Approximate semiclassical solutions are developed for a system of a Morse oscillator coupled to a harmonic oscillator via a nonlinear perturbation. This system serves as a model for the interaction of an excited stretching mode with a bending mode in a polyatomic molecule. Three semiclassical methods are used to treat this model. In particular, a matrix diagonalization, a two-state model, and a...

Mammalian spontaneous otoacoustic emissions (SOAEs) have been suggested to arise by three different mechanisms. The local-oscillator model, dating back to the work of Thomas Gold, supposes that SOAEs arise through the local, autonomous oscillation of some cellular constituent of the organ of Corti (e.g., the "active process" underlying the cochlear amplifier). Two other models, by contrast, bot...

The name Dirac oscillator was first introduced by Moshinky and Szczepaniak [1] for a Dirac equation in which the momentum p is replaced by p → p−imωβr with r being the position vector, m the mass of the particle and ω the frequency of the oscillator. The name was given because the determination of the spectrum and eigenstate of a Dirac oscillator [1] was obtained from that of an ordinary oscill...

In the medicinal leech, a rhythmically active 14-interneuron network composes the central pattern generator for heartbeat. In two segmental ganglia, bilateral pairs of reciprocally inhibitory heart interneurons (oscillator interneurons) produce a rhythm of alternating bursts of action potentials that paces activity in the pattern-generating network. The neuropeptide myomodulin decreases the per...

In this work, the behaviour of systems with three degrees of freedom is modelled for a fixed loss factor. The loss factor used in this work is 0.075. Four models are studied and the displacements as well as the energies stored in the systems are computed using the simulations. The governing equations are numerically solved using MATLAB. The dampers are varied in position and in numbers to deriv...

 In this work, time domain analysis is used to solve Adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. Mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked LC and Ring oscillators considering their time-varying nature. Then, the analysis is verifie...

For auto-oscillators of different nature (e.g. active cells in a human heart under the action of a pacemaker, neurons in brain, spin-torque nano-oscillators, micro and nano-mechanical oscillators, or generating Josephson junctions) a critically important property is their ability to synchronize with each other. The synchronization properties of an auto oscillator are directly related to its sen...

The recently formulated Two Oscillator (TO) model interprets the lowest of the kilohertz frequencies of the twin peak quasi-periodic oscillations in X-ray binaries as the Keplerian frequency νK. The high twin frequency νh in this model holds the upper hybrid frequency relation to the rotational frequency of the neutron star’s magnetosphere Ω: ν h = ν 2 K + 4(Ω/2π) . The vector Ω is assumed to h...

The core circadian oscillator of cyanobacteria consists of three proteins, KaiA, KaiB, and KaiC. This circadian oscillator could be functionally reconstituted in vitro with these three proteins, and therefore has been a very important model in circadian rhythm research. KaiA can bind to KaiC and then stimulate its phosphorylation, but their interaction mechanism remains elusive. In this study, ...

In most organisms, circadian oscillators regulate the daily rhythmic expression of clock-controlled genes (ccgs). However, little is known about the pathways between the circadian oscillator(s) and the ccgs. In Neurospora crassa, the frq, wc-1, and wc-2 genes encode components of the frq-oscillator. A functional frq-oscillator is required for rhythmic expression of the morning-specific ccg-1 an...