Underdamped Behavior Research Articles

On the transient behavior and gain design for a class of second order homogeneous systems

In this note, we consider a class of homogeneous second order systems which contains two relevant sub-classes: the first one in a controller form and the second one in an observer form. For both of them, we provide necessary and sufficient conditions on the gain parameters to guarantee oscillatory or non-oscillatory behavior of the solutions. This is in the same spirit of tuning of second order linear systems, where the gains can be designed to obtain an overdamped, critically damped or underdamped behavior. The analysis of all the cases is performed in a unified framework based on a search for invariant sets which are analogous to the invariant eigenspaces of linear systems.

Aluminum-ferromagnetic Josephson tunnel junctions for high quality magnetic switching devices

The competition between superconducting and ferromagnetic orderings in Josephson devices has promoted fundamental and applicative studies of high impact for superconducting digital technology, cryogenic memories, and spintronics, where the possibility of switching between different magnetic states is a crucial advantage. Here, we report on fabrication and characterization of very high quality tunnel ferromagnetic Josephson junctions (JJs) with aluminum electrodes, demonstrating hysteretic behavior of the magnetic field pattern preserving typical transport properties of Al junctions, underdamped behavior, and very low quasiparticle dissipation. The proposed technology paves the way for the possible implementation of Al tunnel-ferromagnetic JJs in superconducting quantum circuits, toward alternative approaches based on digital control of the Josephson device.

Analysis of the discharge plasma impedance of copper vapor laser

In the pursuit to analyze the impedance of copper vapor lasers (CVLs) in different conditions, a novel approach has been proposed in this paper. The underdamped behavior of the voltage waveform across the CVL is leveraged to compute the impedance of high-voltage discharge plasma in the laser. This methodology provides an accurate idea of the discharge plasma resistance and inductance as it is calculated on the basis of experimental voltage waveforms obtained from the laser system. The laser head inductance remains almost fixed and equivalent to ∼0.47 µH whereas the laser resistance changes between 34 Ω and 11 Ω depending on the discharge condition and its constituents. A critical evaluation of CVL impedance is done in all experimentally possible conditions, and a methodology has been proposed to maintain the CVL impedance, which results in the power stability of the laser in oscillator–amplifier configuration. The laser impedance variation w.r.t. time, pressure, operating voltage and electrode pin configuration has been investigated. The impact of the localized electric field at the electrode on the laser resistance has also been emphasized in this paper. A good concurrence exists between the calculated laser impedance and its experimental behavior.

Adaptive shaper-based filters for fast dynamic filtering of load cell measurements

This paper proposes a novel adaptive model-based filtering technique for dynamic mass measurement through load cells, named Adaptive Shaper-Based Filter (ASBF). Filtering is performed by convolving the oscillating load cell signal with a baseline of few impulses (usually 3) to rapidly compensate for its underdamped behaviour. The correct timings and amplitudes of the impulses are computed by means of a simplified dynamic model of the load cell (that requires the knowledge of the natural frequency and the damping ratio of the empty cell), and the filter output itself (i.e. the estimated mass). The load cell is modelled through the theory of systems with variable mass as a linear time-variant system and the variations of frequency and damping are predicted; in this way, the filter zeros track the load cell poles to cancel them. Robustness specifications are included in the filter design to account for the unavoidable uncertainty and estimation errors. Given the non-rational transfer function of the proposed Adaptive Shaper Based Filter, whose poles have an infinite and negative real part, rapid settling time is ensured. Experimental assessment is proposed by comparing the results with some benchmark filters.

Binocular rivalry subjected to noises and time delay

Neural systems are inherently noisy and time-delay, and these effects influence our perception from time to time. This is particularly apparent in binocular rivalry, where our perception alternates between competing stimuli shown to the two eyes. Here, we investigated the binocular rivalry behavior under the action of time delay and two noise sources. Our numerical results find that (i) the time delay and additive noise make the stationary probability distribution function of the binocular rivalry jump among two, three and four stabilities, breaking or maintaining balance of the binocular rivalry; (ii) the dependence of mean first passage time on multiplicative noise intensity shows a maximum, i.e., noise enhance perceptual stability, while the stability can be enhanced many times by the time delay; (iii) the characteristic correlation time not only exhibits a underdamped oscillation behavior as a function of delay time (i.e., multiple coherence resonances), but also shows a nonmonotonic behavior with the additive noise intensity. These findings have the significant implication for understanding and controlling perception alteration from a new perspective.

Driven-dissipative Ising model: An exact field-theoretical analysis

Driven-dissipative many-body systems are difficult to analyze analytically due to their non-equilibrium dynamics, dissipation and many-body interactions. In this paper, we consider a driven-dissipative infinite-range Ising model with local spontaneous emission, which naturally emerges from the open Dicke model in the large-detuning limit. Utilizing an adaptation of the Suzuki-Trotter quantum-to-classical mapping, we develop an exact field-theoretical analysis and a diagrammatic representation of the spin model that can be understood from a simple scattering picture. With this representation, we are able to analyze critical behavior, finite-size scaling and the effective temperature near the respective phase transition. Our formalism further allows a detailed study of the ordered phase where we find a "heating" region within which the effective temperature becomes negative, thereby exhibiting a truly non-equilibrium behavior. At the phase transition, we find two distinct critical behaviors with overdamped and underdamped critical dynamics at generic and weakly-dissipative critical points, respectively. We further show that the underdamped critical behavior is robust against short-range perturbations and is not an artifact of the mean-field nature of the model. To treat such perturbations, we extend our diagrammatic representation to include the coupling to spin waves due to the short-range interactions. The field-theoretical approach and the diagrammatics developed in this work should prove useful in applications to generic short-range driven-dissipative spin systems.

Solvation Dynamics in Water. 4. On the Initial Regime of Solvation Relaxation

It is shown, by means of numerical and analytic work, that initial molecular momenta play little significant role in the initial fast solvation relaxation that follows electronic excitation of, and charge creation for, a standard model system of a solute in water. Instead, the nonequilibrium dynamics are predominantly described by noninertial "steering" by the torques directly generated by the newly created charge distribution. It is this process that largely overcomes inertia and drives the relaxation dynamics on a time scale of a few tens of femtoseconds in the key initial regime of the dynamics. These results are discussed in the context of commonly employed descriptions such as inertial, Gaussian, and underdamped dynamical behavior.

Extensive study of cage effect and subdiffusion in Pickering emulsions using molecular dynamics simulations

In this work, we aim at an extensive study of the diffusion phenomenon of oil-droplets dispersed in water onto which are strongly adsorbed charged point-like particles (Pickering emulsions). This diffusion that originates from multiple collisions with the molecules of water, is anomalous, due to the presence of relatively strong correlations between the moving oil-droplets. Using Molecular Dynamic simulation, with a pair-potential of Sogami-Ise type, we first observe that the random walkers execute a normal diffusion, at intermediate time, followed by a slow diffusion (subdiffusion) we attribute to the presence of cages, formed by the nearest neighbors (traps). In the cage-regime, we find that the mean-square-displacement increases according to a time-power law, with an anomalous diffusion exponent between 0 and 1. The existence of a cage effect is shown also by computing the velocity auto-correlation function of the random walker. It is found that, in a cage, this function is governed by an underdamped (oscillatory) behavior, for strong densities and surface charges, and low-salt concentration. In the inverse situation, however, we observe that this correlation-function is rather overdamped (non-oscillatory). In the two cases, at large-time, this function fails according to a time-power law.

Study of cage effect and subdiffusion in Pickering emulsions from Molecular Dynamics simulations

In this work, we study the diffusion laws of oil-droplets dispersed in water onto which are strongly adsorbed charged point-like particles (Pickering emulsions). This diffusion that originates from multiple collisions with the molecules of water, is anomalous, due to the presence of relatively strong correlations between the moving oil-droplets. Using Molecular Dynamics simulation, with a pair-potential of Sogami-Ise type, we first observe that the random walkers execute a normal diffusion, at intermediate time, followed by a slow diffusion (subdiffusion) we attribute to the presence of cages, formed by the nearest neighbors (traps). In the cage-regime, we find that the mean-square-displacement increases according to a time-power law, with an anomalous diffusion exponent, α (between 0 and 1). This exponent and the generalized diffusion coefficient are computed varying the relevant parameters (surface charge, density, salt-concentration). We remark that the subdiffusion is significant only for strong surface charges and densities, and low-salt concentrations. The existence of a cage effect is shown computing the velocity auto-correlation function of the random walker. It is found that, in a cage, this function is governed by an underdamped (oscillatory) behavior, for strong densities and surface charges, and low-salt concentration. In the inverse situation, however, we observe that this correlation-function is rather overdamped (non-oscillatory). In the two cases, at large-time, this function fails according to a time-power law, with the exponent α−2. To validate our simulation data, we propose a memory diffusion theory that is based essentially on a generalized Langevin equation. Finally, we demonstrate that the results from simulations are in good agreement with the predictions of the elaborated theory.

Different damping responses explain vertical endpoint error differences between visual conditions.

Upright people making goal-directed movements in dark environments often vertically undershoot remembered target locations when compared to performances in illuminated environments. In this study, we wanted to determine whether influences of the gravitational pull and/or type of muscle activation could explain differences in vertical endpoint precision between movements to visually remembered target locations with and without allocentric cues available. We also used a simple damping model for movement trajectories to describe potential differences in behavior between visual conditions. Subjects performed straight arm pointing movements to REAL target locations or remembered target locations in darkness (DARK) or normal room lighting (LIGHT). Performances were made from UPRIGHT and INVERTED (upside down) body orientations. Starting arm position (UP by the ear; DOWN on the thigh) also varied so that eccentric or concentric muscle contractions for arm flexion or extension movements occurred primarily along the earth-fixed vertical either with or against the gravitational pull. Effects of visual condition (LIGHT, DARK), body orientation (UPRIGHT, INVERTED), starting arm position (UP, DOWN), and target level (Near, Middle, Far) on elevation endpoint errors revealed that subject's errors in the DARK were more negative than those in the LIGHT. Errors correlated well with movement displacement to reveal the common vertical undershooting bias in darkness exacerbated by inverting the body or requiring greater movement excursions. Although influences of gravitational pull and muscle activation type could not explain differences between visual conditions, modeling revealed critically damped behavior in the DARK and under-damped behavior in the LIGHT to indicate muscle energy dissipation without vision.

EFFECTS OF LIQUID AND SURFACE CHARACTERISTICS ON OSCILLATION BEHAVIOR OF DROPLETS UPON IMPACT

Author(s): Banks, D; Ajawara, C; Sanchez, R; Surti, H; Aguilar, G | Abstract: The physical behavior of a single droplet impacting a surface is one of the most fascinating facets of spray research. Under some conditions, a droplet will strike and spread across a solid surface without splashing or rebounding. That droplet will spread and recoil for some time, oscillating between a disk and a hemisphere until these fluctuations diminish due to viscous damping. These oscillations affect the liquid coverage area and are essential in droplet solidification applications; yet little is known about them; Knowing more will, for example, enable higher-precision three-dimensional printing or enhanced droplet and spray cooling. Using mixtures of water and glycerol, oscillations of droplets with kinematic viscosities between 1.0 × 10-6and 1.1 × 10-4m2=s are explored, focusing on the damping behavior. Several impact substrates were used. Droplets freefall onto the target with velocities of 0.5-1.5 m/s. TheWeber number of the droplets ranged from 10 to 100 and the Reynolds number from 15 to 4000. The impact velocity, spreading lamella diameter, and thickness at the center of each droplet were measured. Droplet kinematic viscosity, impact velocity, and surface tension effects are found to play a role in oscillations, which occur at approximately 75-90 Hz. For the liquids tested, a hydrophilic surface thins the droplet, arresting oscillations quickly, whereas a hydrophobic surface sustains oscillations. Correspondingly, a highly viscous droplet tends to stop oscillations sooner than a less viscous droplet. Increasing the velocity of impact restricts oscillations by spreading liquid across a larger area. For the range of conditions studied, viscosity dominates droplet oscillations when compared to the surface effects. We explore the interplay between viscous and surface tension effects in the oscillations. The spring constant and damping coefficient of an analogous harmonic system are calculated for the observed droplet oscillations. The tested liquid droplets generally exhibit underdamped behavior; higher damping coefficients are associated with more wetting and more viscous droplet liquids - a 103increase in viscosity corresponds with an approximately 101increase in damping. The spring constant appears to be influenced by the droplet composition and the surface wettability in a less trivial manner, with similar magnitudes and no discernable pattern in the spring constant (1.5-3.0 N/m) for all droplets and surface conditions examined.

Dynamics of microscopic objects in optical tweezers: experimental determination of underdamped regime and numerical simulation using multiscale analysis

This article presents new experimental observations and numerical simulations to investigate the dynamic behavior of micro–nano-sized objects under the influence of optical tweezers (OTs). OTs are scientific tools that can apply forces and moments to small particles using a focused laser beam. The motions of three polystyrene microspheres of different diameters, 1,950, 990, and 500 nm, are examined. The results show a transition from the overdamped motion of the largest bead to the underdamped motion of the smallest bead. The experiments are verified using a dynamic model of a microbead under the influence of Gaussian beam OTs that is modeled using ray-optics. The time required to numerically integrate the classic Newton–Euler model is quite long because a picosecond step size must be used. This run time can be reduced using a first-order model, and greatly reduced using a new multiscale model. The difference between these two models is the underdamped behavior predicted by the multiscale model. The experimentally observed underdamped behavior proves that the multiscale model predicts the actual physics of a nano-sized particle moving in a fluid environment characterized by a low Reynolds number.

Capillarity-induced resonance of blobs in a 3-D duct: lattice Boltzmann modelling

The present study deals with the analysis of capillarity–wettability interaction of the trapped nonwetting phase. The displacement of a three-dimensional immiscible blob subject to oscillatory acoustic excitation in a duct is explored using the lattice Boltzmann method. The effect of the width of the channel, amplitude of the force, wettability, viscosity and frequency on blob dynamics are investigated. The response of the blob with pinned contact line shows underdamped behavior whereas with that of sliding contact line exhibits overdamped character. It is observed that increasing the amplitude of the force increases the mean displacement and frequency response. The displacement of the blob reveals underdamped character for lesser viscosity and overdamped character for higher viscosity. It is found that the mean displacement of the blob is greater for uniform wettability as compared to mixed wettability surface for the pinned configuration. The surface with strong hydrophobic and hydrophilic nature shows more displacement. The resonance behavior of the blob on the surface with different wettabilities is discussed. It can be inferred that at resonating frequency blob show maximum displacement. The effect of wettability is not so prominent at high capillary numbers. However at low capillary number the wettability is crucial in mobilization of trapped blob.

A simple and effective Verlet-type algorithm for simulating Langevin dynamics

We present a revision to the well known Störmer–Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate that the new algorithm correctly reproduces diffusive behaviour of a particle in a flat potential. For a harmonic oscillator, our algorithm provides the exact Boltzmann distribution for any value of damping, frequency and time step for both underdamped and overdamped behaviour within the usual stability limit of the Verlet algorithm. Given the structure and simplicity of the method, we conclude that this approach can trivially be adapted for contemporary applications, including molecular dynamics with extensions such as molecular constraints.

Skewness variations of switching-current distributions in moderately damped Josephson junctions due to thermally induced multiple escape and retrapping

A crossover at a temperature T* in the temperature dependence of the width σ of the distribution of switching currents of moderately damped Josephson junctions has been reported in a number of recent publications. For T < T*, dσ/dT is positive and the IV characteristics are associated with underdamped behaviour; for T > T*, dσ/dT is negative and the IV characteristics resemble overdamped behaviour. We have investigated in detail the behaviour of Josephson junctions around T* by using Monte Carlo simulations including retrapping from the running state into the supercurrent state as given by a model due to Ben-Jacob et al. Thermally induced multiple escape and retrapping events play an important role for moderate damping. Around T*, not just at lower T < T*, the shape of the distribution and σ(T) are largely determined by the shape of the conventional underdamped thermally activated switching distribution. The behaviour is more fully understood by considering two crossover temperatures. The skewness of the switching distribution parametrises its shape and becomes less negative, then positive, as T increases above the lower crossover temperature.

Exact expressions for the amplitudes and damped normal frequencies of a taut vibrating linear string of coupled masses

We determine exact expressions for the amplitudes and vibrational eigenmodes of a taut linear string of identical masses that are subjected to a viscous damping that is proportional to their momentum. We first examine the damped displacements of the string in the more familiar limit of a continuous distribution of mass. We then derive a damped version of the linear, one-dimensional wave equation and describe the dispersion curve. Next, we find exact expressions for the damped normal eigenmodes for a finite system. We show that a fraction of these modes have imaginary frequencies that correspond to overdamped oscillations. Next, we show that the remaining modes exhibit underdamped oscillatory behaviour and represent that portion of the dispersion curve graphically. We use methods that are at an intermediate level of presentation.

NMR Observation of Rattling Phonons in the Pyrochlore SuperconductorKOs2O6

We report nuclear magnetic resonance studies on the beta-pyrochlore oxide superconductor KOs2O6. The nuclear relaxation at the K sites is entirely caused by fluctuations of the electric field gradient, which we ascribe to highly anharmonic low frequency oscillation (rattling) of K ions. A phenomenological analysis shows a crossover from overdamped to underdamped behavior of the rattling phonons with decreasing temperature and its sudden sharpening below the superconducting transition temperature T(c). Suppression of the Hebel-Slichter peak in the relaxation rate at the O sites below T(c) also indicates strong electron-phonon coupling.

Modeling of DC&amp;#8211;DC Buck Converters for Large-Signal Frequency Response and Limit Cycles

A zeroth-order-hold equivalent discrete-time model of the buck converter for computing its large-signal frequency response is developed and experimentally verified. It is shown that, with a dc bias and a sinusoidal variation of the input duty cycle, the frequency response of the output voltage from the converter shifts from underdamped behavior to damped behavior with increasing amplitude of the input sinusoid. It is observed that, with a given dc input bias and a given input amplitude beyond the range of the state-space linearized small-signal model, the converter behavior varies from exclusively continuous inductor current mode at low frequencies to behavior with continuous and discontinuous inductor current modes at high frequencies. The use of this sinusoidal input large-signal frequency response in predicting limit cycles induced by feedback of the output voltage using proportional and integral controllers for such converters is studied. Experimental results confirming the use of this large-signal frequency response are presented

An Investigation Into the Effect of Subcooled Liquid Inertia on Flow-Change-Induced Transient Flow Surges in Horizontal Condensing Flow Systems

The objective of this research is to investigate large-scale transient flow surges of the condensate leaving in-tube condensing flow systems because of perturbations in the inlet vapor flow rate, and the influence of the subcooled liquid inertia of the condensate on these transient responses. Small changes in the inlet vapor flow rate momentarily cause large transient flow surges in the outlet liquid flow rate. Condensate inertia is seen to destabilize the system into an underdamped behavior where the flow rate can overshoot the final steady-state position several times. A one-dimensional, two-fluid, distributed parameter system mean void fraction (SMVF) model of the time-dependent distribution of liquid and vapor within the two-phase region is developed for predicting these transient characteristics, which it is seen to do quite well, especially when consideration is given to the complex nature of the problem.

Trunk stiffness and dynamics during active extension exertions

Spinal stability is related to the recruitment and control of active muscle stiffness. Stochastic system identification techniques were used to calculate the effective stiffness and dynamics of the trunk during active trunk extension exertions. Twenty-one healthy adult subjects (10 males, 11 females) wore a harness with a cable attached to a servomotor such that isotonic flexion preloads of 100, 135, and 170 N were applied at the T10 level of the trunk. A pseudorandom stochastic force sequence (bandwidth 0–10 Hz, amplitude ±30 N) was superimposed on the preload causing small amplitude trunk movements. Nonparametric impulse response functions of trunk dynamics were computed and revealed that the system exhibited underdamped second-order behavior. Second-order trunk dynamics were determined by calculating the best least-squares fit to the IRF. The quality of the model was quantified by comparing estimated and observed displacement variance accounted for (VAF), and quality of the second-order fits was calculated as a percentage and referred to as fit accuracy. Mean VAF and fit accuracy were 87.8 ± 4.0 % and 96.0 ± 4.3 % , respectively, indicating that the model accurately represented active trunk kinematic response. The accuracy of the kinematic representation was not influenced by preload or gender. Mean effective stiffness was 2.78 ± 0.96 N / mm and increased significantly with preload ( p < 0.001 ), but did not vary with gender ( p = 0.425 ). Mean effective damping was 314 ± 72 N s/m and effective trunk mass was 37.0 ± 9.3 kg . We conclude that stochastic system identification techniques should be used to calculate effective trunk stiffness and dynamics.