Elastic capsule deformation in general irrotational linear flows

AbstractAverages of functionals along trajectories are studied by evaluating the averages along chains. This yields results for the possible limits and, in particular, for ergodic limits. Applications to Lyapunov exponents and to concepts of rotation numbers of linear Hamiltonian flows and of general linear flows are given.

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The Davey-Stewartson equation and constrained linear flows

Physica D Nonlinear Phenomena ◽

10.1016/0167-2789(95)00153-u ◽

1995 ◽

Vol 87 (1-4) ◽

pp. 99-104 ◽

Cited By ~ 1

Author(s):

Francisco Guil ◽

Manuel Mañas

Keyword(s):

Linear Flows

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Linear flows on compact, semisimple Lie groups: stability and periodic orbits

Electronic journal of qualitative theory of differential equations ◽

10.14232/ejqtde.2021.1.84 ◽

2021 ◽

pp. 1-12

Author(s):

Simão Stelmastchuk

Keyword(s):

Lie Groups ◽

Periodic Orbits ◽

Semisimple Lie Groups ◽

Linear Flows ◽

The Stability

Our first purpose is to study the stability of linear flows on real, connected, compact, semisimple Lie groups. Our second purpose is to study periodic orbits of linear and invariant flows. As an application, we present periodic orbits of linear or invariant flows on SO(3) and SU(2) and we study periodic orbits of linear or invariant flows on SO(4).

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Effect of membrane bending stiffness on the deformation of capsules in simple shear flow

Journal of Fluid Mechanics ◽

10.1017/s0022112001004657 ◽

2001 ◽

Vol 440 ◽

pp. 269-291 ◽

Cited By ~ 174

Author(s):

C. POZRIKIDIS

Keyword(s):

Curvature Tensor ◽

Deformation Gradient ◽

Bending Stiffness ◽

Boundary Element Methods ◽

Simple Shear Flow ◽

Normal Vector ◽

Membrane Thickness ◽

Bending Moments ◽

Balance Equations ◽

Capsule Deformation

The effect of interfacial bending stiffness on the deformation of liquid capsules enclosed by elastic membranes is discussed and investigated by numerical simulation. Flow-induced deformation causes the development of in-plane elastic tensions and bending moments accompanied by transverse shear tensions due to the non-infinitesimal membrane thickness or to a preferred configuration of an interfacial molecular network. To facilitate the implementation of the interfacial force and torque balance equations involving the hydrodynamic traction exerted on either side of the interface and the interfacial tensions and bending moments developing in the plane of the interface, a formulation in global Cartesian coordinates is developed. The balance equations involve the Cartesian curvature tensor defined in terms of the gradient of the normal vector extended off the plane of the interface in an appropriate fashion. The elastic tensions are related to the surface deformation gradient by constitutive equations derived by previous authors, and the bending moments for membranes whose unstressed shape has uniform curvature, including the sphere and a planar sheet, arise from a constitutive equation that involves the instantaneous Cartesian curvature tensor and the curvature of the resting configuration. A numerical procedure is developed for computing the capsule deformation in Stokes flow based on standard boundary-element methods. Results for spherical and biconcave resting shapes resembling red blood cells illustrate the effect of the bending modulus on the transient and asymptotic capsule deformation and on the membrane tank-treading motion.

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