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• W1503670406 abstract "We present spectral and scattering theories for a differential operator with a dissipation term that can be used to describe the dynamics of a tectonic plate with dissipative boundary conditions. The generating operator is non-selfadjoint causing some additional complexity. This difficulty has been overcome by developing the selfadjoint-dilation theory. We develop a functional model for the dissipative operator and the associated scattering theory of Lax-Phillips type. 1. Structure & dynamics of tectonic plates. By now the naive idea of the Earth as a hard body is viewed as far from reality. In fact the Earth is similar to an egg with a cracked shell. This shell - the lithosphere - is com- posed of numerous fragments - the most part covered by 14 large fragments, the tectonic plates. The scale of these large tectonic plates varies within a range of several thousand kilometers and bodies of neighboring plates contact directly along relatively small active zones with diameters of about 100 km. Along the remainder of the boundaries, neighbor- ing tectonic plates are often separated by relatively nar- row channels are filled with smaller fragments and disperse materials which cannot accumulate significant amounts of elastic energy, and so transform it into heat, causing the dissipation of stored elastic energy in the form of seismo- gravitational oscillations (SGO). These SGOs admit spec- tral interpretation, see (21, 44) and our discussion below. Tectonic plates are relatively thin (30-100 km thick) under the oceans, but are thicker (200-300 km) on the ancient continental platforms and along the oceanic ridges. The elastic properties of the plates are determined by Young's modulus 17.28 × 10 10 kg m −1 sec −2 , density 3380 kg m −3 and the Poisson coefficient 0.28. The velocity of longi- tudinal waves on the plates is about 8000 m sec −1 , and the velocity of the flexural waves depends on the frequency and varies, with the type of the wave, on a wide range around 4500 m sec −1 . The tectonic plates float on the as- tenosphere. The viscosity of the astenosphere is large for fast motions, but relatively small for slow ones. The exterior dynamics of the tectonic plates is defined by their sliding along the astenosphere (with liquid friction) by convective flows in the Earth's mantle and also due to changes of the rotation speed of Earth caused by fluctu- ations in the moment of inertia. Both factors are caused by irregularities in the energy dissappation from the liq- uid upper core (see §4). Though forced oscillations may be present in the tectonic system most of the elastic dynamics are defined by the SGO of the plates caused by variation of the strain-stress conditions at the active zones. These elastic properties of the plates can be described in terms of thin plate models floating on a liquid with appropriate boundary conditions analogous to the model of floating ice, see (10). Here we base our observations on the assump- tion of the spectral nature of SGO, see (21, 44). This is" @default.
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• W1503670406 date "2012-10-01" @default.
• W1503670406 modified "2023-09-27" @default.
• W1503670406 title "A zero-range model for localized boundary stress on a tectonic plate with dissipative boundary conditions" @default.
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