scholarly journals Applications of Singular Perturbation Techniques to Control Problems

SIAM Review ◽  
1984 ◽  
Vol 26 (4) ◽  
pp. 501-550 ◽  
Author(s):  
Petar V. Kokotović
Keyword(s):  
Singular Perturbation ◽  
Control Problems ◽  
Perturbation Techniques

On the shape of small sessile and pendant drops by singular perturbation techniques

1991 ◽  
Vol 233 ◽  
pp. 519-537 ◽  
Author(s):  
S. B. G. O'Brien
Keyword(s):  
Boundary Layer ◽  
Singular Perturbation ◽  
Asymptotic Expansions ◽  
Numerical Results ◽  
Matched Asymptotic Expansions ◽  
Perturbation Techniques ◽  
Pendant Drop ◽  
Asymptotic Expressions ◽  
Good Agreement ◽  
Pendant Drops

The problem of obtaining asymptotic expressions describing the shape of small sessile and pendant drops is revisited. Both cases display boundary-layer behaviour and the method of matched asymptotic expansions is used to obtain solutions. These give good agreement when compared with numerical results. The sessile solutions are relatively straightforward, while the pendant drop displays a behaviour which is both rich and interesting.

scholarly journals Robust Stability of Multicomponent Membranes: the Role of Glycolipids

2019 ◽  
Author(s):  
Yuan Chen ◽  
Arjen Doelman ◽  
Keith Promislow ◽  
Frits Veerman
Keyword(s):  
Dynamical System ◽  
Singular Perturbation ◽  
Low Energy ◽  
Perturbation Techniques ◽  
Free Energies ◽  
Connecting Orbits ◽  
Amphiphilic Molecules ◽  
Membrane Type ◽  
Connecting Orbit

AbstractWe present the multicomponent functionalized free energies that characterize the low-energy packings of amphiphilic molecules within a membrane through a correspondence to connecting orbits within a reduced dynamical system. To each connecting orbits we associate a manifold of low energy membrane-type configurations parameterized by a large class of admissible interfaces. The normal coercivity of the manifolds is established through criteria depending solely on the structure of the associated connecting orbit. We present a class of examples that arise naturally from geometric singular perturbation techniques, focusing on a model that characterizes the stabilizing role of cholesterol-like glycolipids within phospholipid membranes.

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