Singular perturbation techniques in the study of a dynamical system arising from the kinetic theory of atoms and photons

1998 ◽  
Vol 96 (1) ◽  
pp. 47-63 ◽  
Author(s):  
R. Riganti ◽  
A. Rossani
Keyword(s):  
Dynamical System ◽  
Kinetic Theory ◽  
Singular Perturbation ◽  
Perturbation Techniques

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.

Perturbation Analysis of Diffeomorphisms in Contact Dynamical System

2012 ◽  
Vol 529 ◽  
pp. 264-267
Author(s):  
Da Wei Sun
Keyword(s):  
Dynamical System ◽  
Perturbation Analysis ◽  
Contact System ◽  
Hamiltonian Mechanics ◽  
Perturbation Techniques ◽  
Small Perturbations

This paper studies the perturbations of strictly contact diffeomorphisms in contact dynamical system. By constructing new lifting methods for contact system and using some perturbation techniques in Hamiltonian mechanics, this paper proves that there exists an arbitrary small perturbations such that the corresponding function of the strictly contact isotopy does not equal to a constant at any time.

scholarly journals Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Masatomo Iwasa
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Singular Perturbation ◽  
Symmetry Group ◽  
Group Analysis ◽  
Lie Symmetry ◽  
Symmetry Groups ◽  
Lie Group Analysis ◽  
Constraint Equations ◽  
Perturbation Problems

Lie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. This extension makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics describing the asymptotic behavior.

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.

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