A Whitham–Boussinesq long-wave model for variable topography

Wave Motion ◽  
2016 ◽  
Vol 65 ◽  
pp. 156-174 ◽  
Author(s):  
R.M. Vargas-Magaña ◽  
P. Panayotaros
Keyword(s):  
Wave Model ◽  
Long Wave ◽  
Variable Topography

scholarly journals Far-infrared bands in plasmonic metal-insulator-metal absorbers optimized for long-wave infrared

MRS Advances ◽  
2019 ◽  
Vol 4 (11-12) ◽  
pp. 667-674 ◽  
Author(s):  
Rachel N. Evans ◽  
Seth R. Calhoun ◽  
Jonathan R. Brescia ◽  
Justin W. Cleary ◽  
Evan M. Smith ◽  
...  
Keyword(s):  
Ground Plane ◽  
Wavelength Region ◽  
Wave Model ◽  
Far Infrared ◽  
Resonance Wavelength ◽  
Surface Structures ◽  
Metal Insulator ◽  
Long Wave ◽  
Metal Insulator Metal ◽  
Long Wave Infrared

ABSTRACTMetal–insulator–metal (MIM) resonant absorbers comprise a conducting ground plane, a dielectric of thickness t, and thin separated metal top-surface structures of dimension l. The fundamental resonance wavelength is predicted by an analytic standing-wave model based on t, l, and the dielectric refractive index spectrum. For the dielectrics SiO2, AlN, and TiO2, values for l of a few microns give fundamental resonances in the 8-12 μm long-wave infrared (LWIR) wavelength region. Agreement with theory is better for t/l exceeding 0.1. Harmonics at shorter wavelengths were already known, but we show that there are additional resonances in the far-infrared 20 - 50 μm wavelength range in MIM structures designed to have LWIR fundamental resonances. These new resonances are consistent with the model if far-IR dispersion features in the index spectrum are considered. LWIR fundamental absorptions are experimentally shown to be optimized for a ratio t/l of 0.1 to 0.3 for SiO2- and AlN-based MIM absorbers, respectively, with TiO2-based MIM optimized at an intermediate ratio.

Periodic travelling waves for a generalized long wave model

2015 ◽  
Vol 9 ◽  
pp. 6747-6756
Author(s):  
Alex M. Montes ◽  
Ricardo Cordoba
Keyword(s):  
Travelling Waves ◽  
Wave Model ◽  
Long Wave

An integrable equation governing short waves in a long-wave model

2007 ◽  
Vol 463 (2084) ◽  
pp. 1939-1954 ◽  
Author(s):  
M Faquir ◽  
M.A Manna ◽  
A Neveu
Keyword(s):  
Surface Tension ◽  
Gordon Equation ◽  
Wave Model ◽  
Short Wave ◽  
Lax Pair ◽  
Integrable Equation ◽  
Conserved Quantities ◽  
Long Wave ◽  
Tension Term ◽  
Wave Limit

The dynamics of a nonlinear and dispersive long surface capillary-gravity wave model equation is studied analytically in its short-wave limit. We exhibit its Lax pair and some non-trivial conserved quantities. Through a change of functions, an unexpected connection between this classical surface water-wave model and the sine-Gordon (or sinh-Gordon) equation is established. Numerical and analytical studies show that in spite of integrability their solutions can develop singularities and multivaluedness in finite time. These features can be traced to the fact that the surface tension term in the energy involves second-order derivatives. It would be interesting to see in an experiment whether such singularities actually appear, for which surface tension would be specifically responsible.

A long-wave model for the surface elastic wave in a coated half-space

2010 ◽  
Vol 466 (2122) ◽  
pp. 3097-3116 ◽  
Author(s):  
H.-H. Dai ◽  
J. Kaplunov ◽  
D. A. Prikazchikov
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Half Space ◽  
Elliptic Equations ◽  
Ad Hoc ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Wave Model ◽  
Destructive Testing ◽  
Long Wave

The paper deals with the three-dimensional problem in linear isotropic elasticity for a coated half-space. The coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long-wave limit. An explicit model is derived for the surface wave using the perturbation technique, along with the theory of harmonic functions and Radon transform. The model consists of three-dimensional ‘quasi-static’ elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two-dimensional hyperbolic equation singularly perturbed by a pseudo-differential (or integro-differential) operator. The latter equation governs dispersive surface wave propagation, whereas the elliptic equations describe spatial decay of displacements and stresses. As an illustration, the dynamic response is calculated for impulse and moving surface loads. The explicit analytical solutions obtained for these cases may be used for the non-destructive testing of the thickness of the coating and the elastic moduli of the substrate.

scholarly journals Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves

2018 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Omid Nikan ◽  
◽  
Seyedeh Mahboubeh Molavi-Arabshai ◽  
Hossein Jafari ◽  
◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Wave Model ◽  
Plasma Waves ◽  
Long Wave ◽  
Ion Acoustic

scholarly journals Two-dimensional pulse dynamics and the formation of bound states on electrified falling films

2018 ◽  
Vol 855 ◽  
pp. 210-235 ◽  
Author(s):  
M. G. Blyth ◽  
D. Tseluiko ◽  
T.-S. Lin ◽  
S. Kalliadasis
Keyword(s):  
Electric Field ◽  
Bound States ◽  
Stokes Equations ◽  
Travelling Waves ◽  
Film Surface ◽  
Wave Model ◽  
Bound State ◽  
Long Wave ◽  
Finite Set ◽  
Solitary Pulse

The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. For obtuse angles, gravity is destabilising and solitary pulses exist even in the absence of an electric field. For acute angles, spatially non-uniform solutions exist only beyond a critical value of the electric field strength; moreover, solitary-pulse solutions are present only at sufficiently high supercritical electric-field strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.

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