Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics

2021 ◽  
Vol 84 (1) ◽  
Author(s):  
Christopher E. Overton ◽  
Robert R. Wilkinson ◽  
Adedapo Loyinmi ◽  
Joel C. Miller ◽  
Kieran J. Sharkey
Keyword(s):  
Author(s):  
Oleksandr Barannyk ◽  
Peter Oshkai

Spinning behaviour of diametral acoustic modes associated with self-sustained flow oscillations in a deep, axisymmetric cavity located in a long pipeline was investigated experimentally. High-amplitude pressure fluctuations resulted from the excitation of the diametral acoustic modes by the fully-turbulent flow in the pipeline. The unsteady pressure was measured at three equally spaced azimuthal locations at the bottom of the cavity. This arrangement allowed calculation of the azimuthal orientation of the acoustic modes, which were classified as stationary, partially spinning or spinning. Introduction of shallow chamfers to the upstream and the downstream edges of the cavity resulted in changes of azimuthal orientation and spinning behaviour of the acoustic modes. In addition, introduction of splitter plates in the cavity led to pronounced change in the spatial orientation and the spinning behaviour of the acoustic modes. The short splitter plates changed the behaviour of the dominant acoustic modes from partially spinning to stationary, while the long splitter plates enforced the stationary behaviour across all resonant acoustic modes.


1971 ◽  
Vol 8 (04) ◽  
pp. 708-715 ◽  
Author(s):  
Emlyn H. Lloyd

The present theory of finite reservoirs is not rich in general theorems even when of the simple Moran type, with unit draft and stationary discrete independent-sequence inflows. For the corresponding systems with unbounded capacity however there are two classes of results which have been known for some time. One of these classes is concerned with the time-dependent solution, where the theory provides a functional equation for the generating function of the time to first emptiness (Kendall (1957)), and the other with the asymptotic stationary distribution of reservoir contents, for which an explicit formula for the generating function is available (Moran (1959)).


1974 ◽  
Vol 11 (4) ◽  
pp. 726-741 ◽  
Author(s):  
Richard. L. Tweedie

The quasi-stationary behaviour of a Markov chain which is φ-irreducible when restricted to a subspace of a general state space is investigated. It is shown that previous work on the case where the subspace is finite or countably infinite can be extended to general chains, and the existence of certain quasi-stationary limits as honest distributions is equivalent to the restricted chain being R-positive with the unique R-invariant measure satisfying a certain finiteness condition.


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