1,721,002 research outputs found
A Bifurcation Theorem for Critical Points of Variational Problems
No full textChow, Shui-Nee; Lauterbach, R.. (1985). A Bifurcation Theorem for Critical Points of Variational Problems. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3643
Smoothness of inertial manifolds
No full textChow, Shui-Nee; Lu, Kening; Sell, George R.. (1990). Smoothness of inertial manifolds. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1397
Normal form and linearization for quasiperiodic systems
No full textChow, Shui-Nee; Lu, Kening; Shen, Yun-Qiu. (1990). Normal form and linearization for quasiperiodic systems. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/5138
Smooth invariant foliations in infinite dimensional spaces
No full textChow, Shui-Nee; Lin, Xiao-Biao; Lu, Kening. (1990). Smooth invariant foliations in infinite dimensional spaces. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1399
Adaptive iterative filtering methods for nonlinear signal analysis and applications
No full textTime-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture the changes in these types of signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods were developed by different researchers to deal with non-linear and non-stationary signals. These methods share the feature that a signal is decomposed into finite number of components on which the time-frequency analysis can be applied. Differences lie in the strategies to extract these components: by iteration or by optimization. However, considering the requirements of being local, adaptive and stable, neither of these decompositions are perfectly satisfactory. Motivated to find a local, adaptive and stable decomposition of a signal, this thesis presents Adaptive Local Iterative Filtering (ALIF) algorithm. The adaptivity is obtained having the filter lengths being determined by the signal itself. The locality is ensured by the filter we designed based on a PDE model. The stability of this algorithm is shown and the convergence is proved. Moreover, we also propose a local definition for the instantaneous frequency in order to achieve a completely local analysis for non-linear and non-stationary signals. Examples show that this decomposition
really helps in both simulated data analysis and real world application.Ph.D
Billiards and statistical mechanics
No full textIn this thesis we consider mathematical problems related to different aspects of hard sphere systems.
In the first part we study planar billiards, which arise in the context of hard sphere systems when only one or two spheres are present. In particular we investigate the possibility of elliptic periodic orbits in the general construction of hyperbolic billiards. We show that if non-absolutely focusing components are present there can be elliptic periodic orbits with arbitrarily long free paths. Furthermore, we show that smooth stadium like billiards have elliptic periodic orbits for a large range of separation distances.
In the second part we consider hard sphere systems with a large number of particles, which we model by the Boltzmann equation. We develop a new approach to derive hydrodynamic limits, which is based on classical methods of geometric singular perturbation theory of ordinary differential equations. This method provides new geometric and dynamical interpretations of hydrodynamic limits, in particular, for the of the dissipative Boltzmann equation.Ph.D
Bifurcations, Normal Forms and their Applications
No full textThe first part is a study of an ecological model with one herbivore and plants. The system has a new type of functional response due to the speculation that the plants compete with each other and have different levels of toxin which inhibit the herbivore's ability to eat up to a certain amount. We first derive the model mathematically and then investigate, both analytically and numerically, the possible dynamics for this model, including the bifurcation and chaos. We also discuss the conditions under which all the species can coexist.
The second part is a study in the normal form theory. In particular, we study the relations between the normal forms and the first integrals in analytic vector fields. We are able to generalize one of Poincare's classical results on the nonexistence of first integrals in an
autonomous system. Then in the space of 2n-dimensional analytic autonomous systems with exactly n resonances and n functionally independent first integrals, we obtain some results related to the convergence and generic divergence of the normalizations. Lastly we give a new proof of the necessary and sufficient conditions for a planar Hamiltonian system to have an isochronous center.Ph.D
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