Change in Global Behavior: Bifurcation

1991 ◽  
pp. 111-152
Author(s):  
Huijun Yang
Keyword(s):  
Global Behavior

Motion of Active Fluids: Diffusion Dynamics of Cyanobacteria

2016 ◽  
Author(s):  
Thomas Vourc’h ◽  
Julien Léopoldès ◽  
Annick Méjean ◽  
Hassan Peerhossaini
Keyword(s):  
Time Lapse ◽  
Global Behavior ◽  
Diffusion Dynamics ◽  
Mean Squared Displacement ◽  
Terrestrial Environments ◽  
The Mean ◽  
Micro Organisms ◽  
Synechocystis Sp ◽  
Time Lapse Video ◽  
Pcc 6803

Cyanobacteria are photosynthetic micro-organisms colonizing all aquatic and terrestrial environments. The motility of such living micro-organisms should make their diffusion distinct from typical Brownian motion. This diffusion can be investigated in terms of global behavior (Fickian or not) and in terms of displacement probabilities, which provide more detail about the motility process. Using cyanobacterium Synechocystis sp. PCC 6803 as the model micro-organism, we carry out time-lapse video microscopy to track and analyze the bacteria’s trajectories, from which we compute the mean-squared displacement (MSD) and the distribution function of displacement probabilities. We find that the motility of Synechocystis sp. PCC 6803 is intermittent: high-motility “run” phases are separated by low-motility “tumble” phases corresponding to trapped states. However, this intermittent motility leads to a Fickian diffusive behavior, as shown by the evolution of the MSD with time.

scholarly journals The Global Behavior of a Periodic Epidemic Model with Travel between Patches

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Luosheng Wen ◽  
Bin Long ◽  
Xin Liang ◽  
Fengling Zeng
Keyword(s):  
Epidemic Model ◽  
Transmission Rate ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Periodic Transmission ◽  
Theoretical Results ◽  
Disease Free

We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratioR0and two theorems on the global behavior: ifR0< 1 the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then it is unstable; ifR0> 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.

Effects of Wheel-Shaft-Fluid Coupling and Local Wheel Deformations on the Global Behavior of Shaft Lines

2002 ◽  
Vol 124 (4) ◽  
pp. 953-957 ◽  
Author(s):  
D. Lornage ◽  
E. Chatelet ◽  
G. Jacquet-Richardet
Keyword(s):  
Three Dimensional ◽  
Fluid Film ◽  
Global Behavior ◽  
Three Dimensional Model ◽  
Fluid Films ◽  
Strongly Coupled ◽  
Proposed Model ◽  
Structural Deformations ◽  
Time Marching ◽  
Fluid Coupling

Rotating parts of turbomachines are generally studied using different uncoupled approaches. For example, the dynamic behavior of shafts and wheels are considered independently and the influence of the surrounding fluid is often taken into account in an approximate way. These approaches, while often sufficiently accurate, are questionable when wheel-shaft coupling is observed or when fluid elements are strongly coupled with local structural deformations (leakage flow between wheel and casing, fluid bearings mounted on a thin-walled shaft, etc.). The approach proposed is a step toward a global model of shaft lines. The whole flexible wheel-shaft assembly and the influence of specific fluid film elements are considered in a fully three-dimensional model. In this paper, the proposed model is first presented and then applied to a simple disk-shaft assembly coupled with a fluid film clustered between the disk and a rigid casing. The finite element method is used together with a modal reduction for the structural analysis. As thin fluid films are considered, the Reynolds equation is solved using finite differences in order to obtain the pressure field. Data are transferred between structural and fluid meshes using a general method based on an interfacing grid concept. The equations governing the whole system are solved within a time-marching procedure. The results obtained show significant influence of specific three-dimensional features such as disk-shaft coupling and local disk deformations on global behavior.

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