scholarly journals On the dynamic homogenization of periodic media: Willis’ approach versus two-scale paradigm

2018 ◽  
Vol 474 (2213) ◽  
pp. 20170638 ◽  
Author(s):  
Shixu Meng ◽  
Bojan B. Guzina
Keyword(s):  
Low Frequency ◽  
Second Order ◽  
The Body ◽  
Clear Understanding ◽  
Periodic Media ◽  
Physical Sciences ◽  
Static Approximation ◽  
Long Wavelength ◽  
Modulation Factor ◽  
Effective Impedance

When considering an effective, i.e. homogenized description of waves in periodic media that transcends the usual quasi-static approximation, there are generally two schools of thought: (i) the two-scale approach that is prevalent in mathematics and (ii) the Willis’ homogenization framework that has been gaining popularity in engineering and physical sciences. Notwithstanding a mounting body of literature on the two competing paradigms, a clear understanding of their relationship is still lacking. In this study, we deploy an effective impedance of the scalar wave equation as a lens for comparison and establish a low-frequency, long-wavelength dispersive expansion of the Willis’ effective model, including terms up to the second order. Despite the intuitive expectation that such obtained effective impedance coincides with its two-scale counterpart, we find that the two descriptions differ by a modulation factor which is, up to the second order, expressible as a polynomial in frequency and wavenumber. We track down this inconsistency to the fact that the two-scale expansion is commonly restricted to the free-wave solutions and thus fails to account for the body source term which, as it turns out, must also be homogenized—by the reciprocal of the featured modulation factor. In the analysis, we also (i) reformulate for generality the Willis’ effective description in terms of the eigenfunction approach, and (ii) obtain the corresponding modulation factor for dipole body sources, which may be relevant to some recent efforts to manipulate waves in metamaterials.

Review of Approximations to Evaluate Second-Order Low-Frequency Load

2012 ◽  
Author(s):  
Guillaume de Hauteclocque ◽  
Flávia Rezende ◽  
Olaf Waals ◽  
Xiao-Bo Chen
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Low Frequency ◽  
Second Order ◽  
The Body ◽  
Difference Frequency ◽  
Surface Boundary ◽  
First Order ◽  
Potential Part ◽  
The Difference

The second order low-frequency loads are one of main sources of excitation for moored systems. These loads are usually decomposed into the quadratic part, contributed only by first order quantities and potential part contributed by the second order potentials. In shallow water the second order incoming and diffracted potentials give a significant contribution to the low frequency forces. Therefore, the accuracy on the determination of this parcel of the low-frequency loads is a key issue for the assessment of mooring lines and operability of systems moored in shallow water area, as for example LNG terminals. Due to the complexity in computing the second order diffraction potential, which would involve a non-homogeneous free surface boundary condition, the so-called Pinkster approximation has been proposed. This approximation is based on the assumption that the major contribution to the potential part of low-frequency loads is given by the second order potential of the undisturbed incoming waves. The methods to compute the wave forces related to the second order potentials are based on scaling of the first order wave induced forces. Another approximation recently formulated in Chen and Rezende consists of developing the second-order bi-frequency load into a series of different orders of the difference frequency. The potential contribution to the term proportional to the difference-frequency can be evaluated efficiently by involving an integral over a small zone on the free surface around the body. In the present paper, the existing approximations are revisited and compared to analytical solution of exact second-order load on a vertical cylinder and for the case of floating body (LNG) in shallow water. Some guidelines in the practical use of different approximations will be derived.

scholarly journals Slithering CSF: Cerebrospinal Fluid Dynamics in the Stationary and Moving Viper Boa, Candoia aspera

Biology ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 672
Author(s):  
Bruce A. Young ◽  
Skye Greer ◽  
Michael Cramberg
Keyword(s):  
Cerebrospinal Fluid ◽  
Cardiac Cycle ◽  
Low Frequency ◽  
Mean Amplitude ◽  
The Body ◽  
Body Waves ◽  
Lower Amplitude ◽  
Lateral Undulation ◽  
Recovery From Anesthesia ◽  
The Relationship

In the viper boa (Candoia aspera), the cerebrospinal fluid (CSF) shows two stable overlapping patterns of pulsations: low-frequency (0.08 Hz) pulses with a mean amplitude of 4.1 mmHg that correspond to the ventilatory cycle, and higher-frequency (0.66 Hz) pulses with a mean amplitude of 1.2 mmHg that correspond to the cardiac cycle. Manual oscillations of anesthetized C. aspera induced propagating sinusoidal body waves. These waves resulted in a different pattern of CSF pulsations with frequencies corresponding to the displacement frequency of the body and with amplitudes greater than those of the cardiac or ventilatory cycles. After recovery from anesthesia, the snakes moved independently using lateral undulation and concertina locomotion. The episodes of lateral undulation produced similar influences on the CSF pressure as were observed during the manual oscillations, though the induced CSF pulsations were of lower amplitude during lateral undulation. No impact on the CSF was found while C. aspera was performing concertina locomotion. The relationship between the propagation of the body and the CSF pulsations suggests that the body movements produce an impulse on the spinal CSF.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

scholarly journals The Low-Frequency Array (LOFAR): Opening a New Window on the Universe

2002 ◽  
Vol 199 ◽  
pp. 474-483
Author(s):  
Namir E. Kassim ◽  
T. Joseph W. Lazio ◽  
William C. Erickson ◽  
Patrick C. Crane ◽  
R. A. Perley ◽  
...  
Keyword(s):  
Angular Resolution ◽  
Broad Band ◽  
Low Frequency ◽  
Electromagnetic Spectrum ◽  
Interferometric Imaging ◽  
Very Large Array ◽  
Long Wavelength ◽  
Calibration Techniques ◽  
Long Baselines ◽  
The Universe

Decametric wavelength imaging has been largely neglected in the quest for higher angular resolution because ionospheric structure limited interferometric imaging to short (< 5 km) baselines. The long wavelength (LW, 2—20 m or 15—150 MHz) portion of the electromagnetic spectrum thus remains poorly explored. The NRL-NRAO 74 MHz Very Large Array has demonstrated that self-calibration techniques can remove ionospheric distortions over arbitrarily long baselines. This has inspired the Low Frequency Array (LOFAR)—-a fully electronic, broad-band (15—150 MHz)antenna array which will provide an improvement of 2—3 orders of magnitude in resolution and sensitivity over the state of the art.

A Parametric Study of Low-Frequency Damping of Mooring System

2014 ◽  
Author(s):  
Minglu Chen ◽  
Shan Huang ◽  
Nigel Baltrop ◽  
Ji Chunyan ◽  
Liangbi Li
Keyword(s):  
Low Frequency ◽  
Structure Design ◽  
The Body ◽  
Body Motion ◽  
Mooring Line ◽  
Offshore Structure ◽  
Frequency Oscillation ◽  
Low Frequency Oscillation ◽  
Line System ◽  
Irregular Wave

Mooring line damping plays an important role to the body motion of moored floating platforms. Meanwhile, it can also make contributions to optimize the mooring line system. Accurate assessment of mooring line damping is thus an essential issue for offshore structure design. However, it is difficult to determine the mooring line damping based on theoretical methods. This study considers the parameters which have impact on mooring-induced damping. In the paper, applying Morison formula to calculate the drag and initial force on the mooring line, its dynamic response is computed in the time domain. The energy dissipation of the mooring line due to the viscosity was used to calculate mooring-induced damping. A mooring line is performed with low-frequency oscillation only, the low-frequency oscillation superimposed with regular and irregular wave-frequency motions. In addition, the influences of current velocity, mooring line pretension and different water depths are taken into account.

Drift Forces on a Floating Body of Simple Geometry Due to Second Order Interactions Between Pairs of Harmonics With Different Frequencies

2009 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Order Problem ◽  
Simple Geometry ◽  
The Mean ◽  
Order Quantities ◽  
Drift Forces

The paper presents an investigation of the slowly varying second order drift forces on a floating body of simple geometry. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom and a ratio of diameter to draft of 3.25. The hydrodynamic problem is solved with a second order boundary element method. The second order problem is due to interactions between pairs of incident harmonic waves with different frequencies, therefore the calculations are carried out for several difference frequencies with the mean frequency covering the whole frequency range of interest. Results include the surge drift force and pitch drift moment. The results are presented in several stages in order to assess the influence of different phenomena contributing to the global second order responses. Firstly the body is restrained and secondly it is free to move at the wave frequency. The second order results include the contribution associated with quadratic products of first order quantities, the total second order force, and the contribution associated to the free surface forcing.

scholarly journals The Relationship between Vibratory Sensation and Body Surface Vibration Induced by Low-Frequency Noise

2002 ◽  
Vol 21 (2) ◽  
pp. 87-100 ◽  
Author(s):  
Yukio Takahashi ◽  
Kazuo Kanada ◽  
Yoshiharu Yonekawa
Keyword(s):  
Body Surface ◽  
Mechanical Vibration ◽  
Low Frequency ◽  
The Body ◽  
Frequency Noise ◽  
Low Frequency Noise ◽  
Vibration Acceleration ◽  
Surface Vibration ◽  
Human Body Surface ◽  
The Relationship

Human body surface vibration induced by low-frequency noise was measured at the forehead, the chest and the abdomen. At the same time, subjects rated their vibratory sensation at each of these locations. The relationship between the measured vibration on the body surface and the rated vibratory sensation was examined, revealing that the vibratory sensations perceived in the chest and abdomen correlated closely with the vibration acceleration levels of the body surface vibration. This suggested that a person exposed to low-frequency noise perceives vibration at the chest or abdomen by sensing the mechanical vibration that the noise induces in the body. At the head, on the other hand, it was found that the vibratory sensation correlated comparably with the vibration acceleration level of the body surface vibration and the sound pressure level of the noise stimulus. This finding suggested that the mechanism of perception of vibration in the head is different from that of the perception of vibratory sensation in the chest and the abdomen.

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