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1.
Non-Newtonian fluid flow through a planar symmetric expansion: shear thickenning fluids
Primož Ternik, Jure Marn, Zoran Žunič, 2006, izvirni znanstveni članek

Opis: The incompressible non-Newtonian fluid flow through a symmetric sudden expansion is studied numerically in order to obtain Reynolds number critical value. The Quadratic model is employed to accommodate the shear-thickening behavior of corn-starch and water mixture. Numerical procedure is validated with results for the Newtonian fluid flow in a range of the Reynolds number Re=10,20,.,100. Results for the non-Newtonian fluid show that the shear-thickening behavior lowers the threshold of the transition from flow symmetry to its asymmetry (lowers the onset of the bifurcation and the critical value of the Reynolds number) and increases the reattachment length. In addition, the results for the Quadratic model are compared to the results obtained with the Power law.
Ključne besede: fluid mechanics, bifurcation, sudden expansion, shear thickenningfluid, quadratic model, powr law
Objavljeno: 31.05.2012; Ogledov: 969; Prenosov: 22
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2.
Symmetry breaking phenomena of purely viscous shear-thinning fluid flow in a locally constricted channel
Primož Ternik, 2008, izvirni znanstveni članek

Opis: The goal of a present study is to investigate the effects of generalized Newtonian fluids on the threshold of the transition from flow symmetry to its asymmetry for the flow through a locally constricted channel. We consider purely viscous shear-thinning fluid and compare it with the Newtonian fluid. Fluid flow is studied numerically by solving the two dimensional momentum equations along with the continuity equation and the Carreau-Yasuda rheological model. We report systematic results in a range of generalized Reynolds number 250▫$leq$▫Re▫$leq$▫150 with a focus on its critical value. Results indicate that the shear-thinning viscous behaviour decreases the onset of bifurcation phenomena and the critical value of Reynolds number. Last but not least, a systematic grid refinement analysis and numerical accuracy study is performed and present numerical results may be treated as the benchmark.
Ključne besede: bifurcation, inelastic shear-thinning fluid, Carreau-Yasuda model, numerical modelling
Objavljeno: 31.05.2012; Ogledov: 914; Prenosov: 51
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3.
Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
Feng Liang, Maoan Han, Valery Romanovski, 2012, izvirni znanstveni članek

Opis: In this paper, we study limit cycle bifurcations for a kind of non-smooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with the center at the origin and a homoclinic loop around the origin. By using the first Melnikov function of piecewise near-Hamiltonian systems, we give lower bounds of the maximal number of limit cycles in Hopf and homoclinic bifurcations, and derive an upper bound of the number of limit cycles that bifurcate from the periodic annulus between the center and the homoclinic loop up to the first order in ▫$epsilon$▫. In the case when the degree of perturbing terms is low, we obtain a precise result on the number of zeros of the first Melnikov function.
Ključne besede: mathematics, limit cycle, homoclinic loop, bifurcation
Objavljeno: 07.06.2012; Ogledov: 954; Prenosov: 51
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4.
Limit cycle bifurcations of some Liénard sytems
Yunmin Yang, Maoan Han, Valery Romanovski, 2010, izvirni znanstveni članek

Opis: In this paper we first give some general theorems on the limit cycle bifurcation for near-Hamiltonian systems near a double homoclinic loop or a center as a preliminary. Then we use these theorems to study some polynomial Liénard systems with perturbations and give new lower bounds for the maximal number of limit cycles of these systems.
Ključne besede: mathematics, bifurcation
Objavljeno: 07.06.2012; Ogledov: 704; Prenosov: 23
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5.
Estimating the number of limit cycles in polynomials systems
Maoan Han, Valery Romanovski, 2010, izvirni znanstveni članek

Opis: We describe a method based on algorithms of computational algebra for obtaining an upper bound for the number of limit cycles bifurcating from a center or a focus of polynomial vector field. We apply it to a cubic system depending on six parameters and prove that in the generic case at most six limit cycles can bifurcate from any center or focus at the origin of the system.
Ključne besede: mathematics, limit cycles, bifurcation
Objavljeno: 07.06.2012; Ogledov: 637; Prenosov: 54
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6.
Proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systems
Marko Gosak, Matjaž Perc, 2007, izvirni znanstveni članek

Opis: We show that chaotic states situated in the proximity of periodic windows in bifurcation diagrams are eligible for the observation of coherence resonance. In particular, additive Gaussian noise of appropriate intensity can enhance the temporal order in such chaotic states in a resonant manner. Results obtained for the logistic map and the Lorenz equations suggest that the presented mechanism of coherence resonance is valid beyond particularities of individual systems. We attribute the findings to the increasing attraction of imminent periodic orbits and the ability of noise to anticipate their existence and use a modified wavelet analysis to support our arguments.
Ključne besede: chaotic systems, spatial resonance, coherence resonance, nonlinear systems, noise, spatial dynamics, mathematical models, bifurcation diagrame
Objavljeno: 07.06.2012; Ogledov: 1276; Prenosov: 40
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7.
The study of isochronicity and critical period bifurcations on center manifolds of 3-dim polynomial systems using computer algebra
Matej Mencinger, Brigita Ferčec, 2013, objavljeni znanstveni prispevek na konferenci

Opis: Using the solution of the center-focus problem from [4], we present the investigation of isochronicity and critical period bifurcations of two families of cubic 3-dim systems of ODEs. Both cubic systems have a center manifold filled with closed trajectories. The presented study is performed using computer algebra systems Mathematica and Singular.
Ključne besede: polynomial systems of ODEs, center manifolds, isochronicity, bifurcation of critical periods, CAS
Objavljeno: 10.07.2015; Ogledov: 334; Prenosov: 25
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8.
Limit cycle bifurcations from a nilpotent focus or center of planar systems
Maoan Han, Valery Romanovski, 2012, izvirni znanstveni članek

Opis: We study analytic properties of the Poincaré return map and generalized focal values of analytic planar systems with a nilpotent focus or center. We use the focal values and the map to study the number of limit cycles of this kind of systems and obtain some new results on the lower and upper bounds of the maximal number of limit cycles bifurcating from the nilpotent focus or center. The main results generalize the classical Hopf bifurcation theory and establish the new bifurcation theory for the nilpotent case.
Ključne besede: mathematic, limit cycles, bifurcation, center problem
Objavljeno: 10.07.2015; Ogledov: 445; Prenosov: 147
.pdf Celotno besedilo (1,95 MB)
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9.
Bifurcations of planar Hamiltonian systems with impulsive perturbation
Zhaoping Hu, Maoan Han, Valery Romanovski, 2013, izvirni znanstveni članek

Opis: In this paper, by means of the Melnikov functions we consider bifurcations of harmonic or subharmonic solutions from a periodic solution of a planar Hamiltonian system under impulsive perturbation. We give some sufficient conditions under which a harmonic or subharmonic solution exists.
Ključne besede: matematika, Hamiltonski sistemi, diferencialne enačbe, bifurkacija, mathematics, Hamiltonian systems, differential equations, bifurcation
Objavljeno: 10.07.2015; Ogledov: 321; Prenosov: 52
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10.
Limit cycle bifurcated from a center in a three dimensional system
Bo Sang, Brigita Ferčec, Qin-Long Wang, 2016, izvirni znanstveni članek

Opis: Based on the pseudo-division algorithm, we introduce a method for computing focal values of a class of 3-dimensional autonomous systems. Using the $Є^1$-order focal values computation, we determine the number of limit cycles bifurcating from each component of the center variety (obtained by Mahdi et al). It is shown that at most four limit cycles can be bifurcated from the center with identical quadratic perturbations and that the bound is sharp.
Ključne besede: algorithms, three dimensional systems, focal value, limit cycle, Hopf bifurcation, center
Objavljeno: 08.08.2017; Ogledov: 853; Prenosov: 76
.pdf Celotno besedilo (236,33 KB)
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