Non-negligible Amplitude Research Articles

Comparison of two nonlinear formulations of the Maxwell-Cattaneo equation in heat pulse transmission

The nonlinear terms resulting from temperature dependence of thermal conductivity and relaxation time must be considered when studying systems undergoing very short thermal pulses with non-negligible amplitude of the temperature perturbation. Two nonlinear formulations of the Maxwell-Cattaneo-Vernotte equation for thermal transport with relaxation effects are introduced. A comparison of the consequences of these two different nonlinear Cattaneo type equations on thermal pulse propagation is obtained and discussed. The differences in the corresponding velocities and in the corresponding heights of the perturbation peaks turn out to be significant and could be experimentally detected.

Optimal Design of a Compound Magnetic Shielding Based on Fe-Based Nanocrystalline Alloy

The magnetic field inside the analyzed double-stator high-temperature-superconducting machine (DS-HTSM) has the characteristics of rich harmonics and non-negligible amplitude, which will seriously reduce the critical current <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_c</i> of HTS-excitation coil. Therefore, a new compound magnetic shielding (CMS) is proposed in this paper, which is composed of a copper shield layer and a combined flux diverters (FDs) including the silicon steel sheet (SSS) FD and the Fe-based nanocrystalline alloy (FNA) FD. The key is that the iron loss of SSS FD located in the inner Dewar can be reduced due to the flux pre-diversion of the FNA FD on the outside. In addition, the FEA model based on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> formula for HTS-excitation coil is built, based on which the optimal design of proposed CMS is conducted. The results show that the critical current <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_c</i> of HTS-excitation coil in the analyzed DS-HTSM can be improved by 36% after using the proposed CMS.

Heartbeat Detection in Gyrocardiography Signals without Concurrent ECG Tracings.

A heartbeat generates tiny mechanical vibrations, mainly due to the opening and closing of heart valves. These vibrations can be recorded by accelerometers and gyroscopes applied on a subject's chest. In particular, the local 3D linear accelerations and 3D angular velocities of the chest wall are referred to as seismocardiograms (SCG) and gyrocardiograms (GCG), respectively. These signals usually exhibit a low signal-to-noise ratio, as well as non-negligible amplitude and morphological changes due to changes in posture and the sensors' location, respiratory activity, as well as other sources of intra-subject and inter-subject variability. These factors make heartbeat detection a complex task; therefore, a reference electrocardiogram (ECG) lead is usually acquired in SCG and GCG studies to ensure correct localization of heartbeats. Recently, a template matching technique based on cross correlation has proven to be particularly effective in recognizing individual heartbeats in SCG signals. This study aims to verify the performance of this technique when applied on GCG signals. Tests were conducted on a public database consisting of SCG, GCG, and ECG signals recorded synchronously on 100 patients with valvular heart diseases. The results show that the template matching technique identified heartbeats in GCG signals with a sensitivity and positive predictive value (PPV) of 87% and 92%, respectively. Regression, correlation, and Bland-Altman analyses carried out on inter-beat intervals obtained from GCG and ECG (assumed as reference) reported a slope of 0.995, an intercept of 4.06 ms (R2 > 0.99), a Pearson's correlation coefficient of 0.9993, and limits of agreement of about ±13 ms with a negligible bias. A comparison with the results of a previous study obtained on SCG signals from the same database revealed that GCG enabled effective cardiac monitoring in significantly more patients than SCG (95 vs. 77). This result suggests that GCG could ensure more robust and reliable cardiac monitoring in patients with heart diseases with respect to SCG.

Analytical formulation for estimating power low frequency oscillations between two overhead lines operating at different frequencies

This paper derives an analytical formulation to estimate the period and the amplitude of power low frequency oscillations originated by the mutual coupling of two power systems operating at two slightly different frequencies. This is the typical case of the power system restoration tests, in which the restoration backbone involves two overhead lines installed on the same tower. These oscillations have been detected during several real-world power system restoration tests with a non-negligible amplitude. In some cases, the active power exchanged between the two systems could damage the control and protection equipment of the elements involved in the test, leading to the failure of the restoration test itself. For these reasons, the analytical prediction of the period and the magnitude of these oscillations could constitute a useful and reliable tool for the planning and the simulation of the restoration tests.

Impact of Nearby Lightning Strikes on Wireless Power Transfer Ground Assembly

Direct hits from Lightning Strikes (LS) are commonly recognized as dangerous events for open air installations, but also the much more frequent case of LS hitting nearby can cause overvoltage potentially damaging connected circuits, if not correctly protected. In this paper, adopting a hybrid formulation, we simulate the voltage induced at the terminals of a Wireless Power Transfer (WPT) ground coil by a LS hitting the ground nearby the system. The induced overvoltage has a non-negligible amplitude, depending on the distance of the hit, the tortuosity of the lightning channel, and the inclination of the coil with respect to the ground plane.

Reflected waves and quantum gravity

In the context of canonical quantum gravity, we consider the effects of a nonstandard expression for the gravitational wave function on the evolution of inflationary perturbations. Such an expression and its effects may be generated by a sudden variation in the (nearly constant) inflaton potential. The resulting primordial spectra, up to the leading order, are affected in the short and in the long wavelength regime, where an oscillatory behavior with a non-negligible amplitude is superimposed on the standard semiclassical result. Moreover, a novel, nonperturbative, approach is used to study the evolution. Finally, a simplified application is fully illustrated and commented.

Impact of spot reduction on the effectiveness of rescanning in pencil beam scanned proton therapy for mobile tumours

Objective. In pencil beam scanning proton therapy, individually calculated and positioned proton pencil beams, also referred to as ‘spots’, are used to achieve a highly conformal dose distributions to the target. Recent work has shown that this number of spots can be substantially reduced, resulting in shorter delivery times without compromising dosimetric plan quality. However, the sensitivity of spot-reduced plans to tumour motion is unclear. Although previous work has shown that spot-reduced plans are slightly more sensitive to small positioning inaccuracies of the individual pencil beams, the resulting shorter delivery times may allow for more rescanning. The aim of this study was to assess the impact of tumour motion and the effectiveness of 3D volumetric rescanning for spot-reduced treatment plans. Approach. Three liver and two lung cancer patients with non-negligible motion amplitudes were analysed. Conventional and probabilistic internal target volume definitions were used for planning considering single or multiple breathing cycles respectively. For each patient, one clinical and two spot-reduced treatment plans were created using identical field geometries. 4D dynamic dose calculations were then performed and resulting target coverage (V95%), dose homogeneity (D5%–D95%) and hot spots (D2%) evaluated for 1–25 rescans. Main results. Over all patients investigated, spot reduction reduced the number of spots by 91% in comparison to the clinical plan, reducing field delivery times by approximately 50%. This reduction, together with the substantially increased dose per spot resulting from the spot reduction process, allowed for more rescans in the same amount of time as for clinical plans and typically improved dosimetric parameters, in some cases to values better than the reference static (3D calculated) plans. However, spot-reduced plans had an increased possibility of interference with the breathing cycle, especially for simulations of perfectly repeatable breathing. Significance. For the patients analysed in this study, spot-reduced plans were found to be a valuable option to increase the efficiency of 3D volumetric rescanning for motion mitigation, if attention is paid to possible interference patterns.

The nonlinear evolution of internal tides. Part 1: the superharmonic cascade

In non-uniform stratification, horizontally propagating internal waves with the vertical structure of a single mode self-interact to excite superharmonics. Baker &amp; Sutherland (J. Fluid Mech., vol. 891, 2020, R1) showed that a vertical mode-1 parent wave of sufficiently small amplitude dominantly excites a vertical mode-1 superharmonic with double the horizontal wavenumber. Through theory, assuming a parent wave of sufficiently small amplitude, they showed that the superharmonics grew and decayed periodically due to the parent forcing frequency being off-resonant with the natural frequency of the superharmonic. Here, we extend this theory to allow for larger parent wave amplitudes and/or stronger resonant forcing, as would occur at lower latitudes, where the influence of background rotation is small. The resulting coupled system of nonlinear ordinary differential equations is shown to well predict the evolution of the internal tide as determined in fully nonlinear numerical simulations. With strong nonlinear forcing, successive superharmonics grow to non-negligible amplitudes in what we call the ‘superharmonic cascade’. The phase relationship between the superharmonics is such that when superimposed, the internal tide transforms into a solitary wave train, consistent with the predictions of well-established shallow-water models, particularly that of the Ostrovsky equation, which is an extension of the Korteweg–de Vries equation accounting for background rotation. This work thus gives new insight into internal solitary wave generation. The model equations have less restrictive assumptions than models based upon shallow-water theory, and because they are quickly solved, these provide a potentially powerful new tool to examine the nonlinear evolution of the internal tide.

Numerical Investigation of Unsteady Combustor Turbine Interaction for Flexible Power Generation

AbstractWith the growing importance of regenerative power generation and especially of a hydrogen-based economy, the full potential of gas turbines of the smaller output class (&amp;lt;10 MW) can be ideally exploited to provide peak coverage of the energy need whilst stabilizing the electric grids in the mid- and low-voltage range. Such machines can be typically started in a relatively short time (similarly to aero engines) and are capable, at the same time, of delivering dispatchable power-on-demand. A safe, stable and profitable operation under highly unsteady conditions poses renewed challenges for an optimal thermal management (especially in the HP stages) as well as control and surveillance of the machines. The understanding and hence predictability of the propagation of the temperature inhomogeneities originating at the combustor outlet remains hence a primary objective of current research, as persistent distortion patterns could be adopted at the turbine exhaust as diagnostic indications of a malfunction of the combustor, for example. In the present study, low-frequency disturbances introduced by a periodic load variation have been simulated and superimposed to the inhomogeneous, unsteady flow entering a three-stage, high-pressure industrial gas turbine fed by a can-type combustion chamber comprising six silo-burners. The effects of the unsteadiness realized at the combustor exit have been investigated by means of Detached Eddy Simulations, whereby a density-based solution approach with detailed thermodynamics has been employed. The periodic disturbances at the turbine inlet have been obtained by means of an artificially generated, unsteady field, resulting from a two-dimensional snapshot of the flow field at the combustor exit. Also, a combustor failure has been mimicked by reducing (respectively increasing) the mean temperature in some of the turbine inlet regions corresponding to the outlet of two burners. The propagation and amplitude changes of temperature fluctuations have been analyzed in the frequency domain. Tracking of the temperature fluctuations' maxima at the lowest frequencies revealed characteristic migration patterns indicating that the corresponding fluctuations persist with a non-negligible amplitude up to the last rows. A distinct footprint could also be observed at the same locations when a combustor failure was simulated, showing that, in principle, the early detection of combustor failures is indeed possible.

A compressed data approach for image-domain least-squares migration

We consider the problem of image-domain least-squares migration (LSM) based on efficiently constructing the Hessian matrix with sparse beam data. Specifically, we use the ultra-wide-band phase space beam summation method, in which beams are used as local basis functions to represent scattered data collected at the surface. The beam domain data are sparse. One can identify seismic events with significant contributions so that only beams with nonnegligible amplitudes need to be used to image the subsurface. In addition, due to the beams’ spectral localization, only beams that pass near an imaging point need to be taken into account. These two properties reduce the computational complexity of computing the Hessian matrix — an essential ingredient for LSM. As a result, we can efficiently construct the Hessian matrix based on analyzing the sparse beam domain data.

Nonlinear damping in energy harvesters driven by colored noise

We study the performance of an electromechanical oscillator as an energy harvester driven byfinite-bandwidth random vibrations under the influence of both a stiffness-type nonlinearity and anonlinear damping that has recently been found to be relevant in the dynamics of submicrometermechanical resonators. The device was numerically simulated and its performance assessed by meansof the net electrical power and the efficiency of the conversion of the supplied power by the noiseinto electrical power for exponentially correlated noise. We tune the parameters to achieve a goodperformance of the device for non-negligible amplitudes of the nonlinearity of the oscillator and thedamping.

Soft wall resistance as a necessary condition to validate numerical simulations in thermoacoustic heat transfer within closed cavities

The propagation of confined acoustic waves induced by thermal excitation has been extensively examined in the literature using theoretical, numerical and experimental methods. Despite their ability to predict several important trends, theoretical and numerical studies have not been able to reproduce the long time pressure field behavior observed in experiments. We propose, in the present paper, that this discrepancy arises from the boundary condition models employed in these studies, which assumes all solid walls are hard. In other words, acoustic waves are perfectly reflected upon these solid walls. Considering acoustical resistance alone, a single parameter soft wall model that takes into account the small but non-negligible wave amplitude wall reflection losses is proposed. Numerical simulations of the Navier-Stokes equations are then performed in such a way as to reproduce four different and well known experimental studies. Comparisons between numerical and experimental results reveal that a short time agreement is possible in most cases because reflection losses did not yet have enough time to accumulate. A good asymptotic agreement, i.e. for long times, however, exists only when wall acoustical resistance is not neglected. Since acoustic reactance was neglected in this model to facilitate parameter estimation, phase errors are still present.

Harnessing the Kelvin–Helmholtz instability: feedback stabilization of an inviscid vortex sheet

In this investigation, we use a simple model of the dynamics of an inviscid vortex sheet given by the Birkhoff–Rott equation to obtain fundamental insights about the potential for stabilization of shear layers using feedback control. As actuation, we consider two arrays of point sinks/sources located a certain distance above and below the vortex sheet and subject to the constraint that their mass fluxes separately add up to zero. First, we demonstrate using analytical computations that the Birkhoff–Rott equation linearized around the flat-sheet configuration is in fact controllable when the number of actuator pairs is sufficiently large relative to the number of discrete degrees of freedom present in the system, a result valid for generic actuator locations. Next, we design a state-based linear-quadratic regulator stabilization strategy, where the key difficulty is the numerical solution of the Riccati equation in the presence of severe ill-conditioning resulting from the properties of the Birkhoff–Rott equation and the chosen form of actuation, an issue that is overcome by performing computations with a suitably increased arithmetic precision. Analysis of the linear closed-loop system reveals exponential decay of the perturbation energy and the corresponding actuation energy in all cases. Computations performed for the nonlinear closed-loop system demonstrate that initial perturbations of non-negligible amplitude can be effectively stabilized when a sufficient number of actuators is used. We also thoroughly analyse the sensitivity of the closed-loop stabilization strategies to the variation of a number of key parameters. Subject to the known limitations of inviscid vortex models, our findings indicate that, in principle, it may be possible to stabilize shear layers for relatively large initial perturbations, provided that the actuation has sufficiently many degrees of freedom.

Transmission-error frequency-domain-behavior of failing gears

Abstract Failing gear teeth, either by working-surface-damage (pitting, spalling, scuffing, etc.) or by bending fatigue, causes tooth-to-tooth variations in the loaded tooth working surfaces. Such variations cause changes (generally increases) in the non-tooth-meshing rotational-harmonic amplitudes of the transmission-error contribution from the affected gear. Simple models of missing working-surface material caused by damage are used to show where transmission-error rotational-harmonic spectrum changes will take place. Bending fatigue damage is shown to initially cause maximum changes in rotational-harmonic amplitudes well below the tooth-meshing fundamental harmonic, whereas small pits are shown to cause changes in higher-frequency rotational-harmonic amplitudes. Good agreement is shown between an experimentally obtained rotational-harmonic spectrum caused by tooth-surface damage and that predicted from damage measured on the failing teeth. Substantial increases in high-frequency rotational-harmonic amplitudes are shown to be expected from gear teeth undergoing significant plastic deformation in late stages of bending-fatigue failure. Accurate assessment of damage contributions using before-damage non-negligible rotational-harmonic amplitudes (sideband harmonics, etc.) are shown to suggest use of complex rotational-harmonic amplitudes.

Characterization of the Dynamic Behavior of Shallow Foundations with Full-Scale Dynamic Tests

AbstractThis work provides a detailed description of the full-scale experimental tests performed on the dynamic behavior of a shallow foundation under intermediate strains. A wind tower supported by the foundation was subjected to a snap-off test, i.e., it was first pulled with a cable and then suddenly released, thus inducing free oscillations of nonnegligible amplitude in the whole system. The motion induced was measured with a digital camera, seismometers, and accelerometers attached to the surrounding ground surface and to the wind tower. An innovative interpretation technique based on optimizing a few meaningful parameters obtained from the recorded time histories was required by the heterogeneity of the data collected and the accuracy needed to deduce the behavior of the foundation plinth. The analyses showed that the rotational stiffness of the foundation plinth was approximately 10 times greater than that of the base joint, which in turn was approximately one order of magnitude greater than that o...

Three-dimensional wing behaviors of a rhinoceros beetle during takeoff flights

We investigated the aerodynamic characteristics of a beetle in a takeoff flight by measuring the temporal and spatial changes in body and wing behaviors. In particular, three-dimensional trajectories and/or deformations of rigid outer wing (elytron) and highly flexible inner wing (hindwing) were measured with three high-speed cameras (at 2000 fps) and reconstructed for the analysis using a modified direct linear transform algorithm. From an inclined rod, the beetle is observed to perform a takeoff flight without the aid of legs, i.e., jumping. Although the elytron is flapped passively induced by the hindwing motion, it is found to have non-negligible flapping amplitude and angle of attack, indicating that the aerodynamic force generation by the elytron itself would be influential. Furthermore, the measured trajectories of an elytron and hindwing imply that the beetle may utilize well-known mechanisms such as a delayed stall, clapand- fling, wing-wing (elytron-hindwing) interaction, and figure-eight motion. Finally, the flexibility of a hindwing affects the heaving motion (out of the stroke plane) most significantly; i.e., the local variation of the deviation angle along the wing span is more pronounced compared to that of flapping angle and angle of attack.

Magnetic coupling constants of self-assembled Cu(II) [3×3] grids: alternative spin model from theoretical calculations.

This paper reports a theoretical analysis of the electronic structure and magnetic properties of a ferromagnetic Cu(II) [3×3] grid. A two-step strategy, combining calculations on the whole grid and on binuclear fragments, has been employed to evaluate all the magnetic interactions in the grid. The calculations confirm an S = 7/2 ground state, which is in accordance with the magnetisation versus field curve and the thermal dependence of the magnetic moment data. Only the first-neighbour coupling terms present non-negligible amplitudes, all of them in agreement with the structure and arrangement of the Cu 3d magnetic orbitals. The results indicate that the dominant interaction in the system is the antiferromagnetic coupling between the ring and the central Cu sites (J3 = J4 ≈ -31 cm(-1)). In the ring two different interactions can be distinguished, J1 = 4.6 cm(-1) and J2 = -0.1 cm(-1), in contrast to the single J model employed in the magnetic data fit. The calculated J values have been used to determine the energy level distribution of the Heisenberg magnetic states. The effective magnetic moment versus temperature plot resulting from this ab initio energy profile is in good agreement with the experimental curve and the fitting obtained with the simplified spin model, despite the differences between these two spin models. This study underlines the role that the theoretical evaluations of the coupling constants can play on the rationalisation of the magnetic properties of these complex polynuclear systems.

Obstructions to classically simulating the quantum adiabatic algorithm

We consider the adiabatic quantum algorithm for systems with no sign problem, such as the transverse field Ising model, and analyze the equilibration time for quantum Monte Carlo (QMC) on these systems. We ask: if the spectral gap is only inverse polynomially small, will equilibration methods based on slowly changing the Hamiltonian parameters in the QMC simulation succeed in a polynomial time? We show that this is not true, by constructing counter-examples. In some examples, the space of configurations where the wavefunction has non-negligible amplitude has a nontrivial fundamental group, causing the space of trajectories in imaginary time to break into disconnected components with only negligible probability outside these components. For the simplest example we give with an abelian fundamental group, QMC does not equilibrate but still solves the optimization problem. More severe effects leading to failure to solve the optimization can occur when the fundamental group is a free group on two generators. Other examples where QMC fails have a trivial fundamental group, but still use ideas from topology relating group presentations to simplicial complexes. We define gadgets to realize these Hamiltonians as the effective low-energy dynamics of a transverse field Ising model. We present some analytic results on equilibration times which may be of some independent interest in the theory of equilibration of Markov chains. Conversely, we show that a small spectral gap implies slow equilibration at low temperature for some initial conditions and for a natural choice of local QMC updates.

Obstructions to classically simulating the quantum adiabatic algorithm

We consider the adiabatic quantum algorithm for systems with ``no sign problem", such as the transverse field Ising model, and analyze the equilibration time for quantum Monte Carlo (QMC) on these systems. We ask: if the spectral gap is only inverse polynomially small, will equilibration methods based on slowly changing the Hamiltonian parameters in the QMC simulation succeed in a polynomial time? We show that this is {\it not} true, by constructing counter-examples. In some examples, the space of configurations where the wavefunction has non-negligible amplitude has a nontrivial fundamental group, causing the space of trajectories in imaginary time to break into disconnected components with only negligible probability outside these components. For the simplest example we give with an abelian fundamental group, QMC does not equilibrate but still solves the optimization problem. More severe effects leading to failure to solve the optimization can occur when the fundamental group is a free group on two generators. Other examples where QMC fails have a {\it trivial} fundamental group, but still use ideas from topology relating group presentations to simplicial complexes. We define gadgets to realize these Hamiltonians as the effective low-energy dynamics of a transverse field Ising model. We present some analytic results on equilibration times which may be of some independent interest in the theory of equilibration of Markov chains. Conversely, we show that a small spectral gap implies slow equilibration at low temperature for some initial conditions and for a natural choice of local QMC updates.

Radiometric Performance of SMOS Full Polarimetric Imaging

This work has been conducted in the framework of several projects devoted to assess the performance of the Soil Moisture and Ocean Salinity (SMOS) mission full-pol measurement mode. Since its launch in November 2009, SMOS is producing dual-polarization brightness temperature synthesized images that are yielding a high scientific return. However, these images are affected by a non-negligible spatial amplitude error, the so-called spatial bias (SB), that degrades geophysical parameter retrieval. This effect is particularly detrimental in SMOS polarimetric images where spatial bias is masking the polarimetric physical signature to a large extend. This paper presents a method to mitigate SMOS spatial bias by taking into account the co- and cross-polar antenna patterns in the image reconstruction algorithm through the, so called, full-pol G-matrix (FPG). The method is validated by producing spatial bias maps out of the comparison between SMOS full-pol images and an accurate polarimetric brightness temperature model of the ocean. This model has been provided to SMOS ESLs (Expert Support Laboratories) by LOCEAN (Laboratoire d'Oceanographie et du Climat, France) as a test bench to validate and improve SMOS Level 1 (L1) data. Finally, a radiometric performance summary table comparing spatial bias and radiometric sensitivity between this new FPG approach and SMOS current co-polar G-matrix approach (CPG) is provided. This paper presents the best quality SMOS polarimetric images, which may lead a breakthrough in the science returns of the mission.