Oscillator Model Research Articles

Effect of liquid elasticity on transient cavitation bubbles in the tube

We investigate the effect of liquid elasticity on the transient cavitation bubbles confined in a tube both experimentally and theoretically. In experiments, the tube-arrest apparatus is used to generate cavitation bubbles near the tube bottom with various polyethylene oxide solutions. Our experiments show that bubble dynamics, particularly the maximum bubble length, are significantly influenced by liquid elasticity. We establish a double oscillator model for the liquid column to explain the experimental results and predict the bubble dynamics over a broader range. Finally, we propose that the reciprocal of the cavitation number Ca2 and prR/k determine the regimes of the liquid column separation, where pr is the reference pressure, R is tube radius, and k is the “stiffness coefficient” of the liquid column. Our work provides a quantitative scaling of the dynamics of large cylindrical cavitation bubbles in viscoelastic liquids during the transient process.

Fokker-Planck modeling of the stochastic dynamics of a Rijke tube.

We derive and numerically validate a low-order oscillator model to capture the stochastic dynamics of a prototypical thermoacoustic system (a Rijke tube) undergoing a subcritical Hopf bifurcation in the presence of additive noise. We find that on the fixed-point branch before the bifurcation, the system is dominated by the first duct mode, and the Fokker-Planck solution for the first Galerkin mode can adequately predict the stochastic dynamics of the overall system. We also find that this analytical framework predicts well the dominant mode on the limit-cycle branch, but underperforms in the hysteretic bistable zone where the role of nonlinearities is more pronounced. Besides offering new insights into stochastic thermoacoustic behavior, this study shows that an analytical framework based on the Fokker-Planck equation can facilitate the early detection of thermoacoustic instabilities in a Rijke-tube model subjected to noise.

Quantum-kinetic chemistry model with an anharmonic oscillator model: Model derivation and limitations

Quantum-kinetic chemistry model with an anharmonic oscillator model: Model derivation and limitations

Propagation of transient explosive synchronization in a mesoscale mouse brain network model of epilepsy.

Generalized epileptic attacks, which exhibit widespread disruption of brain activity, are characterized by recurrent, spontaneous, and synchronized bursts of neural activity that self-initiate and self-terminate through critical transitions. Here we utilize the general framework of explosive synchronization (ES) from complex systems science to study the role of network structure and resource dynamics in the generation and propagation of seizures. We show that a combination of resource constraint and adaptive coupling in a Kuramoto network oscillator model can reliably generate seizure-like synchronization activity across different network topologies, including a biologically derived mesoscale mouse brain network. The model, coupled with a novel algorithm for tracking seizure propagation, provides mechanistic insight into the dynamics of transition to the synchronized state and its dependence on resources; and identifies key brain areas that may be involved in the initiation and spatial propagation of the seizure. The model, though minimal, efficiently recapitulates several experimental and theoretical predictions from more complex models and makes novel experimentally testable predictions.

Phase-Dependent Response to Electrical Stimulation of Cortical Networks during Recurrent Epileptiform Short Discharge Generation In Vitro.

The closed-loop control of pathological brain activity is a challenging task. In this study, we investigated the sensitivity of continuous epileptiform short discharge generation to electrical stimulation applied at different phases between the discharges using an in vitro 4-AP-based model of epilepsy in rat hippocampal slices. As a measure of stimulation effectiveness, we introduced a sensitivity function, which we then measured in experiments and analyzed with different biophysical and abstract mathematical models, namely, (i) the two-order subsystem of our previous Epileptor-2 model, describing short discharge generation governed by synaptic resource dynamics; (ii) a similar model governed by shunting conductance dynamics (Epileptor-2B); (iii) the stochastic leaky integrate-and-fire (LIF)-like model applied for the network; (iv) the LIF model with potassium M-channels (LIF+KM), belonging to Class II of excitability; and (v) the Epileptor-2B model with after-spike depolarization. A semi-analytic method was proposed for calculating the interspike interval (ISI) distribution and the sensitivity function in LIF and LIF+KM models, which provided parametric analysis. Sensitivity was found to increase with phase for all models except the last one. The Epileptor-2B model is favored over other models for subthreshold oscillations in the presence of large noise, based on the comparison of ISI statistics and sensitivity functions with experimental data. This study also emphasizes the stochastic nature of epileptiform discharge generation and the greater effectiveness of closed-loop stimulation in later phases of ISIs.

Anxiety is related to slower RSA oscillation during stress response and regulation.

Respiratory sinus arrhythmia (RSA), an index of the parasympathetic nervous system activity, has been considered indicative of stress response and emotion regulation. However, the relationship between RSA and anxiety remains inconclusive, partly because previous research has primarily focused on static RSA levels. In this nonclinical sample (N = 75, Mage = 20.89 ± 1.72 SD, 48 males), we used a damped oscillator model to characterize RSA dynamics across 30-s epochs while participants completed the Trier social stress test. Results showed that RSA constantly oscillated during the three periods of TSST (namely Rest, Stress, and Recovery). Importantly, slower RSA oscillation in the Stress period was related to elevated state anxiety, whereas in the Recovery period, it was related to higher trait anxiety. These findings demonstrated the dynamic nature of RSA during the whole course of stress response. Slower RSA oscillation may indicate inflexible and tardy physiological regulation which may give rise to anxiety issues.

Real-time dynamic and structural behavior estimation of a steel lazy wave riser through finite-element-based digital twin and hull-motion sensor

A digital twin (DT) method is proposed to estimate the dynamic and structural behaviors of a Steel Lazy Wave Riser (SLWR) under environmental conditions. This method uses a 1D finite element (FE) riser model that can include various loads and boundary conditions measured from sensors. We selected a spread-moored Floating Production Storage and Offloading (FPSO) vessel to validate the proposed method, which hosts multiple Production and Injection SLWRs. Using the time-domain dynamics simulation program, we built a reference model considering the fully coupled FPSO with mooring lines and risers in various wind/wave/current conditions. The synthetic sensor data, which represents the motions and internal fluid density changes, were generated from the simulation of the reference model. Then, two riser DT models, the Top Oscillation Model (TOM) and the Two-Point Oscillation Model (TPOM), were built, considering only a single riser made of the 1D FE model. TOM employed vessel motions as boundary conditions while internal fluid density and ocean current could be inputted as external loads. TPOM incorporated an additional motion sensor attached to the riser. The motion data obtained from the reference model were first inputted into the respective riser DT models. Next, we further evaluated their performance with and without the estimated ocean currents and slugs of internal fluid. The time histories, spectra, and statistical data of displacements and stresses along the riser were systematically compared and analyzed for various test cases and environments. While the hull-motion sensor alone can provide practically acceptable results using the developed methodology, additional consideration of current load and internal fluid's density variation improves the overall riser monitoring performance. The present method can significantly reduce the number of sensors compared to traditional riser monitoring methods.

Coherent coupling of localized surface plasmons and surface plasmons in borophene-based metamaterial

The strong coherent coupling in different electromagnetic modes can control the light-matter interaction more conveniently. Here, we theoretically researched the hybridization between the borophene surface plasmon (BSP) mode and the borophene localized surface plasmon (BLSP) mode in borophene grating structure. This coupling effect leads to the emergence of multiple hybrid modes. The absorption spectra of the system are investigated through finite difference time domain (FDTD) simulation and coupled oscillator model (COM). Results show that the coherent coupling of BSP and BLSP can be achieved by adjusting the carrier density of the borophene gratings. A Rabi splitting effect with frequency of 21.6 THz can be observed. Furthermore, we investigated the effects of geometric structural parameters, incident angle, and relaxation time on the correlated coupling spectra. Our work may deepen the understanding of light–matter interactions and provide a reference for borophene-based active photonic devices in the near-infrared region.

Cyanonaphthalene and cyanonaphthyl radicals: Vibrational structures via computed negative ion photoelectron spectra and thermochemistry of 1- and 2-cyanonaphthalene.

A double harmonic oscillator model is applied to compute the negative ion photoelectron spectra (NIPES) of the 1- and 2-cyanonaphthalene (CNN) radical anions. The computed Franck-Condon factors utilize optimized structures and harmonic vibrational frequencies obtained using density functional theory with the B3LYP 6-311++G (2d,2p) basis set while considering the mode-mixing Duschinsky effects. To test the accuracy of our model, the NIPES of α and β naphthyl radical anions were computed, and a strong agreement between the slow electron velocity-map ion imaging spectra and the predicted spectra was found. The adiabatic electron affinities (EAs) of the ground singlet states (S0) in 1-CNN and 2-CNN are 0.856 and 0.798eV, respectively. The origin of the lowest-lying triplet (T1) states in 1-CNN and 2-CNN is found to be 3.226 and 3.266eV, resulting in singlet-triplet energy splittings (ΔEST) of 2.370 and 2.468eV, respectively. Both the NIPES for electron detachment to the S0 and T1 states exhibit well-resolved vibrational features, allowing for the assignment of several vibrational fundamental frequencies. Following deprotonation, several isomers are formed, with the most stable deprotonated radical anions in 1-CNN and 2-CNN, corresponding to the removal of the most acidic proton, with EAs of 2.062 and 2.16eV. The rich spectroscopic and thermochemical data obtained in the current study make the CNN radical anions and their deprotonated species interesting systems for investigation in gas-phase, negative-ion experiments.

Design of near-perfect absorptance in few-layer WSe2 via cooperative enhancement mechanisms

Two-dimensional transition metal dichalcogenides are of growing interest for flexible optoelectronics and power applications, due to their tunable optical properties, lightweight nature, and mechanical pliability. However, their thin nature inherently limits their optical absorption and, therefore, efficiency. Here, we propose a few-layer WSe2 optoelectronic device that achieves near perfect absorption through a combination of optical effects. The WSe2 can be scalably grown below an Al2O3 superstrate. Our device includes a corrugated back reflector, modeled as a plasmonic nanowire array. We investigate the entire range of widths of the corrugations in the back reflector, including the edge cases of a simple back mirror (width equal to period) and a Fabry-Perot cavity (zero width). We demonstrate the zero-mode enhancement arising from the back reflector, the weakly coupled enhancement arising from the Fabry-Perot cavity, and the strongly coupled enhancement arising from the localized surface plasmon resonance of the nanowires, explain the physical nature of the spectral peaks, and theoretically model the hybridization of these phenomena using a coupled oscillator model. Our champion device exhibits 82% peak absorptance in the WSe2 alone, 92% in the WSe2 plus nanowires, and 98% total absorptance. Thus, we achieve a near-perfect absorber in which most of the absorption is in the few-layer WSe2, with a desirable device framework for integration with scalable growth of the WSe2, thereby making our designs applicable to a range of practical optoelectronic devices.

End-to-End Statistical Model Checking for Parameterization and Stability Analysis of ODE Models

We propose a simulation-based technique for the parameterization and the stability analysis of parametric Ordinary Differential Equations. This technique is an adaptation of Statistical Model Checking, often used to verify the validity of biological models, to the setting of Ordinary Differential Equations systems. The aim of our technique is to estimate the probability of satisfying a given property under the variability of the parameter or initial condition of the ODE, with any metrics of choice. To do so, we discretize the values space and use statistical model checking to evaluate each individual value w.r.t. provided data. Contrary to other existing methods, we provide statistical guarantees regarding our results that take into account the unavoidable approximation errors introduced through the numerical integration of the ODE system performed while simulating. In order to show the potential of our technique, we present its application to two case studies taken from the literature, one relative to the growth of a jellyfish population, and the other concerning a well-known oscillator model.

Time-domain constraints for passive materials: The Brendel-Bormann model revisited

This paper presents a systematic approach to derive physical bounds for passive systems, or equivalently for positive real (PR) functions, directly in the time-domain (TD). As a generic, canonical example we explore the TD dielectric response of a passive material. We will furthermore revisit the theoretical foundation regarding the Brendel-Bormann (BB) oscillator model which is reportedly very suitable for the modeling of thin metallic films in high-speed optoelectronic devices. To this end, an important result here is to re-establish the physical realizability of the BB model by showing that it represents a passive and causal system. The theory is based on Cauer's representation of an arbitrary PR function together with associated sum rules (moments of the measure) and exploits the unilateral Laplace transform to derive rigorous bounds on the TD response of a passive system. Similar bounds have recently been reported for more general casual systems with other assumptions. To this end, it is important to note here that the existence of useful sum rules and related physical bounds rely heavily on an assumption about the PR functions having a low- or high-frequency asymptotic expansion at least of odd order 1. As a particular numerical example, we consider here the electric susceptibility of gold (Au) which is commonly modeled by well established Drude or BB models. Explicit physical bounds are given as well as an efficient fast-Fourier transform -based numerical procedure to compute the TD impulse response associated with the nonrational BB model. Published by the American Physical Society 2024

Investigation of the optical properties of Pb1-xCdxTe films using spectroscopic ellipsometry

Using spectroscopic ellipsometry, we studied the optical properties of four Pb1-xCdxTe (0 ≤ x ≤ 0.20) films. The Pb1-xCdxTe films, deposited on silicon substrates using an electron-beam deposition technique, show a rock-salt structure, with their lattice constants decreasing as a function of Cd concentration. Ellipsometry measurements, which covered a wide spectral range between 0.1 eV to 4.1 eV, determined the index of refraction and the extinction coefficient of the films. As the Cd concentration increases from 0 % to 20 % in the Pb1-xCdxTe films, the index of refraction decreases by ∼10 %, across the entire energy range. Similarly, there seems to be a decrease in the extinction coefficient with the increase of Cd concentration. An oscillator model, depicting the optical functions of each Pb1-xCdxTe film, allowed us to obtain the band gap of each film which blue-shifts as the Cd concentration is increased. Besides the fundamental band gap, we recovered the higher-order electronic transitions that occur in the Brillouin zone of the Pb1-xCdxTe lattice.

Delay induced Hopf bifurcation and its control in a fractional p53 protein oscillator model

The p53 protein is essential for cancer prevention. Research on p53 mathematical models is popular since its oscillatory dynamics were observed. However, there is little research on fractional-order p53 oscillators, as well as on Hopf bifurcation control. We therefore introduce fractional-order into a p53 oscillator model and propose a delayed state feedback bifurcation controller. The stability of positive equilibrium and the existence of Hopf bifurcation are studied analytically regarding delay as the bifurcation parameter in both controlled and uncontrolled scenarios. Numerical simulations are consistent with the analytical results. We reveal that a smaller fractional-order facilitates the stability of fixed point and a larger feedback gain advances the Hopf bifurcation point. The work may inspire cancer therapy by artificially controlling the occurrence of p53 oscillations.

DEVELOPMENT OF MODELS COMPLEX OSCILLATIONS FOR AUTOMATION SYSTEMS OF VIBROACOUSTIC OPERATIONAL SAFETY CONTROL OF BUILDINGS AND STRUCTURES

Problem statement. Long-term safe operation of buildings and structures is impossible without determining the stability of their load-bearing elements, especially after shocks and dynamic loads under the influence of explosions and fires. In such conditions, reliable and productive monitoring of the reliability of buildings and structures is a critical element in increasing human safety. Vibroacoustic is an effective and informative method that allows for non-destructive assessment of the condition of concrete, reinforced concrete, brick, multi-layer walls and other types of structures. However, to increase the speed and quality of determining the state of objects, maximum automation of the vibroacoustic method is required. Purpose of the study. Increasing the productivity and reliability of vibroacoustic monitoring of buildings and structures by automating the impact action with specified parameters based on the development of dynamic models of complex oscillations. Methods. Analytical studies of dynamic and kinematic models of the exciter of mechanical vibrations, computer modeling, laboratory tests of the vibration generator control system. Research results. Models of complex oscillations have been developed to improve reliability and implement new control laws that are impossible for classical vibration systems and are necessary for automated vibroacoustic control of buildings and structures and ensure the safety of their operation. The use of reduced bit depth coefficients in the calculation scheme using the Jack W. Crenshaw algorithm is justified in a wider range of argument values than with initial coefficient values for controlling vibration systems with limited computational performance. This is necessary when creating executive bodies of modern systems for automated vibroacoustic monitoring of the cracks and violations of the homogeneity of load-bearing structures of buildings and structures. The oscillation exciter has been tested in laboratory conditions. Scientific novelty. New methods and algorithms for automatic control of vibration exciters have been developed to obtain polyfrequency oscillations, linear waves and wave fields with specified amplitude and frequency characteristics. Practical significance. An oscillation exciter has been developed for a system of automated vibroacoustic control of the buildings and structures operation safety. This provides a necessary and sufficient basis for improving methods for assessing changes in the environment as a result of the appearance of cracks and loss of homogeneity.

Study on the keyhole oscillation mechanism of laser welding based on electro-mechano-acoustical analogy theory

The acoustic emission phenomena generated by the laser welding process are closely related to the keyhole's forced oscillation and the dynamic pressure balance at the keyhole bottom. In this study, we constructed the mechanical equation of keyhole bottom pressure balance and used the “electro-mechano-acoustical” analogy theory to convert it into an acoustic equation, the acoustic resonant frequency as well as the magnification amplification factor of the keyhole oscillation in different penetration states were derived. A monitoring platform combining acoustic sensor and high-speed photography was established to obtain acoustic emission signals and lateral keyhole images. The acoustic and image features extracted from the monitoring data validated the derived formulas. Additionally, the acoustic phenomena of different frequency-energy components were explained according to the derived formulas in turn. The results demonstrated that the derived theory is compatible with experimental comparisons, showcasing its great interpretability and applicability. The introduced analogy theory effectively establishes a bridge between keyhole forced pressure and acoustic emission vibration, aiding in the understanding of keyhole oscillation characteristics. A novel model of keyhole oscillation was proposed and verified using process monitoring data in this study, which provides a new approach for the investigation of keyhole dynamic.

Environmental damping and vibrational coupling of confined fluids within isolated carbon nanotubes

Because of their large surface areas, nanotubes and nanowires demonstrate exquisite mechanical coupling to their surroundings, promising advanced sensors and nanomechanical devices. However, this environmental sensitivity has resulted in several ambiguous observations of vibrational coupling across various experiments. Herein, we demonstrate a temperature-dependent Radial Breathing Mode (RBM) frequency in free-standing, electron-diffraction-assigned Double-Walled Carbon Nanotubes (DWNTs) that shows an unexpected and thermally reversible frequency downshift of 10 to 15%, for systems isolated in vacuum. An analysis based on a harmonic oscillator model assigns the distinctive frequency cusp, produced over 93 scans of 3 distinct DWNTs, along with the hyperbolic trajectory, to a reversible increase in damping from graphitic ribbons on the exterior surface. Strain-dependent coupling from self-tensioned, suspended DWNTs maintains the ratio of spring-to-damping frequencies, producing a stable saturation of RBM in the low-tension limit. In contrast, when the interior of DWNTs is subjected to a water-filling process, the RBM thermal trajectory is altered to that of a Langmuir isobar and elliptical trajectories, allowing measurement of the enthalpy of confined fluid phase change. These mechanisms and quantitative theory provide new insights into the environmental coupling of nanomechanical systems and the implications for devices and nanofluidic conduits.

Studies on ionic conductivity, linear and non-linear optical properties of ecofriendly methyl cellulose: sodium bromide based solid polymer blend electrolytes

Biopolymer electrolytes based on methyl cellulose (MC) and sodium bromide(NaBr) have been prepared through solvent casting technique. Both the concentrations of MC and NaBr are varied. The prepared biopolymer electrolytes have been subjected to AC impedance and UV-Vis spectroscopic techniques. The ionic conductivity reached a maximum value of 4.84 × 10−8 Scm−1 for 0.8 g of MC and 0.2 g of NaBr. UV studies revealed that low direct and indirect band gaps have been observed for the maximum ionic conducting sample. Other optical parameters, such as refractive index, extinction coefficient, skin depth, and optical conductivity, have been estimated. The single-oscillator energy (Eo ) and dispersion energy (Ed ) for all the prepared biopolymer electrolyte samples were calculated with the help of Wemple and DiDomenico single oscillator model. The higher-order non-linear susceptibility values were also calculated. Polymer electrolytes are found to be suitable for optical and electronic devices.

Model integration of circadian- and sleep-wake-driven contributions to rhythmic gene expression reveals distinct regulatory principles

Analyses of gene-expression dynamics in research on circadian rhythms and sleep homeostasis often describe these two processes using separate models. Rhythmically expressed genes are, however, likely to be influenced by both processes. We implemented a driven, damped harmonic oscillator model to estimate the contribution of circadian- and sleep-wake-driven influences on gene expression. The model reliably captured a wide range of dynamics in cortex, liver, and blood transcriptomes taken from mice and humans under various experimental conditions. Sleep-wake-driven factors outweighed circadian factors in driving gene expression in the cortex, whereas the opposite was observed in the liver and blood. Because of tissue- and gene-specific responses, sleep deprivation led to a long-lasting intra- and inter-tissue desynchronization. The model showed that recovery sleep contributed to these long-lasting changes. The results demonstrate that the analyses of the daily rhythms in gene expression must take the complex interactions between circadian and sleep-wake influences into account. A record of this paper's transparent peer review process is included in the supplemental information.

Playing lato–lato is difficult and this is why

Lato–lato, a pendulum-based toy gaining popularity in Indonesian playgrounds, has sparked interest with competitions centered around maintaining its oscillatory motion. While some find it easy to play, the challenge lies in sustaining the oscillation, particularly in maintaining both ‘up and down collisions.’ Through a Newtonian dynamics numerical analysis using Python (code by ChatGPT), this study identifies two equilibrium phases—phase 1, characterized by normal pendulum motion, and phase 2, the double collision mode—using the driven oscillation model. In addition, further analysis and discussion are done using the obtained numeric data. The difficulty in remaining in phase 2 highlights the intricate hand-eye coordination required, shedding light on the toy’s appeal and the skill it demands.