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Time-Dependent Fluid-Structure Interaction
The problem of determining the manner in which an incoming acoustic wave is
scattered by an elastic body immersed in a fluid is one of central importance
in detecting and identifying submerged objects. The problem is generally
referred to as a fluid-structure interaction and is mathematically formulated
as a time-dependent transmission problem. In this paper, we consider a typical
fluid-structure interaction problem by using a coupling procedure which reduces
the problem to a nonlocal initial-boundary problem in the elastic body with a
system of integral equations on the interface between the domains occupied by
the elastic body and the fluid. We analyze this nonlocal problem by the Lubich
approach via the Laplace transform, an essential feature of which is that it
works directly on data in the time domain rather than in the transformed
domain. Our results may serve as a mathematical foundation for treating
time-dependent fluid-structure interaction problems by convolution quadrature
coupling of FEM and BEM
Semiquantum Chaos and the Large N Expansion
We consider the dynamical system consisting of a quantum degree of freedom
interacting with quantum oscillators described by the Lagrangian \bq L
= {1\over 2}\dot{A}^2 + \sum_{i=1}^{N} \left\{{1\over 2}\dot{x}_i^2 - {1\over
2}( m^2 + e^2 A^2)x_i^2 \right\}. \eq In the limit , with
fixed, the quantum fluctuations in are of order . In this
limit, the oscillators behave as harmonic oscillators with a time dependent
mass determined by the solution of a semiclassical equation for the expectation
value \VEV{A(t)}. This system can be described, when \VEV{x(t)}= 0, by a
classical Hamiltonian for the variables G(t) = \VEV{x^2(t)}, ,
A_c(t) = \VEV{A(t)}, and . The dynamics of this latter system
turns out to be chaotic. We propose to study the nature of this large- limit
by considering both the exact quantum system as well as by studying an
expansion in powers of for the equations of motion using the closed time
path formalism of quantum dynamics.Comment: 30 pages, uuencoded LaTeX file (figures included
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