycles near saddle homoclinic points using splines in phase space

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.

Simple period timing device for laser Doppler signals

A period timing device suitable for processing laser Doppler anemometer signals has been described here. The important features of this instrument are: it is inexpensive, simple to operate, and easy to fabricate. When the concentration of scattering particles is low the Doppler signal is in the form of a burst and the Doppler frequency is measured by timing the zero crossings of the signal. But the presence of noise calls for the use of validation criterion, and a 5–8 cycles comparison has been used in this instrument. Validation criterion requires the differential count between the 5 and 8 cycles to be multiplied by predetermined numbers that prescribe the accuracy of measurement. By choosing these numbers to be binary numbers, much simplification in circuit design has been accomplished since this permits the use of shift registers for multiplication. Validation accuracies of 1.6%, 3.2%, 6.3%, and 12.5% are possible with this device. The design presented here is for a 16-bit processor and uses TTL components. By substituting Schottky barrier TTLs the clock frequency can be increased from about 10 to 30 MHz resulting in an extension in the range of the instrument. Review of Scientific Instruments is copyrighted by The American Institute of Physics.

A note on the period of oscillation of non-linear systems

This paper deals with two approximate methods of finding the period of oscillations of non-linear conservative systems excited by step functions. The first method is an extension of the analysis presented by Jonckheere [4] and the second one is based on a weighted bilinear approximation of the non-linear characteristic. An example is presented and the approximate results are compared with the exact results

Simple period timing device for laser Doppler signals

A period timing device suitable for processing laser Doppler anemometer signals has been described here. The important features of this instrument are: it is inexpensive, simple to operate, and easy to fabricate. When the concentration of scattering particles is low the Doppler signal is in the form of a burst and the Doppler frequency is measured by timing the zero crossings of the signal. But the presence of noise calls for the use of validation criterion, and a 5–8 cycles comparison has been used in this instrument. Validation criterion requires the differential count between the 5 and 8 cycles to be multiplied by predetermined numbers that prescribe the accuracy of measurement. By choosing these numbers to be binary numbers, much simplification in circuit design has been accomplished since this permits the use of shift registers for multiplication. Validation accuracies of 1.6%, 3.2%, 6.3%, and 12.5% are possible with this device. The design presented here is for a 16-bit processor and uses TTL components. By substituting Schottky barrier TTLs the clock frequency can be increased from about 10 to 30 MHz resulting in an extension in the range of the instrument. Review of Scientific Instruments is copyrighted by The American Institute of Physics.

Chronopotentiometry with power-law perturbation functions at an expanding plane electrode with and without a preceding blank period for systems with a coupled first-order homogeneous chemical reaction

The systems formalism is used to obtain the interfacial concentration transients for power-law current input at an expanding plane electrode. The explicit results for the concentration transients obtained here pertain to arbitrary homogeneous reaction schemes coupled to the oxidant and reductant of a single charge-transfer step and the power-law form without and with a preceding blank period (for two types of power-law current profile, say, (i) I(t) = I0(t−t0)q for t greater-or-equal, slanted t0, I(t) = 0 for t < t0; and (ii) I(t) = I0tq for t greater-or-equal, slanted t0, I(t) = 0 for t < t0). Finally the potential transients are obtained using Padé approximants. The results of Galvez et al. (for E, CE, EC, aC) (J. Electroanal. Chem., 132 (1982) 15; 146 (1983) 221, 233, 243), Molina et al. (for E) (J. Electroanal. Chem., 227 (1987) 1 and Kies (for E) (J. Electroanal. Chem., 45 (1973) 71) are obtained as special cases.

Observation of the doubling of critical exponents in reentrant phase transitions

Electrical resistance (R) measurements are reported for ternary mixtures of 3-methylpyridine, water and heavy water as a function of temperature (T) and heavy water content in total water. These mixtures exhibit a limited two-phase region marked by a loop size (ΔT) that goes to zero as the double critical point (DCP) is approached. The measurements scanned the ΔT range 1.010°C less-than-or-equals, slant ΔT less-than-or-equals, slant 77.5°C. The critical exponent (θ), which signifies the divergence of ∂R/∂T, doubles within our experimental uncertainties as the DCP is reached very closely.