Bistable Potential Well Research Articles

A bi-stable horizontal diamagnetic levitation based low frequency vibration energy harvester

A new form of bi-stable system based on the passive friction-free horizontal diamagnetic levitation mechanism is proposed in this article. The system is comprised of twelve magnets which create a bi-stable potential well for a centrally located floating magnet. The levitation is stabilized in the horizontal direction by the diamagnetic repulsion from pyrolytic graphite plates which are placed on either side of the floating magnet. Theoretical modeling is discussed involving the superposition of the magnetic fields and magnetic forces, which include semi-analytical equations, from the various magnets in the system to determine the characteristics of the bi-stable potential well. Stability equations for achieving static bi-stability and for maintaining stable levitation during intra-well and inter-well motion were discussed. An experimental prototype is presented whose frequency response characteristics were validated for varying input sinusoidal excitations. Once the dynamics of the bi-stable system were validated, copper coils are incorporated into the diamagnetic plates to enable the vibration energy harvesting capability of the levitation mechanism. The floating magnet underwent chaotic and interwell motions for a range of input sinusoidal excitation frequencies, 5.8 Hz – 8 Hz, at input accelerations of 1.99 m/s2 to 3.79 m/s2, and peak system efficiencies of close to 2.5% were achieved.

Design and Analysis of a Bistable Vibration Energy Harvester Using Diamagnetic Levitation Mechanism

In this paper, a novel bistable vibration energy harvester using the diamagnetic levitation mechanism is conceptualized, designed, fabricated, and experimented comprehensively. The bistable energy harvester consists of a floating magnet, lifting magnets, diamagnetic plates, and coils. The lifting magnets placed symmetrically on the both sides of the base are designed to balance the weight of the floating magnet and produce a bistable potential well. The floating magnet is stabilized in the horizontal direction by diamagnetic plates which are made of pyrolytic graphite. Ring-shaped coils are designed for transduction and flanked by the side of diamagnetic plates. Theoretical modeling and analyses are carried out to compare with experimental data. Throughout the theoretical and experimental results, a peak power of $333.7~\mu \text{w}$ is generated from a vibration level of 0.6 m/ $\text{s}^{2}$ over a range of 0.5–4.5 Hz. It is indicated that the bistable energy harvester can efficiently operate at extremely low frequencies (<5 Hz).

Fault diagnosis of gearbox using multi-time-delayed feedback stochastic resonance

Gearbox vibration signals with defects often show some important characteristic information. However, the feature information is difficult to extract since it is often flooded in the noise. To solve this problem, we present a novel detection approach for weak signals based on the multi-time-delayed feedback stochastic resonance model (MTFSR). Because the shape of the bistable potential well can be changed by the number of time-delayed terms, the MTFSR method can use historical information which is formed by the superposition of multiple time-delayed feedback items to enhance signal periodicity and obtain better output waveform and higher signal-to-noise ratio (SNR). Moreover, the presented method is also insensitive to the noise, and can detect the weak signals with different noise levels. Additionally, by selecting the proper calculation step, the approach has the ability to detect weak signals with different driving frequencies. With these properties, the proposed MTFSR is considered to be very suitable for gearbox fault diagnosis. Both simulation study and practical application confirm that the proposed strategy is feasible and superior in comparison with some traditional methods.

A bistable electromagnetic micro-power generator using FR4-based folded arm cantilever

This paper discusses a wideband, bistable vibrational micro-power generator using a folded cantilever beam. At an acceleration of 0.5g (35Hz frequency) the device generated a peak power of 22μW across an optimum resistive load of 1kΩ. The half-power bandwidth of the nonlinear bistable device was increased by 5Hz (15% of the peak power frequency) with respect to the linear counterpart. The choice of FR4 as the structural material and the utilization of a folded cantilever design are aimed at achieving a low operational frequency within a relatively small footprint. The bistable mechanism which is introduced into the system by means of a magnetic force between a pair of repulsively positioned NdFeB permanent magnets was analytically modelled, numerically simulated and successfully validated with experimental results. The wideband frequency response is further experimentally modified by adjusting the gap between the repulsive magnets. The effect of the depth of the bistable potential well on the performance of the vibration energy harvester at low to medium accelerations is also validated numerically and experimentally.

Fluctuations and dissipations in stochastic energetic resonance

By analyzing the fluctuations and dissipations of a Brownian particle colliding with the molecules in a fluid, the work exchanged between the Brownian particle constrained in a bistable potential well and an external periodic force is investigated. Characters of the stochastic energetic resonance are found and studied at different intensities of fluctuations and dissipations. The microscopic mechanism of energy exchange between the Brownian particle and the external force is revealed. The method used in this study provides a novel way of controlling the stochastic energetic resonance.

Effect of Time Delay on Stochastic Tumor Growth

We study the dynamics of tumor cell growth with time-delayed feedback driven by multiplicative noise in an asymmetrical bistable potential well. For a small delay time, the analytical solutions of the probability distribution and the first passage time show that, with the increasing delay time, the peak of the probability distribution in a lower population state would increase, but in a higher population state it decreases. It is shown that the multiplicative noise and the time delay play opposite roles in the tumor cell growth.

Investigations of a nonlinear energy harvester with a bistable potential well

This paper investigates a nonlinear energy harvester that uses magnetic interactions to create an inertial generator with a bistable potential well. The motivating hypothesis for this work was that nonlinear behavior could be used to improve the performance of an energy harvester by broadening its frequency response. Theoretical investigations study the harvester's response when directly powering an electrical load. Both theoretical and experimental tests show that the potential well escape phenomenon can be used to broaden the frequency response of an energy harvester.

Thermally activated hopping of two ions trapped in a bistable potential well

With two ions in a spheroidal Paul trap, the harmonic trapping potential turns, by Coulomb repulsion, into a bistable well. Two Ba ions have been confined, laser-cooled, and observed, via their laser-excited resonance scattering, by a spatially resolving photomultiplier, or intensifying CCD camera. A repump laser releases the ions from a metastable state. Well-cooled ions are found localized. When the laser is detuned, the Raman cooling rate and the ions’ temperature vary. A transition from the crystallized state to a toroidal gas takes place. The ions are discriminated when one (i) gets excited into a non-fluorescing metastable state, or (ii) is of another isotopic species. Hopping rates of 1 s −1 ar ef ound at high thermal excitation. Elsewhere, the rates drop by two orders of magnitude, and vary resonantly with temperature near potential energy/kinetic energy = 15, where the bright ion’s hopping upstream of the laser beam is five times more likely than downstream. Two discernible ions in a trap represent a microscopic model system for the study of reaction kinetics.

Microscopic Models and Simulations of Local Activation Processes

The classical reaction theory of Kramers describes transitions over a potential barrier (activation processes) by Fokker–Planck equations or the corresponding Langevin equations. Kramers model is based on the assumption of uncorrelated stochastic forces. In this work simple but more realistic microscopic models for transitions are developed. The physical forces leading to transitions are studied by means of molecular dynamics simulations. The investigation is restricted to two-dimensional systems. In particular we study local energy excitations of soft molecules solved in liquids. This investigation makes use of an analogy to Toda lattices. For Toda systems it was shown in earlier work that soliton excitations and soliton fusion at the soft sites may lead to local energy spots. The basic configuration studied here is a soft reacting site imbedded into a thermal bath of hard molecules. In the first part we develop a microscopic model for Kramers bistable potential well and calculate the transition rates by MD-simulations. In the following parts we study models for the dissociation of molecules and for the fusion of molecules.

Escape rates in bistable systems induced by quasimonochromatic noise.

Path-integral techniques are used to understand the behavior of a particle moving in a bistable potential well and acted upon by quasimonochromatic external noise. In the limit of small diffusion coefficient, a steepest-descent evaluation of the path integral to leading order enables mean first-passage times and the transition times from one well to the other to be computed. The results and general approach are compared with computer simulations of the process. It is found that the bandwidth parameter \ensuremath{\Gamma} has a critical value above which particle escape is by white-noise-like outbursts, but below which escape is by oscillatory-type behavior.

Fluctuations in a parametrically excited subharmonic oscillator

The behavior of the classical degenerate parametric oscillator ( \omega_{i} = \omega_{s} ) with small linear dissipation is considered and an expression for the steady-state probability distribution for the subharmonic amplitude is obtained. The treatment is limited to the case 1 \ll Q_{p} \ll Q_{s} where Q p and Q s are the Q factors at respectively the pump and signal frequencies. The behavior is analogous to that of the Brownian motion of a particle in a bistable potential well. This leads to a tractable equation for the relaxation towards the steady-state distribution by thermally activated jumps over the barrier. Near threshold, the behavior is similar to that of a system undergoing a second order phase transition in the mean field approximation. Analogies between first-order phase transitions and transitions in oscillating systems are also pointed out.