The permutation test for positive and negative LA thresholds. (XLSX 12 kb

Xiuqin Xu (4516240)

Min Wang (21070)

Lianbo Li (3545675)

Ronghui Che (4516237)

Peng Li (69518)

Laming Pei (309174)

Hui Li (32376)

EPL (Europhysics Letters)

arXiv

FigShare

Additional file 1: Table S1. of Genome-wide trait-trait dynamics correlation study dissects the gene regulation pattern in maize kernels

Hydroelastic surface waves propagate at the surface of water covered by a thin elastic sheet and can be directly measured with accurate space and time resolution. We present an experimental approach using hydroelastic waves that allows us to control waves down to the sub-wavelength scale. We tune the wave dispersion relation by varying locally the properties of the elastic cover and we introduce a local index contrast. This index contrast is independent of the frequency leading to a dispersion-free Snell-Descartes law for hydroelastic waves. We then show experimental evidence of broadband focusing, reflection and refraction of the waves. We also investigate the limits of diffraction through the example of a macroscopic analog to optical nanojets, revealing that any sub-wavelength configuration gives access to new features for surface waves

L. Domino

M. Fermigier

E. Fort

A. Eddi

EDP Sciences OAI-PMH repository (1.2.0)

Dispersion-free control of hydroelastic waves down to sub-wavelength scale

Domino, L

Fermigier, M

Fort, E

Eddi, A

Oxford University Research Archive (ORA)

Domino, Lucie

Oxford University Research Archive

English

International audienceHydroelastic surface waves propagate at the surface of water covered by a thin elastic sheet and can be directly measured with accurate space and time resolution. We present an experimental approach using hydroelastic waves that allows us to control waves down to the sub-wavelength scale. We tune the wave dispersion relation by varying locally the properties of the elastic cover and we introduce a local index contrast. This index contrast is independent of the frequency leading to a dispersion-free Snell-Descartes law for hydroelastic waves. We then show experimental evidence of broadband focusing, reflection and refraction of the waves. We also investigate the limits of diffraction through the example of a macroscopic analog to optical nanojets, revealing that any sub-wavelength configuration gives access to new features for surface waves. Gravity-capillary waves have been extensively used as model waves to tackle the issue of wave control at macro-scopic scale. Contrary to optics and acoustics, their temporal and spatial typical scales allow for direct and accurate observation of wave propagation inside the medium. The design and fabrication of media with given properties is generally obtained by tuning the local bathymetry, which modifies the wave phase velocity [1]. Immersed structures have been used to obtain Anderson local-ization [2] or to create macroscopic metamaterials for wave focusing [3-6] and cloaking [7, 8]. Wave control is achieved for waves with wavelength larger or comparable to the liquid depth (shallow water approximation). In this regime, damping becomes a major issue in laboratory experiments as viscous friction at the bottom dissipates most of the mechanical wave energy. These two limitations narrow the effective bandwidth of the devices created with gravity-capillary waves. Here, we propose a novel approach based on hydroe-lastic waves i.e. waves that propagate at the surface of water covered with an elastic sheet. These waves were initially introduced to describe motion in ice sheets located in the marginal ice zone [9-12] and later to study floating structures [13], wakes in the lubrication approximation [14] or cloaking [15]. In the limit of thin membranes their dispersion relation writes ω 2 = gk + T ρ k 3 + D ρ k 5 tanh kh 0 , (1) where ω = 2πf is the pulsation, k = 2π/λ is the wavenumber, g = 9.81 m.s −2 is the acceleration of gravity , T is the mechanical tension in the elastic sheet, ρ is the fluid density, D is the flexural modulus of the elastic sheet and h 0 the fluid depth. The flexural modulus D = Ee 3 12(1−ν 2) depends on the Young's modulus E of the material, its Poisson modulus ν and its thickness e. Eq. 1 exhibits three distinct regimes depending on the material properties and the wave pulsation ω: gravity waves, tension waves and flexural waves. So far, very few experiments at the laboratory scale highlighted the flexural regime using whether thin elastic polymer sheets [16, 17] or granular rafts [18]. Here, we propose to achieve spatial control of the propagation of hydroelastic waves by modifying the dispersion relation (eq. 1) through local variations of the sheet's flexural modulus D. We first describe our experimental setup and verify quantitatively the prediction from eq. 1. We introduce a local index contrast using the local phase velocity. This index contrast is independent of the frequency, which allows us to define a dispersion-free Snell-Descartes law for hydroelastic waves. To show the versatility of the system we then implement more complex structures to focus wave energy and probe wave effects due to the finite size of the system. EXPERIMENTAL SETUP We use a glass tank (80 cm × 40 cm × 20 cm) filled to a depth h 0 = 16.5 cm of water. We cover its surface with a 75 cm × 35 cm wide elastic sheet of thickness e = 20-800 µm made of an optically transparent silicone rubber sheet with Young's modulus E = 1.47 ± 0.09 MPa, density ρ s = 970kg/m 3 and Poisson's ratio ν = 0.5. This elastic film floats freely at the surface of water so that the mechanical tension T inside reduces to the water surface tension T = σ = 50 mN/m. The waves are generated with a vibration exciter powered with an amplifier controlled with a waveform generator. We work with frequencies ranging from 2 to 200 Hz and with amplitudes ζ λ to ensure the waves are in the linear regime. In addition, to guarantee that we are in the thin membrane limit we check that ρ s eω 2 {Dk 4 , T k 2 , ρg}, so that equation 1 is valid. To analyze quantitatively the wave field we use the Free-Surface Synthetic Schlieren optical technique [19] based on the apparent displacement of a random dot pattern due to the local slope of the interface. The pattern is located underneath the tank and we observe it from the top using a CCD camera located at H 2 m from th

Fermigier, M.

Fort, E.

Eddi, A.

Hal-Diderot

Dispersion free control of hydroelastic waves down to sub-wavelength scale

Crossref

https://figshare.com/articles/Additional_file_1_Table_S1_of_Genome-wide_trait-trait_dynamics_correlation_study_dissects_the_gene_regulation_pattern_in_maize_kernels/5504398

Additional file 1: Table S1. of Genome-wide trait-trait dynamics correlation study dissects the gene regulation pattern in maize kernels

Abstract

Similar works

Full text