Types Of Oscillators Research Articles

A Study of q-Deformed Bosons, and Their Implications to Quantum Optics

In this study, we investigate three types of q-deformed boson oscillators, focusing on their mathematical frameworks and thermodynamic properties. We calculate key thermodynamic quantities, such as internal energy and entropy, as functions of the deformation parameter q. Our results reveal that these oscillators are eigenstates of specific deformed boson annihilation operators. We also analyze their unique characteristics and implications in deformed quantum optics. Furthermore, we examine the impact of q-deformation on qutrit logic gates, including cycle, self-shift, controlled cycle, controlled self-shift, Feynman, ternary Toffoli, and Fredkin gates, highlighting their altered computational properties. This research contributes to a deeper understanding of q-deformed systems and their applications in quantum computing. Overall, it opens new avenues for exploring the interplay between deformation parameters and quantum information processing.

Robustness and evolvability: Revisited, redefined and applied

Building on and extending existing definitions of robustness and evolvability, we propose and utilize new formal definitions, with matching measures, of robustness and evolvability of systems with genotypes and corresponding phenotypes. We explain and show how these measures are more general and more representative of the concepts they stand for, than the commonly used/referenced measures originally proposed by Wagner. Further, a versatile digital modeling approach (BNK) is proposed that is inspired by NK systems. However, unlike NK systems, BNK incorporates a genotype and a phenotype, in addition to fitness. We develop and apply an Evolutionary Algorithm to a BNK-modeled system to find different types of perfect oscillators. We then map the resulting oscillating systems to possible genetic circuit realizations. Continuing with the synthetic biology theme, we also investigate the effect of noise in DNA synthesis on the predicted functionality of a DNA-based biosensor (i.e., its robustness), and we carry out a theoretical assessment of the evolvability of different types of ribozymes, undergoing directed evolution.

Multiple scales method for analyzing a forced damped rotational pendulum oscillator with gallows

This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces. The multiple scales method (MSM) is applied to solve the proposed problem. Several types of rotational pendulum oscillators are studied and talked about in detail. These include the forced damped rotating pendulum oscillator with gallows, the damped standard simple pendulum oscillator, and the damped rotating pendulum oscillator without gallows. The MSM first-order approximations for all the cases mentioned are derived in detail. The obtained results are illustrated with concrete numerical examples. The first-order MSM approximations are compared to the fourth-order Runge–Kutta (RK4) numerical approximations. Additionally, the maximum error is estimated for the first-order approximations obtained through the MSM, compared to the numerical approximations obtained by the RK4 method. Furthermore, we conducted a comparative analysis of the outcomes obtained by the used method (MSM) and He-MSM to ascertain their respective levels of precision. The proposed method can be applied to analyze many strong nonlinear oscillatory equations.

A study on the flow behavior inside fluidic oscillation tools for friction-reduction in extended reach well

The drilling distance of extended-reach wells is limited by mechanical friction between the drill string and the borehole wall. The fluidic oscillator axial vibratory tools (AVTs) can effectively reduce friction and increase the weight on bit, thereby extending the reach of horizontal wells. However, few studies have delved into the evolutionary mechanism of the internal flow field of fluidic oscillator AVTs. In this paper, two types of fluidic oscillators with different flow path are presented. One is the reverse-feedback oscillator, and the other is sweeping-chamber oscillator. Through computational fluid dynamics method, the internal flow field of these two fluidic oscillator AVTs were analyzed, and the frequency and pressure drop were verified by experiments. The results show that the LES turbulence model provides more accurate simulations, showing an error range of less than 9%. The pressure drop and vibration frequency of the two tools are linearly related to the flow rate. The pressure drop of the reverse feedback oscillation tool is in the range of 0.1–1 MPa, and the vibration frequency is between 13 and 50 Hz. The sweeping-chamber oscillator can reduce vibration frequency to below 15 Hz. The results also show that it is crucial to consider the lag in pressure signals when designing and analyzing fluid oscillator systems, as it can affect the timing and behavior of the system. This research provides profound insights for understanding and optimizing fluidic oscillator systems.

Phosphor thermometry evaluation of heat transfer enhancement on a hot plate achieved by a vortex-based fluidic oscillator

Recently, a vortex-based feedback fluidic oscillator has been proposed as an alternative to conventional feedback fluidic oscillators. This study aimed to compare the heat transfer performance of a newly designed fluidic oscillator with that of conventional feedback fluidic oscillators with and without an output diffuser using phosphor thermometry. To obtain the instantaneous temperature field in a wide range of high temperatures, a lifetime-based method was employed in two-dimensional phosphor thermography, with Mg4FGeO6: Mn serving as the sensor material and being excited by a UV-LED. A high-speed camera was used to capture images of the hot plate at 4,000 fps. The calibration test was conducted in the temperature range of 25–325 ˚C, and the results were compared with data from thermocouples. The study investigated the impact of the mass flow rate and throat-to-plate distance ratio of three fluidic oscillators to obtain the optimum Nusselt number. The results demonstrated that the newly designed fluidic oscillator exhibited significantly superior cooling effects in comparison to other types of fluidic oscillators. At the lowest ratio of the throat-to-wall distance to the outlet throat height (Z/D = 4.5) and a flow rate of 100 Lpm, the vortex-based fluidic oscillator demonstrated 78 % and 45 % higher heat transfer rates compared to the conventional oscillator with and without an external diffuser, respectively. Furthermore, the newly designed oscillator was more sensitive to the mass flow rate and throat-to-plate distance ratio than the other oscillators.

Implementation of Various Chaotic Spiking Oscillators Based on Field Programmable Analog Array

In this paper, a circuit based on a field programmable analog array (FPAA) is proposed for three types of chaotic spiking oscillator (CSO). The input/output conversion characteristics of a specific element in the FPAA can be defined by the user. By selecting the proper characteristics, three types of CSO are realized without changing the structure of the circuit itself. Chaotic attractors are observed in a hardware experiment. It is confirmed that the dynamics of the CSOs are consistent with numerical simulations.

Study on bandgap characteristics and vibration attenuation mechanism of double-oscillator power-exponent prism phononic crystal plate

This study introduces a local resonance mechanism to a periodic acoustic black hole (ABH) structure to achieve vibration control of plate structures and proposes a double-oscillator power-exponent prism phononic crystal. Results show that the periodic power-exponent prism can generate a high-frequency bandgap, the interior oscillator can generate a low-frequency bandgap, and the top oscillator can separate the frequency dispersion curve at around 700 Hz to form a bandgap with a width of 189 Hz. The double-oscillator power-exponent prism phononic crystal, composed of two types of oscillators and a power-exponent prism, can simultaneously have high-, middle-, and low-frequency bandgaps. Simulations and experiments show that it has a good attenuation effect on flexural vibration in the bandgap frequency band. The present results can provide a useful reference for bandgap design based on the combination of multiple mechanisms.

The Krylov–Bogoliubov–Mitropolsky method for modeling a forced damped quadratic pendulum oscillator

In the present investigation, a quadratically forced damped pendulum-type equation is solved analytically using several effective and highly accurate approaches. Some different types of pendulum oscillators linked to the forced and damped terms, in addition to the power of the damping term, are analyzed. In the first part, the Krylov–Bogoliubov–Mitropolsky (KBM) technique and the ansatz method are carried out for analyzing the quadratically damped pendulum oscillator. In the second part, the two variants of the KBM technique are implemented for investigating the quadratically forced damped pendulum oscillator. Some symmetric approximations are derived and compared with the fourth-order Runge–Kutta numerical approximation. In addition, the maximum distance error is estimated in the whole study domain for ensuring that all obtained approximations are accurate. The obtained results are illustrated through concrete examples.

Classical Mechanics with Inequality Constraints and Gravity Models with Limiting Curvature

In this paper, we discuss mechanical systems with inequality constraints Φ(q,q˙,...)≤0. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate this approach, we consider a harmonic oscillator in the model with limiting velocity. We compare the behavior of such an oscillator with the behavior of a relativistic oscillator and demonstrate that when the amplitude of the oscillator is large, the properties of both types of oscillators are quite similar. We also discuss inequality constraints, which contain higher derivatives. At the end of the paper, we briefly discuss possible applications of the developed approach to gravity models with limiting curvature.

Rationally-extended Dunkl oscillator on the line

It is shown that the extensions of exactly-solvable quantum mechanical problems connected with the replacement of ordinary derivatives by Dunkl ones and with that of classical orthogonal polynomials by exceptional orthogonal ones can be easily combined. For such a purpose, the example of the Dunkl oscillator on the line is considered and three different types of rationally-extended Dunkl oscillators are constructed. The corresponding wavefunctions are expressed in terms of exceptional orthogonal generalized Hermite polynomials, defined in terms of the three different types of X m -Laguerre exceptional orthogonal polynomials. Furthermore, the extended Dunkl oscillator Hamiltonians are shown to be expressible in terms of some extended Dunkl derivatives and some anharmonic oscillator potentials.

A high-efficiency C-band coaxial transit time oscillator with a dual-cavity extractor under low-magnetic fields

A high-efficiency C-band coaxial transit time oscillator with a dual-cavity extractor under low-magnetic fields is designed and studied through small-signal theory and particle-in-cell simulation. Small-signal theory analysis indicates that a dual-cavity extractor is superior to a single-cavity extractor in terms of the beam-coupling coefficient, the resonant frequency, and the external quality factor, which are good for high efficiency. Typical simulation results of the proposed device show that an output power of 1.73 GW and a frequency of 6.37 GHz can be obtained with a diode voltage of 455 kV and current of 9.75 kA. The corresponding power efficiency reaches 39%, and the guiding magnetic field is 0.8 T. Further simulation demonstrates that the power efficiency exceeds 34% in a rather large range of diode voltage from 385 kV to 470 kV and can reach higher than 35% with a low guiding magnetic field of 0.4 T. Then this coaxial transit time oscillator is compared with the typical relativistic backward wave oscillators from the magnetic field, efficiency and power saturation time.

Nonlinear model and characteristic analysis of fractional-order high frequency oscillator

Recently, fractional calculus theory has been widely used in various fields, including the design of oscillators. However, there are still some issues that need to be studied in depth. Firstly, it is necessary to classify the fractional-order oscillators according to the properties of the frequency selective network components, and analyze the influence of the fractional order of components on the characteristics of different types of fractional-order oscillators. Secondly, for fractional-order oscillators with nonlinear devices such as transistors, the traditional linear models cannot describe them accurately. Thirdly, due to the complexity of fractional differential equation, it is difficult to obtain the general analytical solution of the fractional-order oscillator. For these reasons, this paper takes the fractional-order capacitive feedback LC oscillator as an example, and establishes a nonlinear model of this oscillator based on the transistor characteristic mechanism. With the help of the equivalent small parameter method, the influence of the fractional-order characteristics of the components on the output waveform is analyzed. It is revealed that for the fractional-order capacitive feedback LC oscillator, the order of capacitance C1 has the most significant effect on frequency and amplitude, followed by the order of inductance L2, and the order of the feedback capacitor C2 has very little effect on the oscillator. In addition, although the introduction of fractional order increases the oscillation frequency, it will also lead to an increase in THD in some cases. Simulation and experimental results verify the correctness of the proposed nonlinear model and characteristic analysis of fractional-order high frequency oscillator.

Numerical Modelling of Flow in Fluidic Oscillator

The systems with fluidic oscillators are intensively studied nowadays because the oscillatory flow can increase heat and mass transfer and decrease energy dissipation. Fluidic oscillators produce an active-type mixing enhancement but in a passive manner as they do not require any moving parts. They convert steady pressurized inlet flow to oscillatory or pulsatile flow at an outlet without the need for external power. In general, there are many types of fluidic oscillators, categorized by the underlying mechanism to create oscillatory output behaviour. The fluidic oscillator with the single feedback loop is analysed in this paper. A numerical simulation of oscillating flow is performed and two approaches for modelling flow, RANS, and LES are applied especially. The results of numerical simulation are compared with experimental measurement. The analysis is focused on pressure drop and oscillation frequency dependent on the inlet conditions. The energy spectrum of oscillating flow is analysed using discrete Fourier transform.

Forced oscillation experiments for each vibration mode of closely spaced parallel pipes in steady flow

In the industrially widespread use of multiple bundled pipes, the effects of mutual interference, in addition to the vibrations generated in single columns, must be considered, and estimating their behavior is critical to the design. In this study, based on previous research that identified the vibration modes occurring in two bundled pipes placed in a steady flow, such as (1) translational motion in the crossflow direction, (2) approaching and moving away, and (3) torsional motion, we developed four types of oscillators that can emulate the oscillation patterns (mode (2) uses different mechanisms for in-line and crossflow direction oscillation.), conducted forced oscillation experiments, and measured fluid forces. The mechanism of generation of the behavior patterns, measured in the towing and vibration measurement experiments of the elastic body model, was examined from the viewpoint of fluid force. A database of added mass and linear damping coefficients with parameters of distance between the center of the column and flow direction, in addition to oscillation patterns, was compiled for the development of a future two-tube behavior estimation program.A comparison of the measured fluid force of two columns with that of a single column, obtained by forced oscillation experiments for three vibration modes, showed that two closely spaced columns may vibrate over a wider frequency band and have larger amplitudes than a single column because of the expanded region of negative linear damping coefficients. Based on the results of the fluid force measurements for each vibration mode, rotational motion is more likely to occur in the tandem configuration, whereas approaching and moving away motion is more likely to occur in the side-by-side configuration because of the interchanged positive and negative added mass coefficients and strength of the negative linear damping coefficient.

Sound transmission loss of meta-acoustic barriers with anomalous effective-mass

Meta-acoustic barriers (MABs) that are inspired by acoustic metamaterials (AM) offer opportunities to defy mass law-driven sound transmission loss (TL) performance that is characteristic of conventional acoustic barriers. In this analytical parametric study, the TL behavior of MABs that incorporate various local oscillator configurations are analyzed using an effective-mass modeling approach. Resonant, damped and inertant local oscillator configurations and combinations thereof that result in negative and complex effective-mass for the meta-acoustic barrier are considered. The influence of the local configuration’s orientation, oblique incidence and the presence of multiple oscillator types are examined using nondimensionalized metrics and compared to the performance of static mass and volume-equivalent limp mass and double wall barriers. It is shown that due to their anomalous effective-mass, such barriers display tunable TL bandwidths exceeding that of mass-equivalent conventional barriers indicating new device implications. The effective-mass modeling approach can easily be adapted to account for the presence of different dynamic features within various types of inclusions considered and is thus an efficient tool to evaluate meta-acoustic barrier designs. Inasmuch as these meta-acoustic barrier structures can be realized using recent advances in additive and hybrid manufacturing techniques, opportunities exist to create lightweight barriers for tonal and broadband acoustic applications.

Suppressing Homoclinic Chaos for Vibro-Impact Oscillators

In this paper, theoretical framework and numerical verification for suppressing homoclinic chaos of a class of vibro-impact oscillators are discussed by adding parametric excitations in the form of [Formula: see text] as the control item. The analytical Melnikov method for planar vibro-impact systems is employed to obtain the corresponding thresholds of parameters as sufficient conditions for suppressing chaos. Two typical oscillators are presented to show the effectiveness of theoretical analysis for suppressing homoclinic chaos by tuning the amplitudes, frequencies and phases of the parametric excitations.

Synchronization of cooperative and competitive oscillators in dynamical network

Synchronization is a collective behavior that occurs spontaneously, describing the coherence of a collection of dynamic units of a system. The competitive and cooperative behavior of the synchronization process as the simplest synergistic behaviors can promote or inhibit each other, which has been widely investigated for its practical significance in recent years. Here, we report that the synchronization phase transition type can be tuned by adjusting the balance between the two oscillator types and the communication radius of the dynamical network in a population dynamical network with uniformly distributed competitive and cooperative oscillators. Agents of both cooperative and competitive oscillators move and interact only with their neighbors in a system. By numerical simulations, we demonstrate a rich process of synchronous transitions, especially that the transition can be regulated between continuous and explosive by adjusting the balance between the two oscillator types under a specific dynamic network. Moreover, the communication radius of the network and the number of oscillators determine both the density of oscillators in the system, thus changing the connectivity and the synchronization characteristics of the network.

Mathematical modeling of typical electrical circuits, oscillators and pendulums

The work is devoted to mathematical and simulation modeling of electromechanical systems, in which oscillations in electrical circuits, oscillators and pendulums are studied under the action of forces of various physical nature. To compile the equations of electromechanical systems, the apparatus of analytical mechanics was used, in which the electromagnetic and mechanical quantities characterizing the system appear as formally equal. The equations of motion are based on the Lagrange-Maxwell equations. The simulation was performed using computer algebra programs.

Greedy optimization for growing spatially embedded oscillatory networks.

The coupling of some types of oscillators requires the mediation of a physical link between them, rendering the distance between oscillators a critical factor to achieve synchronization. In this paper, we propose and explore a greedy algorithm to grow spatially embedded oscillator networks. The algorithm is constructed in such a way that nodes are sequentially added seeking to minimize the cost of the added links' length and optimize the linear stability of the growing network. We show that, for appropriate parameters, the stability of the resulting network, measured in terms of the dynamics of small perturbations and the correlation length of the disturbances, can be significantly improved with a minimal added length cost. In addition, we analyze numerically the topological properties of the resulting networks, and we find that, while being more stable, their degree distribution is approximately exponential and independent of the algorithm parameters. Moreover, we find that other topological parameters related with network resilience and efficiency are also affected by the proposed algorithm. Finally, we extend our findings to more general classes of networks with different sources of heterogeneity. Our results are a step in the development of algorithms for the directed growth of oscillatory networks with desirable stability, dynamical and topological properties.

Oscillator-Network-Based Ising Machine.

With the slowdown of Moore’s law, many emerging electronic devices and computing architectures have been proposed to sustain the performance advancement of computing. Among them, the Ising machine is a non-von-Neumann solver that has received wide attention in recent years. It is capable of solving intractable combinatorial optimization (CO) problems, which are difficult to be solve using conventional digital computers. In fact, many CO problems can be mapped to finding the corresponding ground states of Ising model. At present, Ising machine prototypes based on different physical principles, such as emerging memristive oscillators, have been demonstrated, among which the Ising Hamiltonian solver based on the coupled oscillator network simultaneously holds the advantages of room-temperature operation, compact footprint, low power consumption, and fast speed to solution. This paper comprehensively surveys the recent developments in this important field, including the types of oscillators, the implementation principle of the Ising model, and the solver’s performance. Finally, methods to further improve the performance have also been suggested.