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The mechanism of wave dissipation in different layers of the sun, as well as the solar granules inter-network bright points and internetwork bright points of chromosphoric solar granules, have been explored in this article. This article's data come from the Interface Region Imaging Spectrograph (IRIS). IRIS is a small exploration mission by NASA. That obtains spectra in nearultraviolet (NUV), far-ultraviolet 1 (FUV1), and far-ultraviolet 2 (FUV2), from 1332 to 2834 𝐴̇. Slit jaw images (SJIs) of IRIS, using various filters that can provide images centered on the Mg II h wing, Mg II k, Si IV 1403 𝐴̇, and C ii lines. To begin, bright points in the chromosphere are selected for this goal. These points were first chosen using IRIS Slit Jaw Images (SJI) Si IV 1403 𝐴̇. The time slices of the Doppler velocity of the Mg II k spectrum are then drawn at a specified velocity (+/- 20 km/s) and were fed into the wavelet transform function to perform the time-frequency analysis to obtain the oscillation periods of the Doppler velocity. The wavelet transform used for this purpose is Morlet 5 wavelet. The velocity oscillation period data are utilized to determine the bright points of the network and internetwork solar granules at the chromosphere. The Doppler shift diagram for the Si IV 1394 spectral line is then displayed in time. This graph is a Doppler shift various time graph with attenuation that is caused by wave loss in the solar layers. According to the obtained data, the network and internetwork bright points, the chromospheric solar granules have an attenuation time 3 to 5 min. The oscillations of the solar granules network bright points are damped more intensely than the solar granules inter-network bright points, and hence their damping lifetime is shorter. Si IV 1394 𝐴̇ Doppler velocity shift of bright points placed in the solar granules inter-network is dampened by a lower slope and so has a longer damping life time. Sadeghi and Tavabi researched about the kinetic energy above the bright points of the network and internetwork regions of the solar granules in a part of a paper titled "A new approach to kinetic energy flux at the different frequencies above the IRIS bright points" in 2022. They claim that a substantial percentage of the energy of the network bright points of solar granules is transferred to higher layers, namely the transition region corona, in the network bright points of solar granules. These findings are congruent with the findings of the current study. The oscillations in these locations are dampened for a brief period of time, and the energy is transmitted to higher layers with little loss. Furthermore, it is stated in the cited paper that the majority of the energy at the internetwork bright points of the solar granules does not transfer to higher layers of Sun. This suggests that the energy loss from bright points in the solar granules' internetwork region is rather high in the chromospheric layer. The time period of the wave damping is longer than the length of the damping time in the oscillations, according to the current study on the mechanism of wave dissipation in different layers of the sun and the network and internetwork bright points of the chromosphere. It has also been demonstrated that the time period of the wave damping is greater than the length of the damping time in the oscillations of the bright points of the granules' network region, which is the source of the most energy loss in this layer. [ABSTRACT FROM AUTHOR]

A novel control strategy utilizing the Internal Model Principle (IMP) is introduced to mitigate damped oscillations within power systems, specifically targeting low-frequency electromechanical oscillations. This approach involves first identifying the dynamic behaviors of power system oscillations and then integrating these dynamics into the feedback loop. Consequently, leveraging the IMP, the method effectively eliminates oscillations from the system output. Key benefits of this method include its straightforwardness, resilience, capability for real-time deployment, and independence from specific system models. To assess its efficacy, simulation studies were conducted on two operational power systems, complemented by an empirical study on a two-bus laboratory power system at the University of Calgary. Both simulation and empirical findings affirm the method’s effective performance.

This paper presents a control solution for the problem of slung load transportation, with simultaneous damping of oscillations, using an underactuated autonomous quadrotor vehicle in the presence of external disturbances. The strategy put forward is divided into two parts: (i) resorting to an error definition that encompasses the pendular motion of the suspended load, a controller inspired in sliding‐mode theory is developed to compute a vectored thrust actuation that actively damps out the system's oscillations; (ii) two different approaches are illustrated for the stage of attitude tracking: one stemming from the conventional backstepping technique, which controls the vehicle in angular velocity commands; and another, also based on sliding‐mode theory, and built intrinsically in SO(3)$$ \mathsf{SO}(3) $$, that produces torque commands. The overall control scheme is proved to be robust and stable, with the load oscillations shown to be damped out in the process. Simulation and experimental results are presented in a trajectory tracking scenario to validate and assess the robustness and efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

The characteristics of spatial relaxation of the average electron energy in pure helium and in helium containing an admixture of water vapor in a constant electric field have been investigated by Monte Carlo simulation. The conditions under which the spatial relaxation in helium has a form of damped oscillations are considered. It is shown that even a small (0.1%) additive of water vapor leads to a significant decrease in the relaxation length, and the spatial oscillations almost disappear at 3% H2O. Calculations were also performed for a mixture He : (H2O : H2 : O2 : H), where the composition of atoms and molecules in the parentheses correspond to the composition formed from the initial water vapor in discharge plasma due to the dissociation of water molecules and subsequent plasma-chemical reactions. [ABSTRACT FROM AUTHOR]

The damped oscillating structures recently revealed by a three parametric formula from the proton “effective” form factor data extracted of the measured total cross section σtotbare(e+e−→pp¯) still seem to have an unknown origin. The conjectures of their direct manifestation of the quark-gluon structure of the proton indicate that they are not specific only of the proton and neutron, but they have to be one’s own, similar to other hadrons. Therefore, the oscillatory structures from the charged pion electromagnetic form factor timelike data, extracted of the process e+e−→π+π− are investigated by using the same procedure as in the case of the proton. The analysis shows the appearance of the oscillating structures in the description of the charged pion electromagnetic form factor timelike data by three parametric formula with a rather large value of χ2/ndf, while the description of the data by the physically well-founded Unitary and Analytic model has not revealed any damped oscillating structures. From the obtained result on the most simple object of strong interactions, one can conclude that damped oscillating structures received from the “effective” proton form factor data are probably generated by a utilization of the improper three parametric formula which does not describe these data with sufficient precision.

The present two-part paper concerns the active vibration suppression for the simplest damped continuous system, namely the transverse oscillations of an elastic string, with constant tension and mass density per unit length and friction force proportional to the velocity, described by the telegraph or wave-diffusion equation, in two complementary parts. The initial part I considers non-resonant and resonant forcing, by concentrated point forces or continuous force distributions independent of time, with phase shift between the forced and free oscillations, in the absence of damping, in which case the forced telegraph equation reduces to the forced classical wave equation. The present and final part II uses the forced wave-diffusion equation to model the effect of damping, both as amplitude decay and phase shift in time, for non-resonant and resonant forcing by a single point force, with constant magnitude or magnitude decaying exponentially in time at an arbitrary rate. Assuming a finite elastic string fixed at both ends, the free oscillations are (i) sinusoidal modes in space-time with exponential decay in time due to damping. The non-resonant forced oscillations at an applied frequency distinct from a natural frequency are also (ii) sinusoidal in space-time, with constant amplitude and a phase shift such that the work of the applied force balances the dissipation. For resonant forcing at an applied frequency equal to a natural frequency, the sinusoidal oscillations in space-time have (iii) a constant amplitude and a phase shift of π/2. In both cases, the (ii) non-resonant or (iii) resonant forcing dominates the decaying free oscillations after some time. Even by optimizing the forcing to minimize the total energy of oscillation, it remains below the energy of the free oscillation alone, but only for a short time—generally a fraction of the period. A more effective method of countering the damped free oscillations is to use forcing with amplitude decaying exponentially in time; by suitable choice of the forcing decay relative to the free damping, the total energy of oscillation over all time can be reduced to no more than 1/16th of the energy of the free oscillation.

Droplet bouncing on special wettability surface is common and important in daily life and engineering applications (anti‐icing and drag reduction, etc.). However, there are few studies on the multiple droplets impact and there is a lack of systematic research on the interaction of oscillation and bounce. Here, the impact and oscillation of multiple droplets on the porous superhydrophobic bionic lotus surface are studied by a high‐speed camera system. On the bionic lotus surface (Surf‐1), an impacting droplet can merge another larger sessile droplet and bounce off. Comparing with single droplet impact, it is suggested that multiple droplets impact make more efficient use of the air cushion on the micrometer‐nanometer‐scale binary structure (MNBS) and show the self‐cleaning performance of Surf‐1 better. Moreover, with the theory for damped harmonic oscillators, it is found that Surf‐1 can prolong the oscillation of droplets (last >250 ms) and slow down the attenuation of energy. The energy can be efficiently recycled to the bounce by shortening the droplet impact interval (ti). The fundamental understanding of multiple droplets impact and the reclamation of oscillating energy are beneficial for scientific design of new surface and engineering applications. [ABSTRACT FROM AUTHOR]

The present two-part paper concerns the active vibration suppression for the simplest damped continuous system, namely the transverse oscillations of an elastic string, with constant tension and mass density per unit length and friction force proportional to the velocity, described by the telegraph or wave-diffusion equation, in two complementary parts. The initial part I considers non-resonant and resonant forcing, by concentrated point forces or continuous force distributions independent of time, with phase shift between the forced and free oscillations, in the absence of damping, in which case the forced telegraph equation reduces to the forced classical wave equation. The present and final part II uses the forced wave-diffusion equation to model the effect of damping, both as amplitude decay and phase shift in time, for non-resonant and resonant forcing by a single point force, with constant magnitude or magnitude decaying exponentially in time at an arbitrary rate. Assuming a finite elastic string fixed at both ends, the free oscillations are (i) sinusoidal modes in space-time with exponential decay in time due to damping. The non-resonant forced oscillations at an applied frequency distinct from a natural frequency are also (ii) sinusoidal in space-time, with constant amplitude and a phase shift such that the work of the applied force balances the dissipation. For resonant forcing at an applied frequency equal to a natural frequency, the sinusoidal oscillations in space-time have (iii) a constant amplitude and a phase shift of π / 2 . In both cases, the (ii) non-resonant or (iii) resonant forcing dominates the decaying free oscillations after some time. Even by optimizing the forcing to minimize the total energy of oscillation, it remains below the energy of the free oscillation alone, but only for a short time—generally a fraction of the period. A more effective method of countering the damped free oscillations is to use forcing with amplitude decaying exponentially in time; by suitable choice of the forcing decay relative to the free damping, the total energy of oscillation over all time can be reduced to no more than 1 / 16 th of the energy of the free oscillation. [ABSTRACT FROM AUTHOR]

The damped oscillating structures recently revealed by a three parametric formula from the proton "effective" form factor data extracted of the measured total cross section σ t o t b a r e (e + e − → p p ¯) still seem to have an unknown origin. The conjectures of their direct manifestation of the quark-gluon structure of the proton indicate that they are not specific only of the proton and neutron, but they have to be one's own, similar to other hadrons. Therefore, the oscillatory structures from the charged pion electromagnetic form factor timelike data, extracted of the process e + e − → π + π − are investigated by using the same procedure as in the case of the proton. The analysis shows the appearance of the oscillating structures in the description of the charged pion electromagnetic form factor timelike data by three parametric formula with a rather large value of χ 2 / n d f , while the description of the data by the physically well-founded Unitary and Analytic model has not revealed any damped oscillating structures. From the obtained result on the most simple object of strong interactions, one can conclude that damped oscillating structures received from the "effective" proton form factor data are probably generated by a utilization of the improper three parametric formula which does not describe these data with sufficient precision. [ABSTRACT FROM AUTHOR]

The work is devoted to improving the methods of experimental determination of internal friction parameters in materials. The aim of the laboratory experiments is to obtain physical parameters of the material that allow to take into account the damping forces in a uniaxial stress state. The research is focused on the internal friction model, which is based on the use of the generalized Prandtl model, that gives frequency-independent internal friction and allowing for the dependence of internal friction on the level of time-varying stresses. Damped oscillations during pure bending are recorded on a specially made laboratory installation. The description of the installation, the reference points of which coincide with the fixed points of the realized form of natural oscillations, is provided. The algorithm of cameral processing of experimental data is obtained. It is proposed to use a virtual system equivalent in damping. This is a system with one dynamic degree of freedom. The involvement of an imaginary system permits, after performing tests of the sample for pure bending, to acquire data corresponding to stretching - compression. The technique grants the use of long samples, which reduces the negative effect of stress concentration in the anchorages. The damping equivalent scheme makes it possible to use samples with an arbitrary cross-section. The found damping parameters for low-carbon steel are given.

Abstract Droplet bouncing on special wettability surface is common and important in daily life and engineering applications (anti‐icing and drag reduction, etc.). However, there are few studies on the multiple droplets impact and there is a lack of systematic research on the interaction of oscillation and bounce. Here, the impact and oscillation of multiple droplets on the porous superhydrophobic bionic lotus surface are studied by a high‐speed camera system. On the bionic lotus surface (Surf‐1), an impacting droplet can merge another larger sessile droplet and bounce off. Comparing with single droplet impact, it is suggested that multiple droplets impact make more efficient use of the air cushion on the micrometer‐nanometer‐scale binary structure (MNBS) and show the self‐cleaning performance of Surf‐1 better. Moreover, with the theory for damped harmonic oscillators, it is found that Surf‐1 can prolong the oscillation of droplets (last >250 ms) and slow down the attenuation of energy. The energy can be efficiently recycled to the bounce by shortening the droplet impact interval (ti). The fundamental understanding of multiple droplets impact and the reclamation of oscillating energy are beneficial for scientific design of new surface and engineering applications.

The review summarizes the theoretical and numerical results of analysis of the dispersion equation of standing waves on the surface of a viscous liquid published by L.N. Sretensky in 1941. A mechanism for the viscous regularization of wave motion is proposed, according to which the effects observed in the experiment are associated with the presence of a short-wavelength cutoff region, where viscous dissipation becomes the predominant factor and short-wavelength perturbations responsible for the breaking of a standing wave are suppressed. [ABSTRACT FROM AUTHOR]

Pendulum phenomenon plays an important, role in applied mathematics, earthquake engineering, vibrations mechanics and physics due to its dynamical nonlinear nature. The nonlinear pendulum governing differential-equation is numerically solved herein using the Finite Element Method for the first time. To overcome the nonlinearity resulting from the sine term, Maclaurin’s power-series expansion for the sine function with ten terms (odd powers up to the 19th power) is substituted into the differential equation. The nonlinearity is then shifted from the sine term to terms of powers of the angular displacement. The original initial value pendulum problem is converted into a two-point boundary value problem suitable for the Finite Element Method. This is possible owing to a power series solution that determines an explicit expression of the period of motion in terms of the initial displacement angle (amplitude). In this way the time of motion which is given by the period of motion is considered as a space domain. The periodic nature of the pendulum problem allows specifying the amplitude value at the two ends of the time domain (now becomes the space domain) as the two end boundary conditions. An incremental boundary condition technique and the Newton-Raphson method are used to solve the nonlinear system of equations. The solution is applicable up to maximum amplitude of 179º. The differential form of the pendulum equation facilities investigating damped motion by including the frictional and form drag resistance forces to the differential equation of the pendulum motion in fluids such as air and water. The ability to solve the differential equation form of the nonlinear pendulum allows ease in dealing with tangential forces to the pendulum bob’s direction of motion such as fluid resistance and electromagnetic forces. Comparison with existing analytical solution shows that the present approach succeeded in predicting the pendulum motion profile under damped conditions. The approach developed here could be used to investigate pendulum problems where electromagnetic forces exist. [ABSTRACT FROM AUTHOR]

This paper aims to find the best variant of Cuckoo Search Algorithm that makes the step size of Lévy flight adaptive. For this reason, we introduce a new variant of CSA called Damped Cuckoo Search (DCS) in which the step size of Lévy flight is adaptive via the concept of damped oscillations that exist in most second order control systems. Moreover, we propose two other methods that tune the step size of Lévy flight based on chaotic maps. Then a deep comparative study is conducted among almost all variants of CSA that appeared in the last decade that modifies the step size of Lévy flight. All these variants are tested on CEC2017 benchmark functions. Statistical analyses are performed using the Friedman test followed by four post-hoc procedures to hold paired comparisons between the proposed DCS and the other CSA variants. Also, graphical statistical analyses are conducted on all variants via Box Plots. Finally, convergence graphs for all the variants are illustrated as well to show the speed of solution improvement over generations. Simulation results prove that the proposed DCS outperforms all other variants with a large degree of significance. Moreover, DCS increases the speed of convergence in comparison with the other variants. The box plot graphs prove that DCS has the most compact distribution for all results obtained in all runs on most functions.

The study presents approaches to both electrostatic and magnetostatic levitations. For anisotropic balls, both dielectric and magnetic field distributions are derived in analytical forms by means of the variable separation method. Distributions are given by power functions and polynomials either Legendre's (for the electrostatic problem) or the associated polynomials (for the magnetostatic problem). The levitation forces are evaluated by means of four methods, i.e. Maxwell stress tensor generalised method, co-energy method, material force density, and equivalent dipole analysis for both levitations. Levitation forces versus either electric permittivity or magnetic permeability are presented. The stability of the equilibrium points is investigated. The frequencies of free and damped oscillations are evaluated. [ABSTRACT FROM AUTHOR]

When considering a new vaccine programme or modifying an existing one, economic cost-benefit analysis, underpinned by predictive epidemiological modelling, is a key component. This analysis is intimately linked to the willingness to pay for additional QALYs (quality-adjusted life-years) gained; currently in England and Wales a health programme is economically viable if the cost per QALY gained is less than £ 20,000, and models are often used to assess if a vaccine programme is likely to fall below this threshold cost. Before a programme begins, infection levels are generally high and therefore vaccination may be expected to have substantial effects and therefore will often be economically viable. However, once a programme is established, and infection rates are lower, it might be expected that a re-evaluation of the programme (using current incidence information) will show it to be less cost-effective. This is the scenario we examine here with analytical tools and simple ODE models. Surprisingly we show that in most cases the benefits from maintaining an existing vaccination programme are at least equal to those of starting the programme initially, and in the majority of scenarios the differences between the two are minimal. In practical terms, this is an extremely helpful finding, allowing us to assert that the action of immunising individuals does not de-value the vaccination programme.

In subspace identification, prior information can be used to constrain the eigenvalues of the estimated state‐space model by defining corresponding linear matrix inequality (LMI) regions. In this study, first the authors argue on what kind of practical information can be extracted from historical data or step‐response experiments to possibly improve the dynamical properties of the corresponding model and, also, on how to mitigate the effect of the uncertainty on such information. For instance, prior knowledge regarding the overshoot, the period between damped oscillations and settling time may be useful to constrain the possible locations of the eigenvalues of the discrete‐time model. Then, they show how to map the prior information onto LMI regions and, when the obtaining regions are non‐convex, to obtain convex approximations. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the relaxation process toward the equilibrium regime of saltation transport in the context of nonuniform conditions. Relaxation phenomena can be described in terms of a characteristic length scale that measures the distance for the particle flux to adapt to a spatial change in flow or boundary conditions. We conducted wind tunnel experiments to document the influence of the upwind mass flux on the relaxation process. For zero upwind mass flux conditions, the relaxation process is monotone and the relaxation length is independent of the wind strength. In contrast, for nonzero upwind flux conditions (obtained by releasing particles in the flow from a finite height), the relaxation process is nonmonotone and is well captured by damped harmonic oscillations. Importantly, the relaxation length increases with increasing air flow velocity but is almost insensitive to the magnitude of the upwind flux. Our experimental outcomes clearly indicate that the relaxation of far from equilibrium transport regimes strongly deviates from a simple exponential behavior. [ABSTRACT FROM AUTHOR]

When considering a new vaccine programme or modifying an existing one, economic cost-benefit analysis, underpinned by predictive epidemiological modelling, is a key component. This analysis is intimately linked to the willingness to pay for additional QALYs (quality-adjusted life-years) gained; currently in England and Wales a health programme is economically viable if the cost per QALY gained is less than £ 20,000, and models are often used to assess if a vaccine programme is likely to fall below this threshold cost. Before a programme begins, infection levels are generally high and therefore vaccination may be expected to have substantial effects and therefore will often be economically viable. However, once a programme is established, and infection rates are lower, it might be expected that a re-evaluation of the programme (using current incidence information) will show it to be less cost-effective. This is the scenario we examine here with analytical tools and simple ODE models. Surprisingly we show that in most cases the benefits from maintaining an existing vaccination programme are at least equal to those of starting the programme initially, and in the majority of scenarios the differences between the two are minimal. In practical terms, this is an extremely helpful finding, allowing us to assert that the action of immunising individuals does not de-value the vaccination programme. [ABSTRACT FROM AUTHOR]

The input admittance of a converter, connected to other dynamic subsystems, is a useful tool to investigate whether poorly damped oscillations or even unstable conditions might occur at certain frequencies. This is of interest in applications employing the modular multilevel converter (MMC), where the internal dynamics of the converter and the increased number of control loops greatly affect the MMC's dynamic behaviour, compared to other types of converters. In this study, the dc‐side input admittance of the direct‐voltage controlled MMC is derived analytically and verified via small‐signal perturbation in a detailed non‐linear time‐domain simulation model. The MMC's input admittance is parametrically studied and compared to the dc‐side input admittance of an equivalent two‐level converter. [ABSTRACT FROM AUTHOR]

Time evolution of water surface oscillations in surge tanks is of importance in pipeline and hydropower engineering, and is often solved graphically or numerically because the associated nonlinear second order ordinary differential equation, with a quadratic damping term, cannot be solved exactly. This research then innovates an accurate approximation based on the Lambert function, Padé approximant, and elliptic integral. Specifically, (i) the characteristic length depends on the pipe-tank geometry, the system resistance, and an unsteady factor; and the characteristic time depends on the pipe-tank geometry, the gravity, and the unsteady factor, but independent of the system resistance; (ii) the surge transit squared velocity is approximated by a Padé approximant of order [2/1], resulting in a simple approximation for the surge tank water surface oscillations in terms of an elliptic integral of the second kind; and (iii) the approximate solution accurately reproduces numerical and laboratory data thereby being applicable in practice. [ABSTRACT FROM PUBLISHER]

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The purpose of this study is to suggest a complex model of market price development for liquid assets, which is able to simulate all of the main features particular to the real price development and has a realistic financial explanation. First, the paper defines assumptions for the model construction from empirically observed processes. Then, the model is implemented in the real simulation environment. Finally, the ability of the model is checked to simulate empirically observed features, e.g. leptokurtic characteristics or skewness of the price distribution. Also, this paper newly defines and implements the resonance effect. FFT analysis is used to support oscillation processes. Finally, selected markets are provided with parameter optimisation of the model based on empirical observations. It was found that the model built under the previously mentioned assumptions was able to explain empirically observed effects that reversely support the correctness of those assumptions. The practical value of the constructed model can be found in many areas, including risk management and asset valuation. [ABSTRACT FROM PUBLISHER]

Technology has allowed obtaining experimental data faster and easier through the use of electronic devices that are part of our everyday life, which makes physical experiments more dynamical and even more accurate as compared to traditional measurement methods. This paper presents the results and the analysis of measurements of the moment of inertia of clapboard. The experiment was filmed with a smartphone and the data was analyzed by the free software Tracker. The function that describes the damped oscillation had its own parameters set by the Tracker and the Qtiplot softwares, in order to compare both of them. Comparing the calculations based on the measured parameters with the results from the programs, it is concluded that the Tracker is a platform of study with many features which allows more precise adjustment functions for the data analysis. [ABSTRACT FROM AUTHOR]