Resonant Period Research Articles

Dynamic localization in optical and Zeeman lattices in the presence of spin-orbit coupling

The dynamic localization of a two-level atom in a periodic potential under the action of spin-orbit coupling and a weak harmonically-varying linear force is studied. We consider optical and Zeeman potentials that are either in-phase or out-of-phase in two spinor components, respectively. The expectation value for the position of the atom after one oscillation period of the linear force is recovered in authentic resonances or in pseudo-resonances. The frequencies of the linear force corresponding to authentic resonances are determined by the band structure of the periodic potential and are affected by the spin-orbit coupling. The width/dispersion of the wavepacket in authentic resonances is usually minimal. The frequencies corresponding to pseudo-resonances do not depend on the type of potential and on the strength of the spin-orbit coupling, while the evolution of excitations at the corresponding frequencies is usually accompanied by significant dispersion. Pseudo-resonances are determined by the initial phase of the linear force and by the quasi-momentum of the wavepacket. Due to the spinor nature of the system, the motion of the atom is accompanied by periodic, but not harmonic, spin oscillations. Under the action of spin-orbit coupling the oscillations of the wavepacket can be nearly completely suppressed in optical lattices. Dynamic localization in Zeeman lattices is characterized by doubling of the resonant oscillation periods due to band crossing at the boundary of the Brillouin zone. We also show that higher harmonics in the Fourier expansion of the energy band lead to effective dispersion, which can be strong enough to prevent dynamic localization of the Bloch wavepacket.

Forcing of the Atlantic Equatorial Deep Jets Derived from Observations

AbstractThe equatorial deep jets (EDJs) are a ubiquitous feature of the equatorial oceans; in the Atlantic Ocean, they are the dominant mode of interannual variability of the zonal flow at intermediate depth. On the basis of more than 10 years of moored observations of zonal velocity at 23°W, the vertically propagating EDJs are best described as superimposed oscillations of the 13th to the 23rd baroclinic modes with a dominant oscillation period for all modes of 1650 days. This period is close to the resonance period of the respective gravest equatorial basin mode for the dominant vertical modes 16 and 17. It is argued that since the equatorial basin mode is composed of linear equatorial waves, a linear reduced-gravity model can be employed for each baroclinic mode, driven by spatially homogeneous zonal forcing oscillating with the EDJ period. The fit of the model solutions to observations at 23°W yields a basinwide reconstruction of the EDJs and the associated vertical structure of their forcing. From the resulting vertical profile of mean power input and vertical energy flux on the equator, it follows that the EDJs are locally maintained over a considerable depth range, from 500 to 2500 m, with the maximum power input and vertical energy flux at 1300 m. The strong dissipation closely ties the apparent vertical propagation of energy to the vertical distribution of power input and, together with the EDJs’ prevailing downward phase propagation, requires the phase of the forcing of the EDJs to propagate downward.

Estimation of Variability Characteristics of Regional Drought during 1964–2013 in Horqin Sandy Land, China

Drought has an important influence on the hydrological cycle, ecological system, industrial and agricultural production, and social life. Based on the different time scales of characteristics of drought variability, the standardized precipitation evapotranspiration index (SPEI), a multi-timescale index with consideration of evaporation, was used in this study to estimate the spatial and temporal variability characteristics of drought. Climatic data from 15 meteorological stations across Horqin Sandy Land during 1964–2013 were used to calculate the SPEI of 1, 3, 6, and 12 months. In order to examine the relationship between droughts and other variables, 10 extreme climate indices were calculated based on the daily precipitation and maximum/mean/minimum temperature data of 15 meteorological stations, and linkages between SPEI-12 and atmosphere indices were established using by the cross wavelet transform method. The results indicated that the climate of Horqin Sandy Land had a tendency towards drought conditions, which is particularly apparent from the year 2000 onwards. During the study period, drought events were frequent in the region. Mild drought occurred in a quarter of the month, with that of moderate, severe, and extreme drought accounting for 0.11, 0.05, and 0.02 of the total months. The spatial trend of multi-timescale drought revealed that there was an increase in the severity of drought throughout Horqin Sandy Land, among which the magnitude in southern parts was larger than that of northern parts. The results also showed that the short time scale drought negatively correlated with precipitation extremes and positively correlated with temperature extremes. Furthermore, the long time scale drought (SPEI-12) was associated with atmosphere indices. Significant resonance periods were found between El Nino southern oscillation (ENSO), the East Asian summer monsoon index (EASMI), and SPEI-12.

Hydroelectromechanical modelling of a piezoelectric wave energy converter

We investigate the hydroelectromechanical-coupled dynamics of a piezoelectric wave energy converter. The converter is made of a flexible bimorph plate, clamped at its ends and forced to motion by incident ocean surface waves. The piezoceramic layers are connected in series and transform the elastic motion of the plate into useful electricity by means of the piezoelectric effect. By using a distributed-parameter analytical approach, we couple the linear piezoelectric constitutive equations for the plate with the potential-flow equations for the surface water waves. The resulting system of governing partial differential equations yields a new hydroelectromechanical dispersion relation, whose complex roots are determined with a numerical approach. The effect of the piezoelectric coupling in the hydroelastic domain generates a system of short- and long-crested weakly damped progressive waves travelling along the plate. We show that the short-crested flexural wave component gives a dominant contribution to the generated power. We determine the hydroelectromechanical resonant periods of the device, at which the power output is significant.

An innovative procedure for monitoring the change in soil seismic response by InSAR data: application to the Mexico City subsidence

We developed an empirical procedure to evaluate the effect of the ground subsidence on the spatial and temporal seismic response of soils. The proposed method exploits the capabilities of the spaceborne SAR Interferometry technique to detect and map the ground subsidence with unprecedented spatial and temporal coverage. The information provided by satellites is combined with a-priori geological/geotechnical information to assess the soil compaction and the shortening of the soil vibration periods. The procedure was applied to estimate the shortening of the soil resonant period of Mexico City between 2005 and 2013. The results show that in approximately nine years the ground surface has subsided by approximately 0.5⿿3.5m and the soil resonant period has decreased by approximately 0.1⿿0.4s. The obtained results, validated with field measurements, highlight the effectiveness of the proposed procedure for the continuous monitoring of the soil resonant periods. The estimated change in resonant period on Mexico City has a great impact on the response spectra used for design, it is then necessary to update the map of the soil resonant period in order to account for the change of dynamic properties of soils caused by subsidence.

Earth's core and inner-core resonances from analysis of VLBI nutation and superconducting gravimeter data

Geophysical parameters of the deep Earth’s interior can be evaluated through the resonance effects associated with the core and inner-core wobbles on the forced nutations of the Earth’s figure axis, as observed by very long baseline interferometry (VLBI), or on the diurnal tidal waves, retrieved from the time-varying surface gravity recorded by superconducting gravime- ters (SGs). In this paper, we inverse for the rotational mode parameters from both techniques to retrieve geophysical parameters of the deep Earth. We analyse surface gravity data from 15 SG stations and VLBI delays accumulated over the last 35 yr. We show existing correlations between several basic Earth parameters and then decide to inverse for the rotational modes parameters. We employ a Bayesian inversion based on the Metropolis-Hastings algorithm with a Markov-chain Monte Carlo method. We obtain estimates of the free core nutation resonant period and quality factor that are consistent for both techniques. We also attempt an inversion for the free inner-core nutation (FICN) resonant period from gravity data. The most probable solution gives a period close to the annual prograde term (or S1 tide). However the 95 per cent confidence interval extends the possible values between roughly 28 and 725 d for gravity, and from 362 to 414 d from nutation data, depending on the prior bounds. The precisions of the estimated long-period nutation and respective small diurnal tidal constituents are hence not accurate enough for a correct determination of the FICN complex frequency.

Destructive near-fault strong ground motion from the 2016 Kumamoto prefecture, Japan, M7.3 earthquake

The sequence of the 2016 Kumamoto, Japan, earthquake, which included an initial M6.5 foreshock on April 14, followed by a larger M7.3 mainshock on April 16, and subsequently occurred high aftershock activity, caused significant damage in Kumamoto and neighboring regions. The near-field strong motion record by strong motion network (K-NET and KiK-net) and the intensity meter network demonstrated clearly the characteristics of the strong ground motion developed by the shallow (H = 12 km), inland earthquake comprising short-time duration ( 1G) ground accelerations. The velocity response spectra of the near-fault motion at Mashiki and Nishihara showed large levels (>300–550 cm/s) in the short-period range (T = 1–2 s), several times larger than that of the near-field record of the destructive 1995 Kobe earthquake (M7.3) and that of the 2004 Mid-Niigata earthquake (M6.8). This period corresponds to the collapse vulnerability of Japanese wooden-frame houses, and is the major cause of severe damage during the Kumamoto earthquake. The response spectra also showed extremely large levels (>240–340 cm/s) in the long-period (T > 3 s) band, which is potentially disastrous for high-rise buildings, large oil storage tanks, etc. to have longer resonant period. Such long-period motion was, for the most parts, developed by the static displacement of the fault movement rather than by the seismic waves radiating from the source fault. Thus, the extreme near-fault long-period motion was hazardous only close to the fault but it attenuated very rapidly away from the fault.

Localized field-aligned currents and 4-min TEC and ground magnetic oscillations during the 2015 eruption of Chile’s Calbuco volcano

The Calbuco volcano in southern Chile erupted on April 22, 2015. About 2 h after the first eruption, a Swarm satellite passed above the volcano and observed enhancement of small-amplitude (~0.5 nT) magnetic fluctuations with wave-packet structure which extends 15° in latitude. Similar wave packet is seen at the geomagnetic conjugate point of the volcano. Just after the eruption, geomagnetic fluctuations with the spectral peaks around the vertical acoustic resonance periods, 215 and 260 s, were also observed at Huancayo Geomagnetic Observatory located on the magnetic equator. Besides these observations, around 4-min, i.e., 175, 205 and 260 s, oscillations of total electron content (TEC) were observed at global positioning system stations near the volcano. The horizontal propagation velocity and the spatial scale of the TEC oscillation are estimated to be 720 m/s and 1600 km, respectively. These observations strongly suggest that the atmospheric waves induced by explosive volcanic eruption generate TEC variation and electric currents. The Swarm observation may be explained as a manifestation of their magnetic effects observed in the topside ionosphere.

Nanoscale TiO2 dielectric resonator absorbers.

We demonstrate a narrow-band plasmonic absorber based on a uniform array of nanoscale cylindrical dielectric resonators (DRs) on a metallic substrate at visible frequencies. Under a normally incident plane-wave excitation, the DRs resonate in their horizontal magnetic dipolar mode, which can be seen as localized plasmonic hot spots. Such a localized resonance also couples incident waves into surface plasmon polaritons (SPPs) bidirectionally, and perfect absorption is achieved by creating SPP standing waves. The simulation shows perfect absorption at 633 nm and 1.8% relative bandwidth with >90% absorption, while the measurement demonstrates maximum absorption of 90% at 636 nm. Both simulation and measurement results are analyzed with coupled mode theory. An additional numerical study elaborates on the dependence of absorption on the resonator size, period, and incidence angle.

Simultaneous investigation of shear modulus and torsional resonance of solidHe4

We investigate the origin of a resonant period drop of a torsional oscillator (TO) containing solid ${}^{4}$He by inspecting its relation to a change in elastic modulus. To understand this relationship directly, we measure both phenomena simultaneously using a TO with a pair of concentric piezoelectric transducers inserted in its annulus. Although the temperature, ${}^{3}$He concentration, and frequency dependence are essentially the same, a marked discrepancy in the drive amplitude dependence is observed. We find that this discrepancy originates from the anisotropic response of polycrystalline solid ${}^{4}$He connected with low-angle grain boundaries by studying the shear modulus parallel to and perpendicular to the driving direction.

High-Frequency High-Efficiency GaN-Based Interleaved CRM Bidirectional Buck/Boost Converter with Inverse Coupled Inductor

This paper presents a high-frequency high-efficiency GaN device-based interleaved critical current mode (CRM) bidirectional buck/boost converter with an inverse coupled inductor. The switching frequency is continually driven to megahertz range with GaN devices due to their small switching loss and driving loss, which greatly reduces the size of the passive components. The coupled inductor further reduces the core volume due to certain dc flux reductions. The equivalent inductance and the impact of the inverse coupled inductor on the CRM buck–boost converter are analyzed in detail. The resonant period in CRM is less with an inverse coupled inductor than with a noncoupled inductor, which is beneficial for the high-frequency operation. The soft-switching range and the circulating energy are both improved using an inverse coupled inductor in CRM. Experimental results validate the theoretical analysis, and the coupled inductor prototype efficiency is 98.5% at 1 MHz, which is 0.3% higher than a prototype with a noncoupled inductor.

Tunneling effects in resonant acoustic scattering of an air bubble in unbounded water.

The problem of acoustic scattering of a gaseous spherical bubble immersed within unbounded liquid surrounding is considered in this work. The theory of partial wave expansion related to this problem is revisited. A physical model based on the analogy between acoustic scattering and potential scattering in quantum mechanics is proposed to describe and interpret the acoustical natural oscillation modes of the bubble, namely, the resonances. In this context, a physical model is devised in order to describe the air water interface and the implications of the high density contrast on the various regimes of the scattering resonances. The main results are presented in terms of resonance lifetime periods and quality factors. The explicit numerical calculations are undertaken through an asymptotic analysis considering typical bubble dimensions and underwater sound wavelengths. It is shown that the resonance periods are scaled according to the Minnaert's period, which is the short lived resonance mode, called breathing mode of the bubble. As expected, resonances with longer lifetimes lead to impressive cavity quality Q-factor ranging from 1010 to 105. The present theoretical findings lead to a better understanding of the energy storage mechanism in a bubbly medium.

STOCHASTIC TRANSIENTS AS A SOURCE OF QUASI-PERIODIC PROCESSES IN THE SOLAR ATMOSPHERE

ABSTRACT Solar dynamics and turbulence occur at all heights of the solar atmosphere and could be described as stochastic processes. We propose that finite-lifetime transients recurring at a certain place could trigger quasi-periodic processes in the associated structures. In this study, we developed a mathematical model for finite-lifetime and randomly occurring transients, and found that quasi-periodic processes with periods longer than the timescale of the transients, are detectable intrinsically in the form of trains. We simulate their propagation in an empirical solar atmospheric model with chromosphere, transition region, and corona. We found that, due to the filtering effect of the chromospheric cavity, only the resonance period of the acoustic resonator is able to propagate to the upper atmosphere; such a scenario is applicable to slow magnetoacoustic waves in sunspots and active regions. If the thermal structure of the atmosphere is less wild and acoustic resonance does not take place, the long-period oscillations could propagate to the upper atmosphere. Such a case would be more likely to occur in polar plumes.

DYNAMICS AND TRANSIT VARIATIONS OF RESONANT EXOPLANETS

ABSTRACT Transit timing variations (TTVs) are deviations of the measured midtransit times from the exact periodicity. One of the most interesting causes of TTVs is the gravitational interaction between planets. Here we consider a case of two planets in a mean motion resonance (orbital periods in a ratio of small integers). This case is important because the resonant interaction can amplify the TTV effect and allow planets to be detected more easily. We develop an analytic model of the resonant dynamics valid for small orbital eccentricities and use it to derive the principal TTV terms. We find that a resonant system should show TTV terms with two basic periods (and their harmonics). The resonant TTV period is proportional (m/M *)−2/3, where m and M * are the planetary and stellar masses. For m = 10−4 M *, for example, the TTV period exceeds the orbital period by about two orders of magnitude. The amplitude of the resonant TTV terms scales linearly with the libration amplitude. The ratio of the TTV amplitudes of two resonant planets is inversely proportional to the ratio of their masses. These and other relationships discussed in the main text can be used to aid the interpretation of TTV observations.

Seismic response of Beirut (Lebanon) buildings: instrumental results from ambient vibrations

Resonance period is a key parameter in the seismic design of a structure, thus dynamic parameters of buildings in Beirut (Lebanon) were investigated based on ambient vibration method for risk and vulnerability assessment. Lebanon is facing high seismic hazard due to its major faults, combined to a high seismic risk caused by dense urbanization in addition to the lack of a seismic design code implementation. For this study, ambient vibration recordings have been performed on 330 RC buildings, period parameters extracted and statistically analyzed to identify correlations with physical building parameters (height, horizontal dimensions, age) and site characteristics (rock sites or soft sites). The study shows that (1) the building height or number of floors (N) is the primary statistically robust parameter for the estimation of the fundamental period T; (2) the correlation between T and N is linear and site dependent: T ≈ N/23 for rock sites and N/18 for soft sites; (3) the measured damping is inversely proportional to the period: the taller the building the lower is the damping; (4) a significant overestimation of the period exists in current building codes. However part of the large discrepancy with building code recommendations may be due to the very low level of loading.

Effect of inclination on oscillation characteristics of an oscillating water column wave energy converter

Oscillating water column (OWC) wave energy converters are adopted in many marine applications such as buoys. This research investigates how inclination-induced changes in motion affect the oscillation characteristics of an OWC. As the collector of the OWC wave energy converter is inclined, the direction of motion of the water column is also inclined because it is constrained by collector walls. To investigate this idea, we developed a mechanical 1-degree-of-freedom oscillator model of an inclined OWC. The usefulness of the mechanical model was confirmed in a water tank test with OWCs inclined at 90° (vertical), 45°, and 18.4°. We then investigated the effect of inclination on the resonance period and the optimum power take-off damping of the OWC. The resonance period was mainly prolonged by the reduced restoring force as the motion direction changed. The optimum power take-off damping of an inclined OWC equaled the radiation damping, as observed in vertical OWCs. Finally, we varied the air chamber volume and observed much smaller effects than when varying the inclination. We conclude that changing the direction of motion affects the oscillation characteristics of OWCs mostly because of the reduction of gravity restoring force.

Deepwater overflow observed by three bottom-anchored moorings in the Bashi Channel

Three moorings equipped with 10 current meters and 7 CTDs were deployed in the Bashi Channel, the main deep connection between the northwestern Pacific Ocean and the South China Sea, from August 2010 to April 2011 to investigate the deepwater overflow of the North Pacific Deep Water through it. Results from these observations provide, for the first time, valuable information on the spatial structure of the deep current and allow us to estimate the overflow transport with greater accuracy. The observed current is coherent both vertically and horizontally but exhibits a much stronger velocity in the central area compared to near the edges of the channel. The core of the overflow is found near 2600m, with mean velocity, potential temperature, and salinity of 22.5cms−1, 1.79°C, and 34.64psu, respectively. The current is approximately geostrophic, with isopycnals sloping upward to the right-hand side of the flow. The local Froude number is found much less than 1, implying that the deep flow in the Bashi Channel could not be hydraulically controlled. The observations yield an 8-month mean transport of 0.78Sv with an rms error of 0.18Sv. The transport time series exhibits significant intraseasonal variabilities, including variability on time scale close to the resonance period of the deep channel in the Luzon Strait (~30 days). Higher transports are connected with a higher velocity and a thicker overflow layer, allowing colder and saltier (thus denser) North Pacific Deep Water to flow into the South China Sea.

헬름홀츠 공진에서 톱니 효과에 대한 수치적 연구

ABSTRACT The flow-excited Helmholtz resonance phenomenon was investigated numerically using Reynolds averaged Navier-Stokes approach. The fundamental cause of the Helmholtz resonance phenomenon is known as shedding of a single discrete vortex from orifice edge that travels during one period of the oscillation. In this study, serrated deflector, which is biomimetic design of the owl’s feather, is used to split a single vortex into small vortices. Rectangular deflector and serrated deflector are com-pared with numerical results of pressure and streamline inside the cavity. Consequently, the serration breaks the shedding period of vortex core and eliminates the resonance. Also, it changes the flow pattern in according to the location of different serration height. By making inflows and outflows occur simultaneously in spanwise direction in the cavity, the period of Helmholtz resonance disappears. Comparing between rectangular deflector and serrated deflector, the serrated deflector can deal with the Helmholtz resonance more effectively.

Theoretical model and spectrum characteristics of superimposed photonic crystal fiber grating

The superimposed gratings have attracted considerable interest because they can extend the potential applications of gratings. Superimposed gratings are fabricated by inscribing multiple gratings at the same section of the fiber, and they can demonstrate various features simultaneously. A number of optical devices based on superimposed gratings have been reported, such as multi-wavelength filters, beam shapers, ultrahigh repetition rate optical pulse generators, etc. Photonic crystal fiber (PCF) can bring new optical characteristics by changing the sizes, spacings and arrangements of the air holes in the fiber. In this paper, we present the spectra of the superimposed gratings inscribed in a photonic crystal fiber. A numerical mode is proposed based on the V-I transmission matrices. The traditional cosinoidal variation of refractive index is replaced with a square-type refractive index variation, and the scattering occurs at a localized discrete location. According to the simulations, the reflection spectra and time delays of a superimposed Bragg grating and superimposed chirped Bragg grating are analyzed. A superimposed Bragg grating and a superimposed chirped Bragg grating are fabricated in the single mode photosensitive PCFs under the irradiation of a 193 nm ultraviolet laser. The superimposed Bragg grating is composed of four subgratings with resonance wavelengths at set spacings. And under a phase mask displacement of 1.03 mm, the superimposed chirped Bragg grating has a periodic resonance with a period of 0.82 nm. The results show that the spectrum of superimposed Bragg grating can be flexibly customized by the parameters of each subgrating. Superimposed chirped Bragg gratings have good linear group delays and flat periodic resonance amplitudes, and the resonance period can be adjusted by displacing the phase mask. The grating spectra obtained from experiments are in good agreement with the theoretical analyses. The research results in this paper provide an important basis for designing, fabricating, and applying the superimposed PCF gratings.

Dynamic Resonant Matching Method for a Wireless Power Transmission Receiver

Wireless power transmission systems can be optimized by matching the resonance frequency of a receiver. However, in certain applications, such as, e.g., a multireceiver system, it is desired to match the individual resonance frequencies of the receiver to a fixed (e.g., common) operation frequency. In this publication, a method is proposed to match the resonant frequency dynamically without changing the physical value of the components. Instead, it is changed “virtually” by a method, which is named “frozen resonance state” by the author. The basic idea is to maintain the state of a resonant circuit (to “freeze” the state) for a fraction of the resonant period, e.g., by freewheeling the current of the resonant inductor or maintaining the voltage of the resonant capacitor. This additional time extends virtually the resonant period leading to an effective lower resonant frequency. By adjusting the additional time, the effective resonant frequency can be matched to the operation frequency individually for each receiver. This publication explains the basic idea more in detail and gives an overview of the different possible circuit topologies. Furthermore, the method is applied to an exemplary receiver of a capacitive wireless power transmission system, where measurements are presented.