| 1. |
- Fredriksson, M. H., et al.
(author)
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On normal form calculations in impact oscillators
- 2000
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In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 456:1994, s. 315-329
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Journal article (peer-reviewed)abstract
- Normal form calculations are useful for analysing the dynamics close to bifurcations. However, the application to non-smooth systems is a topic for current research. Here we consider a class of impact oscillators, where we allow systems with several degrees of freedom as well as nonlinear equations of motion. Impact is due to the motion of one body, constrained by a motion limiter. The velocities of the system are assumed to change instantaneously at impact. By defining a discontinuity mapping, we show how Poincare mappings can be obtained as an expansion in a local coordinate. This gives the mapping the desired form, thus making it possible to employ standard techniques. All calculations are algorithmic in spirit, hence computer algebra routines can easily be developed.
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| 2. |
- Kozlov, Vladimir, et al.
(author)
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On the two-dimensional sloshing problem
- 2004
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In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 460:2049, s. 2587-2603
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Journal article (peer-reviewed)abstract
- We study an eigenvalue problem with a spectral parameter in a boundary condition. This problem for the two-dimensional Laplace equation is relevant to sloshing frequencies that describe free oscillations of an inviscid, incompressible, heavy fluid in a canal having uniform cross-section and bounded from above by a horizontal free surface. It is demonstrated that there exist domains such that at least one of the eigenfunctions has a nodal line or lines with both ends on the free surface (earlier, Kuttler tried to prove that there are no such nodal lines for all domains but his proof is erroneous). It is also shown that the fundamental eigenvalue is simple, and for the corresponding eigenfunction the behaviour of the nodal line is characterized. For this purpose, a new variational principle is proposed for an equivalent statement of the sloshing problem in terms of the conjugate stream function. © 2004 The Royal Society.
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| 3. |
- Landen, Camilla
(author)
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Finite-dimensional Markovian realizations for stochastic volatility forward-rate models
- 2004
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In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 460:2041, s. 53-83
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Journal article (peer-reviewed)abstract
- We consider forward-rate models of Heath-Jarrow-Morton type, as well as more general infinite-dimensional stochastic differential equations, where the volatility-diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework, we use the previously developed Hilbert-space-realization theory in order to provide general necessary and sufficient conditions for the existence of a finite-dimensional Markovian realization for the stochastic volatility models. We illustrate the theory by analysing a number of concrete examples.
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