Damping Length Research Articles

Parameters affecting the reduction factor in pedestrian load model based on pulsating stationary force

All dynamic pedestrian load models for serviceability control on pedestrian bridges which can be found in Eurocodes (EC) or guides to EC are based on dynamic load model of single pedestrian. Though the model of moving pulsating force is similar to the real character of pedestrian loading (walking along the bridge) the load model based on stationary pulsating force acting at the most adverse position of the bridge deck may be concurrent in bridge design for the reason of simplicity of acceleration assessment. Pulsating force moving along the bridge span do not produce the same dynamic response as a same pulsating stationary force. Therefore, the amplitude of stationary pulsating force have to be factorised by the reduction factor in a way that both load models (stationary and moving) cause the same maximum structural dynamic response. In this paper the structural parameters (structural system, span length, structural frequency and structural damping) affecting the reduction factor in pedestrian load model based on stationary pulsating force are researched. From conducted analyses it can be concluded changes in structural frequency does not affect the reduction factor, while changes in structural damping, structural system and span length affect the reduction factor, i.e. reduction factor is not a constant value as it is defined in load models proposed in some codes or guides.

A mixing‐length model for magnetohydrodynamic flows in channels and ducts with wall‐parallel magnetic field

AbstractA spanwise magnetic field leads to turbulent drag reduction in channel flow of a conducting liquid due to the selective Joule damping of certain flow structures. This effect can be captured by a simple modification of Prandtl's classical mixing‐length idea. The mixing length over which a turbulent fluctuation loses its momentum is not only constrained geometrically but also by magnetic damping. We therefore introduce a magnetic damping length that is proportional to friction velocity and the Joule damping time. The limitation of mixing length is implemented by using the harmonic mean between wall distance and this damping length. By combining this ansatz with the van‐Driest model for turbulent stresses in channel flow we obtain a satisfactory prediction for the mean velocity distribution in magnetohydrodynamic channel flow with spanwise field for different Reynolds and Hartmann numbers. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Spectral response of localized surface plasmon in resonance with mid-infrared light

We study spectral responses of localized surface plasmons (LSPs) in gold nanorods, which resonate at mid-infrared frequencies, by transmission spectroscopy and electromagnetic field analyses. The resonance linewidth is found to be linearly proportional to the resonance frequency, indicating that the dephasing due to Drude relaxation is suppressed and that the overall dephasing is dominated by radiative damping. Owing to the reduced radiative/non-radiative damping and large geometrical length of the nanorod, near-field intensity enhancement exceeds several hundred times. Nonetheless the resonance linewidth is comparable with or larger than the bandwidth of a 100-fs pulse, and therefore the enhanced near-field as short as 100-fs can be created upon pulsed excitation. The large enhancements with appropriate bandwidths make LSPs promising for enhanced nonlinear spectroscopies, coherent controls, and strong-field light-matter interactions in the mid-infrared range.

A mixing-length model for side layers of magnetohydrodynamic channel and duct flows with insulating walls

We propose a simple extension of Prandtl's classical mixing-length model for channel flow in order to describe the effects of a uniform spanwise magnetic field. The mixing length is assumed to be constrained by an additional length scale called the Joule damping length. It is based on the friction velocity and the Joule damping time. The limitation of mixing length is implemented by using the harmonic mean of the wall distance and the Joule damping length. Near the wall, the model captures the combined linear-logarithmic dependence of velocity on the wall distance observed in direct numerical simulations. It also provides a satisfactory prediction for the overall velocity distribution for different Reynolds and Hartmann numbers. The velocity profile of turbulent side layers in magnetohydrodynamic duct flows in a strong field can also be computed with the help of the model provided that the Hartmann layers are already laminar.

Spin injection from topological insulator tunnel-coupled to metallic leads

We study theoretically helical edge states of 2D and 3D topological insulators (TI) tunnel-coupled to metal leads and show that their transport properties are strongly affected by contacts as the latter play a role of a heat bath and induce damping and relaxation of electrons in the helical states of TI. A simple structure that produces a pure spin current in the external circuit is proposed. The current and spin current delivered to the external circuit depend on relation between characteristic lengths: damping length due to tunneling, contact length and, in case of 3D TI, mean free path and spin relaxation length caused by momentum scattering. If the damping length due to tunneling is the smallest one, then the electric and spin currents are proportional to the conductance quantum in 2D TI, and to the conductance quantum multiplied by the ratio of the contact width to the Fermi wavelength in 3D TI.

DETERMINATION OF TRANSVERSE DENSITY STRUCTURING FROM PROPAGATING MAGNETOHYDRODYNAMIC WAVES IN THE SOLAR ATMOSPHERE

We present a Bayesian seismology inversion technique for propagating magnetohydrodynamic (MHD) transverse waves observed in coronal waveguides. The technique uses theoretical predictions for the spatial damping of propagating kink waves in transversely inhomogeneous coronal waveguides. It combines wave amplitude damping length scales along the waveguide with theoretical results for resonantly damped propagating kink waves to infer the plasma density variation across the oscillating structures. Provided the spatial dependence of the velocity amplitude along the propagation direction is measured and the existence of two different damping regimes is identified, the technique would enable us to fully constrain the transverse density structuring, providing estimates for the density contrast and its transverse inhomogeneity length scale.

Acoustic wave-based nondestructive control of the damaged layer and roughness parameters of the free surface of an anisotropic solid

A method of nondestructive control of the damaged layer and roughness parameters of the surface of a hexagonal crystal and an isotropic solid with the use of Rayleigh and shear-polarized surface acoustic waves has been proposed. The surface under study borders on vacuum and can be a rough surface or an isotropic damaged surface layer. The problem is considered in the long-wavelength limit (as compared to the roughness amplitude or the thickness of the damaged layer, as well as to the characteristic radius of the surface heterogeneity). It has been shown that, in the long-wavelength limit, the dispersion of phase velocity and the damping length of shear-polarized waves can be found from the known values of the phase velocity dispersion and the damping length of the Rayleigh surface acoustic waves or vice versa. The problem for an isotropic damaged surface layer is treated in a special case where only the density fluctuates.

Omnipresent long-period intensity oscillations in open coronal structures

Quasi-periodic propagating disturbances in coronal structures have been interpreted as slow magneto-acoustic waves and/or periodic upflows. Here we aim to understand their nature from the observed properties using a three-hour imaging sequence from AIA/SDO in two different temperature channels. We also compare the characteristics with a simple wave model. We searched for propagating disturbances in open-loop structures at three different locations; a fan loop-structure off-limb, an on-disk plume-like structure and the plume/interplume regions in the north pole of the sun. In each of the subfield regions chosen to cover these structures, the time series at each pixel location was subjected to wavelet analysis to find the different periodicities. We then constructed powermaps in three different period ranges. We also constructed space-time maps for the on-disk plume structure to estimate the propagation speeds in different channels. We find propagating disturbances in all three structures. Powermaps indicate that the power in the long-period range is significant up to comparatively longer distances along the loop than that in the shorter periods. This nature is observed in all three structures. A detailed analysis on the on-disk plume structure gives consistently higher propagation speeds in the 193 \AA channel and also reveals spatial damping along the loop. The amplitude and the damping length values are lower in hotter channels, indicating their acoustic dependence. These properties can be explained very well with a propagating slow-wave model. We suggest that these disturbances are more likely to be caused by propagating slow magneto-acoustic waves than by high-speed quasi-periodic upflows. We find that intensity oscillations in longer periods are omnipresent at larger heights even in active regions.

Modelling and parametric analysis of a squeeze film damper with central groove

In this work, a theoretical analysis of a squeeze film damper (SFD) with central groove has been carried out. A program has been developed, using Microsoft Visual C++. Damper length and diameter of 50 mm and 60 mm have been taken. Input data include the damper clearance, damper length and groove parameters and oil specification. Effect of all these factors on the resonance frequency, damping and inertia coefficient has been examined. Results of this study show that the damper parameters have a clear effect on the damping and inertia coefficients. A good agreement was found for the excitation frequency effect on the normalised inertia and damping coefficients.

Waves in Cassini UVIS stellar occultations: 2. The C ring

We performed a complete wavelet analysis of Saturn’s C ring on 62 stellar occultation profiles. These profiles were obtained by Cassini’s Ultraviolet Imaging Spectrograph High Speed Photometer. We used a WWZ wavelet power transform to analyze them. With a co-adding process, we found evidence of 40 wavelike structures, 18 of which are reported here for the first time. Seventeen of these appear to be propagating waves (wavelength changing systematically with distance from Saturn). The longest new wavetrain in the C ring is a 52-km-long wave in a plateau at 86,397 km. We produced a complete map of resonances with external satellites and possible structures rotating with Saturn’s rotation period up to the eighth order, allowing us to associate a previously observed wave with the Atlas 2:1 inner Lindblad resonance (ILR) and newly detected waves with the Mimas 6:2 ILR and the Pandora 4:2 ILR. We derived surface mass densities and mass extinction coefficients, finding σ = 0.22(±0.03) g cm −2 for the Atlas 2:1 ILR, σ = 1.31(±0.20) g cm −2 for the Mimas 6:2 ILR, and σ = 1.42(±0.21) g cm −2 for the Pandora 4:2 ILR. We determined a range of mass extinction coefficients ( κ = τ/ σ) for the waves associated with resonances with κ = 0.13 (±0.03) to 0.28(±0.06) cm 2 g −1, where τ is the optical depth. These values are higher than the reported values for the A ring (0.01–0.02 cm 2 g −1) and the Cassini Division (0.07–0.12 cm 2 g −1 from Colwell et al. (Colwell, J.E., Cooney, J.H., Esposito, L.W., Sremčević, M. [2009]. Icarus 200, 574–580)). We also note that the mass extinction coefficient is probably not constant across the C ring (in contrast to the A ring and the Cassini Division): it is systematically higher in the plateaus than elsewhere, suggesting smaller particles in the plateaus. We present the results of our analysis of these waves in the C ring and estimate the mass of the C ring to be between3.7(±0.9) × 10 16 kg and 7.9(±2.0) × 10 16 kg (equivalent to an icy satellite of radius between 28.0(±2.3) km and 36.2(±3.0) km with a density of 400 kg m −3, close to that of Pan or Atlas). Using the ring viscosity derived from the wave damping length, we also estimate the vertical thickness of the C ring between 1.9(±0.4) m and 5.6(±1.4) m, comparable to the vertical thickness of the Cassini Division.

SPATIAL DAMPING OF PROPAGATING KINK WAVES DUE TO RESONANT ABSORPTION: EFFECT OF BACKGROUND FLOW

Observations show the ubiquitous presence of propagating magnetohydrodynamic (MHD) kink waves in the solar atmosphere. Waves and flows are often observed simultaneously. Due to plasma inhomogeneity in the perpendicular direction to the magnetic field, kink waves are spatially damped by resonant absorption. The presence of flow may affect the wave spatial damping. Here, we investigate the effect of longitudinal background flow on the propagation and spatial damping of resonant kink waves in transversely nonuniform magnetic flux tubes. We combine approximate analytical theory with numerical investigation. The analytical theory uses the thin tube (TT) and thin boundary (TB) approximations to obtain expressions for the wavelength and the damping length. Numerically, we verify the previously obtained analytical expressions by means of the full solution of the resistive MHD eigenvalue problem beyond the TT and TB approximations. We find that the backward and forward propagating waves have different wavelengths and are damped on length scales that are inversely proportional to the frequency as in the static case. However, the factor of proportionality depends on the characteristics of the flow, so that the damping length differs from its static analogue. For slow, sub-Alfvenic flows the backward propagating wave gets damped on a shorter length scale than in the absence of flow, while for the forward propagating wave the damping length is longer. The different properties of the waves depending on their direction of propagation with respect to the background flow may be detected by the observations and may be relevant for seismological applications.

SPATIAL DAMPING OF PROPAGATING KINK WAVES IN PROMINENCE THREADS

Transverse oscillations and propagating waves are frequently observed in threads of solar prominences/filaments and have been interpreted as kink magnetohydrodynamic (MHD) modes. We investigate the spatial damping of propagating kink MHD waves in transversely nonuniform and partially ionized prominence threads. Resonant absorption and ion-neutral collisions (Cowling's diffusion) are the damping mechanisms taken into account. The dispersion relation of resonant kink waves in a partially ionized magnetic flux tube is numerically solved by considering prominence conditions. Analytical expressions of the wavelength and damping length as functions of the kink mode frequency are obtained in the Thin Tube and Thin Boundary approximations. For typically reported periods of thread oscillations, resonant absorption is an efficient mechanism for the kink mode spatial damping, while ion-neutral collisions have a minor role. Cowling's diffusion dominates both the propagation and damping for periods much shorter than those observed. Resonant absorption may explain the observed spatial damping of kink waves in prominence threads. The transverse inhomogeneity length scale of the threads can be estimated by comparing the observed wavelengths and damping lengths with the theoretically predicted values. However, the ignorance of the form of the density profile in the transversely nonuniform layer introduces inaccuracies in the determination of the inhomogeneity length scale.

Selective spatial damping of propagating kink waves due to resonant absorption

There is observational evidence of propagating kink waves driven by photospheric motions. These disturbances, interpreted as kink magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the solar corona. In this paper we show that resonant absorption provides a simple explanation to the spatial damping of these waves. Kink MHD waves are studied using a cylindrical model of solar magnetic flux tubes which includes a non-uniform layer at the tube boundary. Assuming that the frequency is real and the longitudinal wavenumber complex, the damping length and damping per wavelength produced by resonant absorption are analytically calculated. The damping length of propagating kink waves due resonant absorption is a monotonically decreasing function of frequency. For kink waves with low frequencies the damping length is exactly inversely proportional to frequency and we denote this as the TGV relation. When moving to high frequencies the TGV relation continues to be an exceptionally good approximation of the actual dependency of the damping length on frequency. This dependency means that resonant absorption is selective as it favours low frequency waves and can efficiently remove high frequency waves from a broad band spectrum of kink waves. It is selective as the damping length is inversely proportional to frequency so that the damping becomes more severe with increasing frequency. This means that radial inhomogeneity can cause solar waveguides to be a natural low-pass filter for broadband disturbances. Hence kink wave trains travelling along, e.g., coronal loops, will have a greater proportion of the high frequency components dissipated lower down in the atmosphere. This could have important consequences with respect to the spatial distribution of wave heating in the solar atmosphere.

OBSERVATIONAL EVIDENCE OF RESONANTLY DAMPED PROPAGATING KINK WAVES IN THE SOLAR CORONA

In this Letter we establish clear evidence for the resonant absorption damping mechanism by analyzing observational data from the novel Coronal Multi-Channel Polarimeter (CoMP). This instrument has established that in the solar corona there are ubiquitous propagating low amplitude ($\approx$1 km s$^{-1}$) Alfv\'{e}nic waves with a wide range of frequencies. Realistically interpreting these waves as the kink mode from magnetohydrodynamic (MHD) wave theory, they should exhibit a frequency dependent damping length due to resonant absorption, governed by the TGV relation showing that transversal plasma inhomogeneity in coronal magnetic flux tubes causes them to act as natural low-pass filters. It is found that observed frequency dependence on damping length (up to about 8 mHz) can be explained by the kink wave interpretation and furthermore, the spatially averaged equilibrium parameter describing the length scale of transverse plasma density inhomogeneity over a system of coronal loops is consistent with the range of values estimated from TRACE observations of standing kink modes.

The spatial damping of magnetohydrodynamic waves in a flowing partially ionised prominence plasma

Solar prominences are partially ionised plasmas displaying flows and oscillations. These oscillations show time and spatial damping and, commonly, have been explained in terms of magnetohydrodynamic (MHD) waves. We study the spatial damping of linear non-adiabatic MHD waves in a flowing partially ionised plasma, having prominence-like physical properties. We consider single fluid equations for a partially ionised hydrogen plasma including in the energy equation optically thin radiation, thermal conduction by electrons and neutrals, and heating. Keeping the frequency real and fixed, we have solved the obtained dispersion relations for the complex wavenumber, k, and have analysed the behaviour of the damping length, wavelength and the ratio of the damping length to the wavelength, versus period, for Alfven, fast, slow and thermal waves.

COUPLED ALFVÉN AND KINK OSCILLATIONS IN CORONAL LOOPS

Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. However, there is ongoing discussion regarding their interpretation as kink or Alfven waves. To investigate the nature of transverse waves propagating in the solar corona and their potential for use as a coronal diagnostic in MHD seismology, we perform three-dimensional numerical simulations of footpoint-driven transverse waves propagating in a low β plasma. We consider the cases of both a uniform medium and one with loop-like density structure and perform a parametric study for our structuring parameters. When density structuring is present, resonant absorption in inhomogeneous layers leads to the coupling of the kink mode to the Alfven mode. The decay of the propagating kink wave as energy is transferred to the local Alfven mode is in good agreement with a modified interpretation of the analysis of Ruderman & Roberts for standing kink modes. Numerical simulations support the most general interpretation of the observed loop oscillations as a coupling of the kink and Alfven modes. This coupling may account for the observed predominance of outward wave power in longer coronal loops since the observed damping length is comparable to our estimate based on an assumption of resonant absorption as the damping mechanism.

Superconducting current in hybrid structures with an antiferromagnetic interlayer

It is shown experimentally that the superconducting current density in Nb/Au/Ca1 − x Sr x CuO2/YBa2Cu3O7 − δ hybrid superconducting heterostructures with a Ca1 − x Sr x CuO2 anti-ferromagnetic (AF) cuprate interlayer is anomalously high for interlayer thicknesses d M = 10–50 nm and the characteristic damping length for superconducting correlations is on the order of 10 nm. The experimental results are explained on the basis of theoretical analysis of a junction of two superconductors (S′ and S) connected by a magnetic multilayer with the AF ordering of magnetization in the layers. It is shown that with such a magnetization ordering, anomalous proximity effect determined by the singlet component of the condensate wavefunction may take place. As a result, the critical currents in S′/I/AF/S and S′/I/N/S structures (I denotes an insulator, and N, the normal metal) may coincide in order of magnitude even when the thickness of the AF interlayer considerably exceeds the decay length of the condensate wavefunction in ferromagnetic layers.

10.1007/s11452-008-3006-0

The propagation and damping of waves excited by a poloidal antenna in a hydrogen plasma at the ion cyclotron resonance (ICR) frequency were investigated. The longitudinal wavenumber and damping length of waves excited in the ohmically heated plasma of the L-2M stellarator, the dependence of the damping length of fast magnetosonic waves on the magnetic field strength, and the dependence of the antenna load resistance on the plasma density were measured. It is the first time that such complex measurements were performed in experiments on ICR heating of a hydrogen plasma at the fundamental harmonic of the ion gyrofrequency in toroidal magnetic confinement systems.

Difference between penetration and damping lengths in photonic crystal mirrors

Different mirror geometries in two-dimensional photonic crystal slabs are studied with fully vectorial calculations. We compare their optical properties and, in particular, we show that, for heterostructure mirrors, the penetration length associated with the delay induced by distributed reflection is not correlated with the characteristic damping length of the electromagnetic energy distribution in the mirror. This unexpected result evidences that the usual trade-off between short damping lengths and large penetration lengths that is classically encountered in distributed Bragg reflectors can be overcome with carefully designed photonic crystal structures.

Photovoltaic effect in a gated two-dimensional electron gas in magnetic field

The photovoltaic effect induced by terahertz radiation in a gated two-dimensional electron gas in magnetic field is considered theoretically. It is assumed that the incoming radiation creates an ac voltage between the source and gate and that the gate length is long compared to the damping length of plasma waves. In the presence of pronounced Shubnikov-de Haas oscillations, an important source of non-linearity is the oscillating dependence of the mobility on the ac gate voltage. This results in a photoresponse oscillating as a function of magnetic field, which is enhanced in the vicinity of the cyclotron resonance, in accordance with recent experiments. Another, smooth component of the photovoltage, unrelated to SdH oscillations, has a maximum at cyclotron resonance.