A theoretical study is made of the nonlinear wave loading on offshore structures using the diffraction theory of hydrodynamics. A nonlinear modification of the classical Morison equation, D F + FD for estimating wave forces on offshore structures is suggested in this paper. The modified equation is found in the form D F% + Fn% + D where Fn -= Fd + F + F is the nonlinear contriw q bution made up...

The propagation of surface waves in a fluid- saturated porous isotropic layer over a semi-infinite homogeneous elastic medium with an irregularity for free and rigid interfaces have been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for Love waves is derived by simple mathematical techniques followed by Fourier transformations.  It can be seen t...

A general theory for fiber-optic, evanescent-wave spectroscopy and sensors is presented for straight, uncladded, step-index, multimode fibers. A three-dimensional model is formulated within the framework of geometric optics. The model includes various launching conditions, input and output end-face Fresnel transmission losses, multiple Fresnel reflections, bulk absorption, and evanescent-wave a...

We begin by considering the one-dimensional analogue of Kac's question: a vibrating string of length L. Idealize this string by the interval [0,L] and represent the possible configuration of the vibrating string as a function f(x,t) defined for x (the position variable) in [0,L] and any non-negative number t (the time variable). Since the endpoints are fixed, f must satisfy the boundary conditi...

An extended Burgers' enuation, suitable for media which exhibit both thermoviscous acoustic absorption as well as various mechanisms °f relaxational absorption, is presented. The equation is applied to the specific problem or piane wave propagation through an air-water fog, a medium which contains relaxation sources arising both from gas molecular motions and from mass, momentum, and energy tra...

If A q (β, α, k) is the scattering amplitude, corresponding to a potential q ∈ L 2 (D), where D ⊂ R 3 is a bounded domain, and e ikα·x is the incident plane wave, then we call the radiation pattern the function A(β) := A q (β, α, k), where the unit vector α, the incident direction, is fixed, and k > 0, the wavenumber, is fixed. It is shown that any function f (β) ∈ L 2 (S 2), where S 2 is the u...

If Aq(β, α, k) is the scattering amplitude, corresponding to a potential q ∈ L 2(D), where D ⊂ R3 is a bounded domain, and eikα·x is the incident plane wave, then we call the radiation pattern the function A(β) := Aq(β, α, k), where the unit vector α, the incident direction, is fixed, and k > 0, the wavenumber, is fixed. It is shown that any function f(β) ∈ L2(S2), where S2 is the unit sphere i...

If A q (β, α, k) is the scattering amplitude, corresponding to a potential q ∈ L 2 (D), where D ⊂ R 3 is a bounded domain, and e ikα·x is the incident plane wave, then we call the radiation pattern the function A(β) := A q (β, α, k), where the unit vector α, the incident direction, is fixed, and k > 0, the wavenumber, is fixed. It is shown that any function f (β) ∈ L 2 (S 2), where S 2 is the u...

If A q (β, α, k) is the scattering amplitude, corresponding to a potential q ∈ L 2 (D), where D ⊂ R 3 is a bounded domain, and e ikα·x is the incident plane wave, then we call the radiation pattern the function A(β) := A q (β, α, k), where the unit vector α, the incident direction, is fixed, and k > 0, the wavenumber, is fixed. It is shown that any function f (β) ∈ L 2 (S 2), where S 2 is the u...