• 유변학
• /
• 제8권1호
• /
• pp.39-48
• /
• 1996

최근에 본 연구자에 의하여 기존 스크류의 간단한 수정을 통해 단축 압출공정에서 의 혼합성능을 증진시키는 카오스 스크류를 개발하였고, 단축압출기에서의 기존스크류와 비 교하여 카오스 스크류를 사용하였을 경우 혼합성능이 월등하게 증진됨을 실험적으로 얻은 혼합형태로부터 알수 있었다. 본논문에서는 카오스 스크류에서 일어나는 카오스 유동을 집 중적으로 수치모사 하였으며 그결과를 중요한 무차원 변수에 대하여 입자 궤적,포인카레 단 면 본 논문에서 제안한 쉘사상법을 통하여 나타내었다. 쉘사사아법은 혼합형태와 불변체군 을 얻기에 매우 효과적인 방법이며 수치해석으로 얻은 불변체군은 실험결과와 잘 일치하였다.

• 한국전산유체공학회지
• /
• 제20권4호
• /
• pp.58-62
• /
• 2015

Recent studies on wall-bounded shear flow have emphasized the significance of the stable manifold of simple nonlinear invariant solutions to the Navier-Stokes equation in the formation of the boundary between the laminar and turbulent regions in state space. In this paper we present newly discovered homoclinic orbits of the Kawahara and Kida(2001) periodic solution in plane Couette flow. We show that as the Reynolds number decreases a pair of homoclinic orbits move closer to each other until they disappear to exhibit homoclinic tangency.

• 대한수학회논문집
• /
• 제24권1호
• /
• pp.127-144
• /
• 2009

Let f be a diffeomorphism of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper we introduce the notion of $C^1$-stable inverse shadowing for a closed f-invariant set, and prove that (i) the chain recurrent set $\cal{R}(f)$ of f has $C^1$-stable inverse shadowing property if and only if f satisfies both Axiom A and no-cycle condition, (ii) $C^1$-generically, the chain component $C_f(p)$ of f associated to p is hyperbolic if and only if $C_f(p)$ has the $C^1$-stable inverse shadowing property.

• 충청수학회지
• /
• 제33권2호
• /
• pp.237-253
• /
• 2020

This article studies asymptotic stability of non-auto nomous linear systems with time-dependent coefficient matrices {A(t)}_t∈ℝ. The classical theorem of Levinson has been widely used to science and engineering non-autonomous systems, but systems with defective eigenvalues could not be covered because such a family does not allow continuous diagonalization. We study systems where the family allows to have upper triangulation and to have defective eigenvalues. In addition to the wider applicability, working with upper triangular matrices in place of Jordan form matrices offers more flexibility. We interpret our and earlier works including Levinson's theorem from the perspective of invariant manifold theory.

• 대한수학회지
• /
• 제59권2호
• /
• pp.337-352
• /
• 2022

We consider the set of points with historic behavior (which is also called the irregular set) for continuous flows and suspension flows. In this paper under the hypothesis that (X_t)_t is a continuous flow on a d-dimensional Riemaniann closed manifold M (d ≥ 2) with gluing orbit property, we prove that the set of points with historic behavior in a compact and invariant subset ∆ of M is either empty or is a Baire residual subset on ∆. We also prove that the set of points with historic behavior of a suspension flows over a homeomorphism satisfyng the gluing orbit property is either empty or Baire residual and carries full topological entropy.