Fractional Oscillator -- Harmonic Oscillator with Memory Effects
The importance of fractional time-derivative to take care of memory effects has been brought out by considering the example of a simple oscillator.
physics.class-ph↗
arXiv subjects
Vishwamittar
Publications and source records attributed to Vishwamittar.
A comparative study of asymmetric dichotomous noise and symmetric trichotomous noise induced stochastic resonance in the globally coupled fractional oscillators
The collective behaviour, in respect of stochastic resonance, has been studied in globally coupled oscillators (with fractional-order intrinsic and external damping), driven by a sinusoidal force which is either noise-free or noise-modulated, and subjected to multiplicative quadratic asymmetric dichotomous or symmetric trichotomous noise perturbing the potential parameter, the coupling factor and the local drift force. The influence of coupling between the heat bath and the applied force has been included through a simple model. The effect of variation in mass, friction and potential parameters on the output amplitude gains as function of noise-intensity, has been meticulously investigated for both types of noise and the exponents governing the dependence of collective SR peak amplitude on the three oscillator parameters have been determined and analysed. The special case arising from the zero value of the potential parameter, which implies rectilinear motion of the system particles in the absence of fluctuations, has been dealt with under the influence of the second-order asymmetric dichotomous noise and stochastic resonance has been found to occur at justifiably quite low frequencies of the external force. This brings out the importance of nonlinear term in this coloured noise, for which this phenomenon is unique. The accuracy of the analytical results has been substantiated through numerical simulations.
cond-mat.stat-mech↗
A comparative study of some analytic approximate methods for the anharmonic oscillator described by cubic quartic potential
The improved formulations of the Lindstedt Poincare perturbation method, the harmonic balance method and its modifications using the rational functions, the energy balance method and the two terms Fourier series expansion have been employed to find approximate solution to the equation of motion for the cubic quartic potential AHO and its special cases (the cubic, the quartic, and the purely cubic quartic potential AHOs), to assess the relative merits and demerits of these techniques. Two new rational functions as approximate solution for the harmonic balance method have been proposed and the rational functions have been used as trial functions in the energy balance method for the first time. The time periods T+ (for q(t) > 0), T- (for q(t) < 0) and the total period T so determined have been compared with the corresponding exact values for an extensive range of the AHO parameter values. The results have been thoroughly analysed in terms of their percentage difference from the relevant exact time period. It is concluded that the methods based on the Lindstedt Poincare perturbation approach do not lead to reliable results for T+ and T-, which makes their applicability for the asymmetric potential AHOs doubtful. The harmonic balance technique together with its different variants is the most successful, while the Fourier series approach also yields commendably accurate results. The outcome of the third-order energy balance method is reasonably good though the usage of the rational functions for this has not been encouraging.
physics.comp-ph↗