• Title/Summary/Keyword: Bifurcation

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The Numerical study for flow characteristics of bifurcation in blood vessel (혈관 분지부의 유동 특성에 대한 수치해석 연구)

  • Lee, In-Sub;Ryou, Hong-Sun
    • Proceedings of the KSME Conference
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    • 2003.11a
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    • pp.741-746
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    • 2003
  • The main objective of present study is to obtain information for flow characteristics, such as velocity and wall shear stress, of bifurcation in blood vessel. Branch flows for Newtonian fluids are simulated by using Fluent V.6.0. The numerical simulations are carried out for five cases divided by different values of bifurcation angle and area ratio. As a result of simulation, high wall shear stress is appeared at the bifurcated region. As increasing bifurcation angle, pressure drop is increasing. In addition, as the area is decreasing, pressure drop and wall shear stress is increasing.

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Global Periodic Solutions in a Delayed Predator-Prey System with Holling II Functional Response

  • Jiang, Zhichao;Wang, Hongtao;Wang, Hongmei
    • Kyungpook Mathematical Journal
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    • v.50 no.2
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    • pp.255-266
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    • 2010
  • We consider a delayed predator-prey system with Holling II functional response. Firstly, the paper considers the stability and local Hopf bifurcation for a delayed prey-predator model using the basic theorem on zeros of general transcendental function, which was established by Cook etc.. Secondly, special attention is paid to the global existence of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf bifurcation result due to Wu, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Finally, several numerical simulations supporting the theoretical analysis are given.

A Study of Head Loss with Geometry Modification of Bifurcation (수압 분기관 형상 변화에 따른 수두손실 고찰)

  • Kang, Seung-Kyu;Yoon, Joon-Yong;Kang, Sin-Hyoung;Sung, Nak-Won
    • 유체기계공업학회:학술대회논문집
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    • 2005.12a
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    • pp.789-795
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    • 2005
  • This study proposes a modified bifurcation model with a computational fluid analysis according to variation of a bifurcation geometry. FLUENT is used for a calculation of the head losses in case of a generation and a pumping. The pressure, velocity field and turbulent intensity are simulated in a bifurcation. With consideration about these flow properties, we propose the modified model to improve a flow efficiency and reduce a sound. The proposed model is able to cut down a head loss by 45% when a generation and 36% when a pumping.

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A Construction of the Principal Period-2 Component in the Degree-9 Bifurcation Set with Parametric Boundaries (9차 분기집합의 2-주기 성분의 경계방정식에 관한 연구)

  • Geum, Young-Bee
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.7 no.6
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    • pp.1421-1424
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    • 2006
  • By extending the Mandelbrot set for the complex polynomial $$M={c\in C\;:\; _{k\rightarrow\infty}^{lim}P_c^k(0)\;{\neq}\;{\infty}$$ we define the degree-n bifurcation set. In this paper, we formulate the boundary equation of a period-2 component on the main component in the degree-9 bifurcation set by parameterizing its image. We establish an algorithm constructing a period-2 component in the degree-9 bifurcation set and the typical implementations show the satisfactory result with Mathematica codes grounded on the analysis.

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Discretization of laser model with bifurcation analysis and chaos control

  • Qamar Din;Waqas Ishaque;Iqra Maqsood;Abdelouahed Tounsi
    • Advances in nano research
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    • v.15 no.1
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    • pp.25-34
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    • 2023
  • This paper investigates the dynamics and stability of steady states in a continuous and discrete-time single-mode laser system. By using an explicit criteria we explored the Neimark-Sacker bifurcation of the single mode continuous and discrete-time laser model at its positive equilibrium points. Moreover, we discussed the parametric conditions for the existence of period-doubling bifurcations at their positive steady states for the discrete time system. Both types of bifurcations are verified by the Lyapunov exponents, while the maximum Lyapunov ensures chaotic and complex behaviour. Furthermore, in a three-dimensional discrete-time laser model, we used a hybrid control method to control period-doubling and Neimark-Sacker bifurcation. To validate our theoretical discussion, we provide some numerical simulations.

Impact of the geometric properties of intracranial vascular bifurcation and the mechanism of aneurysm occurrence and rupture

  • Liu, Jun;Zhang, Qingyun;Chen, Hua
    • Advances in nano research
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    • v.13 no.4
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    • pp.379-391
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    • 2022
  • One factor that can heighten the risk of the rapture intracranial aneurysm (IA) is bifurcations, which can cause the IA to evaluate. This study presents the effect of geometric of intracranial vascular on the bifurcation analysis of the aneurysm occurrence. The aneurysm mechanism is mathematically modeled based on the nano pipe structures under the thermal stresses, and the impact of the aneurysm geometric on the stability and bifurcation points is analyzed. Because of the dimension of these structures, the classical theories could not predict their behavior perfectly, so the nonclassical and nonlocal theories are required for the mechanical modeling of the aneurysm. The presented results show that the bifurcation point of the aneurysm mechanism is dependent on the environment temperature, and the temperature change plays an essential role in the stability of these structures.

Characteristics of Bifurcation Phenomena of Symmetric Flow Pattern in a Plane Sudden-Expansion Flow (평면급확장유동내 대칭유동분기현상의 특성에 관한 연구)

  • Cho, Jin-Ho;Lee, Moon-J.;Kim, Ki-Tae
    • Proceedings of the KSME Conference
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    • 2001.06e
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    • pp.33-38
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    • 2001
  • Bifurcation of unstable symmetric flow patterns to stable asymmetric ones in laminar sudden-expansion flow has been numerically investigated. Computations were carried out for an expansion ratio of 3 and over a range of the flow Reynolds numbers by using numerical methods of second-order time accuracy and a fractional-step method that guarantees divergence-free flowfields at all times. The critical Reynolds number above which bifurcation of pitchfork type to asymmetric flow pattern takes place is lower in a flow with a higher expansion ratio, in agreement with the previously reported results. The bifurcation diagrams show that the bifurcation takes place at a Reynolds number, $Re_c = 86.3$, higher than the value that has been reported. The lower critical Reynolds number may be due to deficiencies in their computations which employed SIMPLE-type relaxation methods rather than the initial-value approach of the present study. Characteristics of the flow development during the transition to asymmetric stable flow have been investigated by using spectral analysis of the velocity signals obtained by the simulations.

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Numerical investigation on the bifurcation of natural convection in a horizontal concentric annulus (수평동심환상공간내 자연대류의 다중해에 관한 수치적 연구)

  • Jeong, Jae-Dong;Kim, Chan-Jung;Lee, Jun-Sik;Yu, Ho-Seon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.21 no.2
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    • pp.252-263
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    • 1997
  • Steady-state two-dimensional natural convective heat transfer in horizontal cylindrical annuli was studied by solving the governing equations based on the primitive variables. Emphasis was put on the occurrence of the multiple solutions at a given set of parameter values, and on the determination of the bifurcation points at which those multiple solutions begin to branch out. The multicellular flow pattern from the results of melting process in an isothermally heated horizontal cylinder for high Rayleigh numbers, was used as initial guesses for the field variables. This was succeeded in new bifurcation point to tetracellular solutions for an identical set of parameter variables of previous works. The close examination of flow pattern transition around bifurcation point was also conducted. It was found that the mechanisms of flow transition are different depending on the critical Rayleigh number of bifurcation point.

On Constructing Fractal Sets Using Visual Programming Language (Visual Programming을 활용한 Fractal 집합의 작성)

  • Geum Young Hee;Kim Young Ik
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.3 no.3
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    • pp.177-182
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    • 2002
  • In this paper, we present a mathematical theory and algorithm consoucting some fractal sets. Among such fractal sets, the degree-n bifurcation set as well as the Julia sets is defined by extending the concept of the Mandelbrot set to the complex polynomial $Z^n$+c($c{\epsilon}C$, $n{\ge}2$). Some properties of the degree-n bifurcation set and the Julia sets have been theoretically investigated including the symmetry, periodicity, boundedness, and connectedness. An efficient algorithm constructing both the degree-n bifurcation let and the Julia sets is proposed using theoretical results. The mouse-operated software called "MANJUL" has been developed for the effective construction of the degree-n bifurcation set and the Julia sets in graphic environments with C++ programming language under the windows operating system. Simple mouse operations can construct ann magnify the degree-n bifurcation set as well af the Julia sets. They not only compute the component period but also save the images of the degree-n bifurcation set and the Julia sets to visually confirm various properties and the geometrical structure of the sets. A demonstration has verified the useful versatility of MANJUL.of MANJUL.

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A Development of Analytical Strategies for Elastic Bifurcation Buckling of the Spatial Structures (공간구조물의 탄성 분기좌굴해석을 위한 수치해석 이론 개발)

  • Lee, Kyung Soo;Han, Sang Eul
    • Journal of Korean Society of Steel Construction
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    • v.21 no.6
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    • pp.563-574
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    • 2009
  • This paper briefly describes the fundamental strategies--path-tracing, pin-pointing, and path-switching--in the computational elastic bifurcation theory of geometrically non-linear single-load-parameter conservative elastic spatial structures. The stability points in the non-linear elasticity may be classified into limit points and bifurcation points. For the limit points, the path tracing scheme that successively computes the regular equilibrium points on the equilibrium path, and the pinpointing scheme that precisely locates the singular equilibrium points were sufficient for the computational stability analysis. For the bifurcation points, however, a specific procedure for path-switching was also necessary to detect the branching paths to be traced in the post-buckling region. After the introduction, a general theory of elastic stability based on the energy concept was given. Then path tracing, an indirect method of detecting multiple bifurcation points, and path switching strategies were described. Next, some numerical examples of bifurcation analysis were carried out for a trussed stardome, and a pin-supported plane circular arch was described. Finally, concluding remarks were given.