Amplitude Response Functions Research Articles

Phase and amplitude responses for delay equationsusing harmonic balance.

Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations(DDEs). Motivated by the success of phase-amplitude reductions for ordinary differential equationswith limit cycle oscillations, there is now a growing interest in the development of analogous approaches for DDEs to understand their response to external forcing. When combined with Floquet theory, the fundamental quantities for this reduction are phase and amplitude response functions. Here, we develop a framework for their construction that utilizes the method of harmonic balance.

Research on the conceptual design and performance analysis of a 10 MW SPIC concept floating wind turbine foundation in intermediate water depth

The sea area in China demands high requirements for water depth adaptability, stability, structural integrity, dynamic response characteristics, and economic performance of large-scale floating wind turbines (FWTs). The aim of the research is to propose the 10 megawatts (MW) SPIC concept (Semi-submersible platform with Partially Inclined Columns, SPIC for short) FWT in intermediate water depth, providing guidance for the concept design of large-scale FWT. The SPIC concept FWT incorporates partially tilted outward side columns, which effectively minimize the risk of bottom contact and significantly enhance the stability of the floating wind turbine. This is achieved by increasing the inertia moment of the waterplane without increasing the displaced water or water surface area. The 10 MW SPIC concept FWT exhibits superior performance in terms of smaller static heeling angle, motion amplitude response function, and wave force transfer function. It also features lower steel consumption and less displaced water, achieving good stability, hydrodynamic performance, and low cost. The rationality of the concept design and the accuracy of the numerical simulation process were validated in this study using experimental results. The study assessed the extreme responses of the 10 MW SPIC concept FWT in its six degrees of freedom (DOFs) under various scenarios, including power production, power production with faults, parked condition, and parked condition with faults, thus verifying the safety of the SPIC concept.

Higgs-like modes in two-dimensional spatially indirect exciton condensates

Higgs-like modes in condensed-matter physics have drawn attention because of analogies to the Higgs bosons of particle physics. Here we use a microscopic time-dependent mean-field theory to study the collective mode spectra of two-dimensional spatially indirect exciton (electron-hole pair) condensates, focusing on the Higgs-like modes, i.e., those that have a large weight in electron-hole pair amplitude response functions. We find that in the low exciton density (Bose-Einstein condensate) limit, the dominant Higgs-like modes of spatially indirect exciton condensates correspond to adding electron-hole pairs that are orthogonal to the condensed pair state. We comment on the previously studied Higgs-like collective excitations of superconductors in light of this finding.

Effect of functionalized multi-wall carbon nanotubes/Biresin CR82 epoxy nanocomposite on vibration attenuation of aluminum plate

This article focused on further investigation of passive vibration damping of a cantilever plate using carbon nanotube/epoxy nanocomposite. A damping ratio depends on many factors, for example carbon nanotube content, type of carbon nanotubes, and frequency, so the epoxy composite reinforced with 0.2 wt. % multi-wall carbon nanotubes has been used with structural damping. Dynamic analysis for an aluminum cantilever plate has been studied to determine the effect of the epoxy nanocomposite material on the plate vibration. The main goal of the study was to minimize the frequency response function amplitude and shift the resonant frequency of the plate as high as possible, especially for the fundamental frequency. An finite element model exhibited an increase in the resonant frequency by 10.6% and 1.2% in addition to a reduction in the frequency response function amplitude by 79.5% and 43.26% at the first and second bending modes, respectively, when using 0.2 wt. % multi-wall carbon nanotubes/epoxy circular patches at an optimal position compared with the bare plate. In case of using a stiffener below the plate, the results exposed an increase in resonant frequency by 154.6% and 181.7%, whereas the frequency response function amplitude showed reduction by 95.9% and 98.2% at the first and second bending modes, respectively, when using three stiffeners of multi-wall carbon nanotubes/epoxy nanocomposite with the same mass of circular patches compared also with the bare plate.

Global phase-amplitude description of oscillatory dynamics via the parameterization method.

In this paper, we use the parameterization method to provide a complete description of the dynamics of an n-dimensional oscillator beyond the classical phase reduction. The parameterization method allows us, via efficient algorithms, to obtain a parameterization of the attracting invariant manifold of the limit cycle in terms of the phase-amplitude variables. The method has several advantages. It provides analytically a Fourier-Taylor expansion of the parameterization up to any order, as well as a simplification of the dynamics that allows for a numerical globalization of the manifolds. Thus, one can obtain the local and global isochrons and isostables, including the slow attracting manifold, up to high accuracy, which offer a geometrical portrait of the oscillatory dynamics. Furthermore, it provides straightforwardly the infinitesimal phase and amplitude response functions, that is, the extended infinitesimal phase and amplitude response curves, which monitor the phase and amplitude shifts beyond the asymptotic state. Thus, the methodology presented yields an accurate description of the phase dynamics for perturbations not restricted to the limit cycle but to its attracting invariant manifold. Finally, we explore some strategies to reduce the dimension of the dynamics, including the reduction of the dynamics to the slow stable submanifold. We illustrate our methods by applying them to different three-dimensional single neuron and neural population models in neuroscience.

CEVAP YÜZEYİ YAKLAŞIMI İLE TAŞIT KOLTUĞU SONLU ELEMAN MODELİNİN GÜNCELLENMESİ

Ana sanayi firmaları üretimini talep ettikleri taşıt koltuklarının belirli şartnamelere uygun olmasını isterler. İmalatçı firma bu durumda koltuğun prototipini üretip birtakım değiştirme ve iyileştirmelerle teknik şartları sağlamaya çalışabilir. Fakat bu yol pahalı ve zaman alıcıdır. Bu durumda alternatif yöntem koltuğun sonlu eleman modelini geliştirmek ve üzerinde parametrik çalıştırmalar gerçekleştirmektir. Bu çalışmada öncelikle bir ticari araç koltuğunun iskelet aksamına eklenen sünger, kılıf, sırt tahtası gibi katmanların koltuğun ileri-geri ve yanal doğrultudaki modal parametrelere etkisi deneysel olarak incelenmiştir. Buradan elde edilen sonuçlara göre koltuk iskeleti sonlu eleman modeline katmanlar çeşitli kütle ve katılık parametreleriyle eklenmiştir. Daha sonra sonlu eleman modelinin gerçek koltuk modeliyle uyumlu olması için bu parametrelerin uygun değerleri cevap yüzeyi yaklaşımı ile belirlenmiştir. Ayrıca bu yöntemle, ilgili katmanların hangilerinin daha etkili olduğu da görülmüştür. Sonuç olarak, sonlu eleman modeli ile elde edilen temel frekansların her iki doğrultu için deneysel frekanslarla uyumlu olduğu, özellikle ileri-geri harekette frekans cevabı fonksiyonu genliklerinin de birbirine oldukça yakın olduğu görülmüştür.

Phase-amplitude dynamics in terms of extended response functions: Invariant curves and arnold tongues

Phase response curves (PRCs) have been extensively used to control the phase of oscillators under perturbations. Their main advantage is the reduction of the whole model dynamics to a single variable (phase) dynamics. However, in some adverse situations (strong inputs, high-frequency stimuli, weak convergence,...), the phase reduction does not provide enough information and, therefore, PRC lose predictive power. To overcome this shortcoming, in the last decade, new contributions have appeared that allow to reduce the system dynamics to the phase plus some transversal variable that controls the deviations from the asymptotic behaviour. We call this setting extended response functions. In particular, we single out the phase response function (PRF, a generalization of the PRC) and the amplitude response function (ARF) that account for the above-mentioned deviations from the oscillating attractor. It has been shown that in adverse situations, the PRC misestimate the phase dynamics whereas the PRF-ARF system provides accurate enough predictions. In this paper, we address the problem of studying the dynamics of the PRF-ARF systems under periodic pulsatile stimuli. This paradigm leads to a two-dimensional discrete dynamical system that we call 2D entrainment map. By using advanced methods to study invariant manifolds and the dynamics inside them, we construct an analytico-numerical method to track the invariant curves induced by the stimulus as two crucial parameters of the system increase (the strength of the input and its frequency). Our methodology also incorporates the computation of Arnold tongues associated to the 2D entrainment map. We apply the method developed to study inner dynamics of the invariant curves of a canonical type II oscillator model. We further compare the Arnold tongues of the 2D map with those obtained with the map induced only by the PRC, which give already noticeable differences. We also observe (via simulations) how high-frequency or strong enough stimuli break up the oscillatory dynamics and lead to phase-locking, which is well captured by the 2D entrainment map.

A Geometric Approach to Phase Response Curves and Its Numerical Computation Through the Parameterization Method

The Phase Response Curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the limit cycle. In this paper we present a new approach to PRCs based on the parameterization method. The underlying idea relies on the construction of a periodic system whose corresponding stroboscopic map has an invariant curve. We demonstrate the relationship between the internal dynamics of this invariant curve and the PRC, which yields a method to numerically compute the PRCs. Moreover, we link the existence properties of this invariant curve as the amplitude of the perturbation is increased with changes in the PRC waveform and with the geometry of isochrons. The invariant curve and its dynamics will be computed by means of the parameterization method consisting of solving an invariance equation. We show that the method to compute the PRC can be extended beyond the breakdown of the curve by means of introducing a modified invariance equation. The method also computes the amplitude response functions (ARCs) which provide information on the displacement away from the oscillator due to the effects of the perturbation. Finally, we apply the method to several classical models in neuroscience to illustrate how the results herein extend the framework of computation and interpretation of the PRC and ARC for perturbations of large amplitude and not necessarily pulsatile.

Passive and Active Vibration Isolation Methods in Discrete Mechatronic Systems

Piezoelectric actuators are more and more common in many different technical and precision industries. Mechatronic systems which combine them with mechanical models and steering recently are used in plenty practical applications. In this paper, discrete mechatronic systems have been compared relating to known passive vibration isolation method and active that has been additionally introduced to considered systems. Requirements for the systems have been given in form of poles and zeros. Basing on amplitude response functions and dynamical flexibilities, damping performance in both cases has been investigated.

The Response of the Dines Anemometer to Gusts and Comparisons with Cup Anemometers

Abstract The Dines pressure tube anemometer was the primary wind speed recording instrument used in Australia until it was replaced by Synchrotac cup anemometers in the 1990s. Simultaneous observations of the gust wind speeds recorded using both types of anemometers during tropical cyclones have, however, raised questions about the equivalency of the gust wind speeds recorded using the two instruments. An experimental study of the response of both versions of the Dines anemometer used in Australia shows that the response of the anemometer is dominated by the motion of the float manometer used to record the wind speed. The amplitude response function shows the presence of two resonant peaks, with the amplitude and frequency of the peaks depending on the instrument version and the mean wind speed. Comparison of the gust wind speeds recorded using Dines and Synchrotac anemometers using random process and linear system theory shows that, on average, the low-speed Dines anemometer records values 2%–5% higher than those recorded using a Synchrotac anemometer under the same conditions, while the high-speed Dines anemometer records values 3%–7% higher, depending on the mean wind speed and turbulence intensity. These differences are exacerbated with the adoption of the WMO-recommended 3-s moving average gust wind speed when reporting the Synchrotac anemometer gust wind speeds, rising to 6%–12% and 11%–19% for low- and high-speed Dines anemometers, respectively. These results are consistent with both field observations and an independent extreme value analysis of simultaneously observed gust wind speeds at seven sites in northern Australia.

Phase-Amplitude Response Functions for Transient-State Stimuli

The phase response curve (PRC) is a powerful tool to study the effect of a perturbation on the phase of an oscillator, assuming that all the dynamics can be explained by the phase variable. However, factors like the rate of convergence to the oscillator, strong forcing or high stimulation frequency may invalidate the above assumption and raise the question of how is the phase variation away from an attractor. The concept of isochrons turns out to be crucial to answer this question; from it, we have built up Phase Response Functions (PRF) and, in the present paper, we complete the extension of advancement functions to the transient states by defining the Amplitude Response Function (ARF) to control changes in the transversal variables. Based on the knowledge of both the PRF and the ARF, we study the case of a pulse-train stimulus, and compare the predictions given by the PRC-approach (a 1D map) to those given by the PRF-ARF-approach (a 2D map); we observe differences up to two orders of magnitude in favor of the 2D predictions, especially when the stimulation frequency is high or the strength of the stimulus is large. We also explore the role of hyperbolicity of the limit cycle as well as geometric aspects of the isochrons. Summing up, we aim at enlightening the contribution of transient effects in predicting the phase response and showing the limits of the phase reduction approach to prevent from falling into wrong predictions in synchronization problems.List of AbbreviationsPRC phase response curve, phase resetting curve.PRF phase response function.ARF amplitude response function.

Neighborhood size and spatial scale in raster-based slope calculations

Raster-based slope estimation is routine in GIS. Like many other terrain attributes, the slope at a location is determined from elevations of surrounding cells. This spatial extent – ‘neighborhood size’ – is often treated as the ‘spatial scale’ of the calculation. In fact, neighborhood size and spatial scale are two connected yet different concepts, but few studies have investigated the relationship between them. The distinction is important because neighborhood size is under user control whereas spatial scale is merely implicit in the computational method. This article attempts to clarify and provide a more precise meaning of the two terms by considering slope operators from the standpoint of the frequency (or wavenumber) domain. This article derives analytical expressions for the amplitude response functions of four popular slope estimators. These are used to characterize the individual methods and also to show that the neighborhood size and spatial scale of a slope calculation are not numerically the same. In fact, because there is no single spatial scale that can be unambiguously associated with a given neighborhood size, neighborhood size cannot be an adequate indicator of spatial scale. Furthermore, this article shows that different indices of ‘scale’ yield different impressions about the action of a slope estimator and its response to changing neighborhood size. Therefore, it is necessary to examine the amplitude response function when investigating the spatial scale. The article also provides guidance for GIS practitioners when selecting a slope estimation method.

Aging of human short-wave cone pathways.

The retinal image is sampled concurrently, and largely independently, by three physiologically and anatomically distinct pathways, each with separate ON and OFF subdivisions. The retinal circuitry giving rise to an ON pathway receiving input from the short-wave-sensitive (S) cones is well understood, but the S-cone OFF circuitry is more controversial. Here, we characterize the temporal properties of putative S-cone ON and OFF pathways in younger and older observers by measuring thresholds for stimuli that produce increases or decreases in S-cone stimulation, while the middle- and long-wave-sensitive cones are unmodulated. We characterize the data in terms of an impulse response function, the theoretical response to a flash of infinitely short duration, from which the response to any temporally varying stimulus may be predicted. Results show that the S-cone response to increments is faster than to decrements, but this difference is significantly greater for older individuals. The impulse response function amplitudes for increment and decrement responses are highly correlated across individuals, whereas the timing is not. This strongly suggests that the amplitude is controlled by neural circuitry that is common to S-cone ON and OFF responses (photoreceptors), whereas the timing is controlled by separate postreceptoral pathways. The slower response of the putative OFF pathway is ascribed to different retinal circuitry, possibly attributable to a sign-inverting amacrine cell not present in the ON pathway. It is significant that this pathway is affected selectively in the elderly by becoming slower, whereas the temporal properties of the S-cone ON response are stable across the life span of an individual.

PARAMETRIC AND EXTERNAL RESONANCES IN KINEMATICALLY AND EXTERNALLY EXCITED NONLINEAR SPRING PENDULUM

A weakly nonlinear 2-DOF system, parametrically and externally excited, is studied. An intensive energy transfer between modes of vibrations is discovered. Multiple scales method is used for recognizing resonances occurring in the system. The amplitude response functions for some chosen cases of resonances are obtained and studied. Many of the engineering systems can be investigated in the presented way.

Limits of 2D-TCA in detecting BOLD responses to epileptic activity

Two-dimensional temporal clustering analysis (2D-TCA) is a relatively new functional MRI (fMRI) based technique that breaks blood oxygen level dependent activity into separate components based on timing and has shown potential for localizing epileptic activity independently of electroencephalography (EEG). 2D-TCA has only been applied to detect epileptic activity in a few studies and its limits in detecting activity of various forms (i.e. activation size, amplitude, and frequency) have not been investigated. This study evaluated 2D-TCA's ability to detect various forms of both simulated epileptic activity and EEG-fMRI activity detected in patients. When applied to simulated data, 2D-TCA consistently detected activity in 6min runs containing 5 spikes/run, 10 spikes/run, and one 5s long event with hemodynamic response function amplitudes of at least 1.5%, 1.25%, and 1% above baseline respectively. When applied to patient data, while detection of interictal spikes was inconsistent, 2D-TCA consistently produced results similar to those obtained by EEG-fMRI when at least 2 prolonged interictal events (a few seconds each) occurred during the run. However, even for such cases it was determined that 2D-TCA can only be used to validate localization by other means or to create hypotheses as to where activity may occur, as it also detects changes not caused by epileptic activity.

The effect of endcap electrode holes on the resonant ejection from an ion trap

The presence of endcap holes greatly influences the performance of an ion trap mass spectrometer. Optimizing the shape and size of the holes may significantly improve ion trap performance. The field contours have been numerically simulated at varying hole sizes and the potentials were numerically fitted. The presence of holes in the electrodes adds higher order negative components to the field inside the trap. The absolute values of the field components were found to increase with increasing hole size. The fitted potentials were then used to reexamine the amplitude response functions. The addition of negative higher order field components produces up to four jump points in the amplitude response function. The new jump points may produce multiple jump phenomena in forward scans as well as a jump condition in the reverse scan mode that has not previously been considered. The shape of the amplitude response function is dependent on the hole size and the amplitude of the dipole excitation waveform at constant buffer gas pressure. The shape of the function has interesting implications for the resonance ejection process. This work provides new insights into the resonance excitation process in nonlinear ion traps.

Modal analysis of a small ship sea keeping trial

Data from sea keeping trials of a Scottish trawler are analyzed. The trawler sailed an octagonal course, each leg took over 20 minutes and data recorded twice a second. The natural frequencies of vibration for each of the six rigid body modes are estimated from the heave, surge, sway, pitch, yaw and roll time series. The time series are investigated for evidence of non-linearity. A time domain model is fitted to a roll time series, and second order amplitude response functions are then obtained using autoregressive estimators.

Generation of electromagnetic radiation in a vircator system with controlled feedback

The electrodynamic structure of a vircator with controlled feedback is numerically simulated and parametrically optimized. A numerical method for the synthesis of a complicated electrodynamic structure is proposed. The amplitude response functions of the electrodynamic structure are obtained for various feedbacks. The results of the numerical simulation are compared with the experimental data.

Probing collective dynamics of active particles using modulation force spectroscopy

In this letter, we report a method of measuring the dynamic viscosity of self-propelled active particles using an intensity-modulated optical tweezer. We have used a 6μm trapped polystyrene bead suspended in a bath of motile bacterial cells as a probe. The response function amplitude of the oscillatory bead directly measures the dynamics of the spatiotemporal structure of the motile particles. We find that unlike passive systems, the viscosity is defined by distributions of response function amplitudes that represent the long-range active temporal structures. Appropriate Langevin equations are set up that capture all these essential features.

Investigation of diffraction gratings with the use of a differential heterodyne microscope

A theory of image formation in a scanning differential heterodyne microscope is developed using the results of observations of a metallized periodic structure with a rectangular profile. The phase and amplitude response functions are calculated for TE and TM polarizations. It is demonstrated that the width of grating elements can be measured with a superresolution. The experimental phase and amplitude responses from a metallized grating with a trapezoidal profile are obtained and compared with the results of theoretical calculations.