Oscillator Research Articles

Bifurcations and Dynamics Emergent From Lattice and Continuum Models of Bioactive Porous Media

We study the dynamics emergent from a two-dimensional reaction–diffusion process modeled via a finite lattice dynamical system, as well as an analogous PDE system, involving spatially nonlocal interactions. These models govern the evolution of cells in a bioactive porous medium, with the evolution of the local cell density depending on a coupled quasi-static fluid flow problem. We demonstrate differences emergent from the choice of a discrete lattice or a continuum for the spatial domain of such a process. We find long-time oscillations and steady states in cell density in both lattice and continuum models, but that the continuum model only exhibits solutions with vertical symmetry, independent of initial data, whereas the finite lattice admits asymmetric oscillations and steady states arising from symmetry-breaking bifurcations. We conjecture that it is the structure of the finite lattice which allows for more complicated asymmetric dynamics. Our analysis suggests that the origin of both types of oscillations is a nonlocal reaction–diffusion mechanism mediated by quasi-static fluid flow.

The low-temperature heat capacity of the Sb2Te3−xSex solid solution from experiment and theory

The lattice dynamics of Sb2Te3−xSex (x = 0, 0.6, 1.2, 1.8, 3) mixed crystals have been studied by a combination of low-temperature heat-capacity measurements between 2–300 K and first-principles calculations. The results from the experimental and theoretical investigations are in excellent agreement. While Sb2Se3 can be considered as a harmonic lattice oscillator in this temperature range, for the isostructural compounds Sb2Te3, Sb2Se0.6Te2.4, Sb2Se1.2Te1.8 and Sb2Se1.8Te1.2 (tetradymite structure type; Rm) a small anharmonic contribution to the total heat capacity has to be taken into account at temperatures above 250 K. For the compounds which crystallize in the tetradymite structure type the experimental and theoretical data show unambiguously that the exchange of Te by Se leads to an increase of the bonding polarity and consequently to a hardening of the bonding which is reflected in an increase of the Debye temperatures with increasing Se contents. In addition, our studies clearly demonstrate that the mixed crystals in the stability field of the tetradymite structure type are characterized by a strong non-ideal mixing behavior.

407 W specially-designed fiber laser at 1018 nm using a gain fiber with a low core/cladding ratio of 20/400 μm

In this paper, two monolithic 1018 nm Yb-doped fiber laser systems—one as an oscillator (OSC) and another as a specially-designed amplifier (SDA)—are investigated using 20/400 μm Yb-doped fibers (YDF). 394 W of output power and a slope efficiency of 39.4% was obtained from the OSC setup. The SDA setup resulted in 407 W of output power with a slope efficiency of 39.9%, which is the highest reported output power via the 20/400 μm YDF. The beam quality factor M2 is also measured to be ~1.5 for both setups. Considerations regarding the gain fiber length were taken into account so as to suppress any detrimental effects such as ASE and self-pulsing. The output power behavior of both setups indicate that further power scaling would be possible.

Quantum-enhanced sensing of a mechanical oscillator

The use of special quantum states to achieve sensitivities below the limits established by classically behaving states has enjoyed immense success since its inception. In bosonic interferometers, squeezed states, number states and cat states have been implemented on various platforms and have demonstrated improved measurement precision over interferometers based on coherent states. Another metrologically useful state is an equal superposition of two eigenstates with maximally different energies; this state ideally reaches the full interferometric sensitivity allowed by quantum mechanics. By leveraging improvements to our apparatus made primarily to reach higher operation fidelities in quantum information processing, we extend a technique to create number states up to $n=100$ and to generate superpositions of a harmonic oscillator ground state and a number state of the form $\textstyle{\frac{1}{\sqrt{2}}}(\lvert 0\rangle+\lvert n\rangle)$ with $n$ up to 18 in the motion of a single trapped ion. While experimental imperfections prevent us from reaching the ideal Heisenberg limit, we observe enhanced sensitivity to changes in the oscillator frequency that initially increases linearly with $n$, with maximal value at $n=12$ where we observe 3.2(2) dB higher sensitivity compared to an ideal measurement on a coherent state with the same average occupation number. The quantum advantage from using number-state superpositions can be leveraged towards precision measurements on any harmonic oscillator system; here it enables us to track the average fractional frequency of oscillation of a single trapped ion to approximately 2.6 $\times$ 10$^{-6}$ in 5 s. Such measurements should provide improved characterization of imperfections and noise on trapping potentials, which can lead to motional decoherence, a leading source of error in quantum information processing with trapped ions.

Directed polaron propagation in linear polypeptides induced by intramolecular vibrations and external electric pulses.

We study the propagation of α-helix polarons in a model describing the nonadiabatic interaction between an electron and a lattice of quantum mechanical oscillators at physiological temperature. We show that when excited by a subpicosecond electric pulse, as induced by experimentally observed subpicosecond charge separation, the polaron is displaced by up to hundreds of lattice sites before the electron becomes delocalised. We discuss biophysical implications of our results.

OPTIMAL CONTROL OF NONLINEAR DUFFING OSCILLATORS: LIE-GROUP APPROACHES

In the optimal control theory, the Hamiltonian formulation is a famous one convenient to find an optimal designed control force. However, when the performance index is a complicated function of control force, the Hamiltonian method is not easy to find the optimal solution, because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations (DAEs). In this paper we address this issue via a quite novel and effective approach, of which the optimally controlled vibration problem of Duffing oscillator is recast into a two-point nonlinear DAEs by identifying the unknown control force. We develop the corresponding SL(n, R) and GL(n, R) shooting methods, as well as a Lie-group differential algebraic equations (LGDAE) method to numerically solve the optimal control forces. Eight examples of a single Duffing oscillator and one coupled Duffing oscillators are used to test the performance of the present method.

Beating pattern in radiation-induced oscillatory magnetoresistance in 2DES: Coupling of plasmon-like and acoustic phonon modes

We present a microscopic theory on the observation of a beating pattern in the radiation-induced magnetoresistance oscillations at a very low magnetic field. We consider that such a beating pattern develops as a result of the coupling between two oscillatory components: the first is a system of electron Landau states being harmonically driven by radiation. The second is a lattice oscillation, i.e., an acoustic phonon mode. We analyze the dependence of the beating pattern on temperature, radiation frequency, and power. We conclude that the beating pattern is an evidence of the radiation-driven nature of the irradiated Landau states that makes them behave as a collective plasma oscillation at the radiation frequency. Thus, the frequency of such plasmons could be tuned from microwave to terahertz in the same nanodevice with an apparent technological application.

Lattice and quintic nonlinearity induced stripe phase in Bose–Einstein condensate under non-inertial and inertial motion

We consider a parametrically forced Bose–Einstein condensate in the combined presence of an optical lattice and harmonic oscillator potential in the mean field approach. A spatial symmetry broken Bose-condensed phase in non-inertial and inertial frame yields a stripe phase in the presence of both cubic and quintic nonlinearities. We show that the existence of such stripe phase solely depends on the interplay between the quintic nonlinearity and the lattice potential. Furthermore, we observe that a time-dependent harmonic oscillator frequency destroys such stripe ordering. A linear stability analysis of the obtained solution is performed and we found that the solution is stable. In order to gain a better understanding of the underlying physics, we compute the energy, showing nonlinear compression of the condensate in some parameter domain.

Nonreciprocal signal routing in an active quantum network

As superconductor quantum technologies are moving towards large-scale integrated circuits, a robust and flexible approach to routing photons at the quantum level becomes a critical problem. Active circuits, which contain parametrically driven elements selectively embedded in the circuit offer a viable solution. Here, we present a general strategy for routing nonreciprocally quantum signals between two sites of a given lattice of oscillators, implementable with existing superconducting circuit components. Our approach makes use of a dual lattice of overdamped oscillators linking the nodes of the main lattice. Solutions for spatially selective driving of the lattice elements can be found, which optimally balance coherent and dissipative hopping of microwave photons to nonreciprocally route signals between two given nodes. In certain lattices these optimal solutions are obtained at the exceptional point of the dynamical matrix of the network. We also demonstrate that signal and noise transmission characteristics can be separately optimized.

A Loop Filter Size and Spur Reduced PLL with Two-Input Voltage Controlled Oscillator

A Loop Filter Size and Spur Reduced PLL with Two-Input Voltage Controlled Oscillator

Genetic and epigeneticregulations of mammalian circadian rhythms.

The circadian clocks are vital to many organisms for their survival and adaption to the surrounding environment. More and more people are interested in the circadian clock and related researches. One of the key characteristics of this endogenous clock is its periodicity. Mechanisms underlying the mammalian circadian rhythms with ~24 h periodicity involve interlocked transcriptional and translational feedback loops. The circadian clock system in mammals consists of hierarchical structures, with the suprachiasmatic nucleus (SCN) as the central pacemaker and peripheral oscillators in other organs. In spite of the central and peripheral oscillators, the molecular mechanisms are the same within the SCN and peripheral organs. In the past decades, major achievements are accomplished by using forward and reverse genetics, as well as epigenetic approaches. In this review, we recapitulate the history of how clock-related genes were identified, and summarize the main achievements in genetics and epigenetics to understand the molecular underpinnings. We hope it can offer basic knowledge for further researches, a reference for experimental designs aiming to adjust organisms' homeostasis by modulating the clock, and provide a foundation to build interdisciplinary research networks.

Towards Infinite Bifurcation Trees of Period-1 Motions to Chaos in a Time-delayed, Twin-well Duffing Oscillator

In this paper, bifurcation trees of periodic motions to chaos in a periodically forced, time-delayed, twin-well Duffing oscillator are pre- dicted by a semi-analytical method. The twin-well Duffing oscilla tor is extensively used in physics and engineering. The bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is very significant for determine motion complexity. Thus, the bi furcation trees for periodic motions to chaos in such a time-delayed, twin-well Duffing oscillator are obtained analytically. From the fi nite discrete Fourier series, harmonic frequency-amplitude character istics for period-1 to period-4 motions are analyzed. The stability and bifurcation behaviors of the time-delayed Duffing oscillator are different from the non-time-delayed Duffing oscillator. From the an alytical prediction, numerical illustrations of periodic motions in the time-delayed, twin-well Duffing oscillator are completed. The com plexity of period-1 motions to chaos in nonlinear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes. As a slowly varying excitation becomes very slow, the excitation amplitude will approach infinity for the infinite bifurcation trees of period-1 motion to chaos. Thus infinite bifurca tion trees of period-1 motion to chaos can be obtained.

Large scale density perturbations from a uniform distribution by wave transport

It has long been known that a uniform distribution of matter cannot produce a Poisson distribution of density fluctuations on very large scales 1/k > ct by the motion of discrete particles over timescale t. The constraint is part of what is sometimes referred to as the Zel'dovich bound. We investigate in this paper the transport of energy by the propagation of waves emanating incoherently from a regular and infinite lattice of oscillators, each having the same finite amount of energy reserve initially. The model we employ does not involve the expansion of the Universe; indeed there is no need to do so, because although the scales of interest are all deeply sub-horizon the size of regions over which perturbations are evaluated do far exceed ct, where t is the time elapsed since a uniform array of oscillators started to emit energy by radiation (it is assumed that t greatly exceeds the duration of emission). We find that to lowest order, when only wave fields ∝ 1/r are included, there is exact compensation between the energy loss of the oscillators and the energy emitted into space, which means P(0)=0 for the power spectrum of density fluctuations on the largest scales. This is consistent with the Zel'dovich bound; it proves that the model employed is causal, has finite support, and energy is strictly conserved. To the next order when near fields ∝ r−2 are included, however, P(0) settles at late times to a positive value that depends only on time, as t−2 (the same applies to an excess (non-conserving) energy term). We further observe that the behavior is peculiar to near fields. Even though this effect may give the impression of superluminal energy transport, there is no violation of causality because the two-point function vanishes completely for r>t if the emission of each oscillator is sharply truncated beyond some duration. The result calls to question any need of enlisting cosmic inflation to seed large scale density perturbations in the early Universe.

On Optimization of Manufacturing of a Voltage Controlled Oscillator to Increase Density of Elements

On Optimization of Manufacturing of a Voltage Controlled Oscillator to Increase Density of Elements

Single-qubit quantum memory exceeding ten-minute coherence time

A long-time quantum memory capable of storing and measuring quantum information at the single-qubit level is an essential ingredient for practical quantum computation and communication 1,2 . Currently, the coherence time of a single qubit is limited to less than 1 min, as demonstrated in trapped ion systems 3–5 , although much longer coherence times have been reported in ensembles of trapped ions 6,7 and nuclear spins of ionized donors 8,9 . Here, we report the observation of a coherence time of over 10 min for a single qubit in a 171Yb+ ion sympathetically cooled by a 138Ba+ ion in the same Paul trap, which eliminates the problem of qubit-detection inefficiency from heating of the qubit ion 10,11 . We also apply a few thousand dynamical decoupling pulses to suppress ambient noise from magnetic-field fluctuations and phase noise from the local oscillator 8,9,12–16 . The long-time quantum memory of the single trapped ion qubit would be the essential component of scalable quantum computers 1,17,18 , quantum networks 2,19,20 and quantum money 21,22 . The longest coherence time of a single qubit of more than ten minutes is observed in a 171Yb+ ion. After sympathetically cooling the 171Yb+ ion qubit with a 138Ba+ ion, noise from magnetic-field fluctuations and the local oscillator is suppressed by a dynamic decoupling scheme.

Obstructive sleep apnea (OSA) and driving safety.

Intermittent hypoxia and sleep fragmentation cause excessive daytime sleepiness (EDS) and cognitive impairment in obstructive sleep apnoea (OSA); neuroimaging and neurophysiological studies in patients with OSA have delineated a putative regional "fingerprint" of OSA-induced brain injury: a disconnection of the fronto-parietal regions and a disruption of the thalamocortical oscillator, with involvement of the hippocampal formation with impaired attention, awareness, working memory, time reaction, visuoconstructive and executive functions. For these reasons OSA is the main medical cause of EDS and is also associated with an increased risk of motor vehicle accidents (MVAs). About 7% of MVAs for a population of male drivers involved in MVAs are attributable to OSA. Subjects with OSA have nearly twofold increased odds of work accidents. Professional drivers add fatigue to sleep deprivation. A higher risk of MVAs cannot be adequately explained by OSA and sleep deprivation (SD), and EDS is a further, independent risk factor like the other two. There is an association between the amount of hours of sleep per night and MVA or near miss accidents (NMA) rates with an inverse linear correlation. When OSA, SD or EDS are present, the risk of MVAs or NMAs in truck drivers is severely increased. Taking a rest break or a nap appear to be protective against MVAs e NMAs and they should be considered a primary prevention strategy together with screening for OSA, EDS, and SD.

Ultrafast optical pulse convertor caused by oscillations of the energy level structure in the conjugated polymer poly(p-phenylenevinylene).

For a conjugated polymer irradiated by two optical pulses, the whole process of excitation, involving lattice oscillations, oscillations of the energy level structure, and evolution of the electron cloud, is investigated. Localization of the electron cloud appears in the first 100 fs of irradiation, which in turn induces vibrations of lattice of the polymer chain as well as oscillations of the band gap. These oscillations filter the absorption of the external optical field inversely and convert the original optical field to an ultrafast light field whose intensity varies with a certain period. Based on the mechanism, oscillations of the energy level structure, induced by the external excitation, can be designed as an ultrafast response optical convertor that is able to change the external optical pulse into a new effective light field with a certain oscillation period. This helps provide new insight into designing nanostructures for polymeric optoelectronics.

From Kardar-Parisi-Zhang scaling to explosive desynchronization in arrays of limit-cycle oscillators.

Phase oscillator lattices subject to noise are one of the most fundamental systems in nonequilibrium physics. We have discovered a dynamical transition which has a significant impact on the synchronization dynamics in such lattices, as it leads to an explosive increase of the phase diffusion rate by orders of magnitude. Our analysis is based on the widely applicable Kuramoto-Sakaguchi model, with local couplings between oscillators. For one-dimensional lattices, we observe the universal evolution of the phase spread that is suggested by a connection to the theory of surface growth, as described by the Kardar-Parisi-Zhang (KPZ) model. Moreover, we are able to explain the dynamical transition both in one and two dimensions by connecting it to an apparent finite-time singularity in a related KPZ lattice model. Our findings have direct consequences for the frequency stability of coupled oscillator lattices.

Характеристики поверхности щелочных металлов с учетом дискретности кристаллической решетки и фриделевских осцилляций электронной плотности

Характеристики поверхности щелочных металлов с учетом дискретности кристаллической решетки и фриделевских осцилляций электронной плотности

Analysis of gas-liquid two-phase flow characteristics based on double coupled Duffing oscillator

Analysis of gas-liquid two-phase flow characteristics based on double coupled Duffing oscillator