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Academic literature on the topic 'Bifurcation problems'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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Journal articles on the topic "Bifurcation problems"

1

TURAEV, D. "ON DIMENSION OF NON-LOCAL BIFURCATIONAL PROBLEMS." International Journal of Bifurcation and Chaos 06, no. 05 (May 1996): 919–48. http://dx.doi.org/10.1142/s0218127496000515.

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An analogue of the center manifold theory is proposed for non-local bifurcations of homo- and heteroclinic contours. In contrast with the local bifurcation theory it is shown that the dimension of non-local bifurcational problems is determined by the three different integers: the geometrical dimension dg which is equal to the dimension of a non-local analogue of the center manifold, the critical dimension dc which is equal to the difference between the dimension of phase space and the sum of dimensions of leaves of associated strong-stable and strong-unstable foliations, and the Lyapunov dimension dL which is equal to the maximal possible number of zero Lyapunov exponents for the orbits arising at the bifurcation. For a wide class of bifurcational problems (the so-called semi-local bifurcations) these three values are shown to be effectively computed. For the orbits arising at the bifurcations, effective restrictions for the maximal and minimal numbers of positive and negative Lyapunov exponents (correspondingly, for the maximal and minimal possible dimensions of the stable and unstable manifolds) are obtained, involving the values dc and dL. A connection with the problem of hyperchaos is discussed.

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Chien, C. S., Z. Mei, and C. L. Shen. "Numerical Continuation at Double Bifurcation Points of a Reaction–Diffusion Problem." International Journal of Bifurcation and Chaos 08, no. 01 (January 1998): 117–39. http://dx.doi.org/10.1142/s0218127498000097.

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We study double bifurcations of a reaction–diffusion problem, and numerical methods for the continuation of bifurcating solution branches. To ensure a correct reflection of the bifurcation scenario in discretizations and to reduce imperfection of bifurcations, we consider a preservation of multiplicities of the bifurcation points in the discrete problems. A continuation-Arnoldi algorithm is exploited to trace the solution branches, and to detect secondary bifurcations. Numerical results on the Brusselator equations confirm our analysis.

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Postlethwaite, C. M., G. Brown, and M. Silber. "Feedback control of unstable periodic orbits in equivariant Hopf bifurcation problems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1999 (September 28, 2013): 20120467. http://dx.doi.org/10.1098/rsta.2012.0467.

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Symmetry-breaking Hopf bifurcation problems arise naturally in studies of pattern formation. These equivariant Hopf bifurcations may generically result in multiple solution branches bifurcating simultaneously from a fully symmetric equilibrium state. The equivariant Hopf bifurcation theorem classifies these solution branches in terms of their symmetries, which may involve a combination of spatial transformations and temporal shifts. In this paper, we exploit these spatio-temporal symmetries to design non-invasive feedback controls to select and stabilize a targeted solution branch, in the event that it bifurcates unstably. The approach is an extension of the Pyragas delayed feedback method, as it was developed for the generic subcritical Hopf bifurcation problem. Restrictions on the types of groups where the proposed method works are given. After addition of the appropriately optimized feedback term, we are able to compute the stability of the targeted solution using standard bifurcation theory, and give an account of the parameter regimes in which stabilization is possible. We conclude by demonstrating our results with a numerical example involving symmetrically coupled identical nonlinear oscillators.

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Armbruster, D., and G. Dangelmayr. "Coupled stationary bifurcations in non-flux boundary value problems." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 1 (January 1987): 167–92. http://dx.doi.org/10.1017/s0305004100066500.

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AbstractCoupled stationary bifurcations in nonlinear operator equations for functions, which are defined on a real interval with non-flux boundary conditions at the ends, are analysed in the framework of imperfect bifurcation theory. The bifurcation equations resulting from a Lyapunov–Schmidt reduction possess a natural structure which can be obtained by taking real parts of a diagonal action in ℂ2 of the symmetry group 0(2). A complete unfolding theory is developed and bifurcation equations are classified up to codimension two. Structurally stable bifurcation diagrams are given and their dependence on the wave numbers of the unstable modes is clarified.

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WU, ZHIQIANG, PEI YU, and KEQI WANG. "BIFURCATION ANALYSIS ON A SELF-EXCITED HYSTERETIC SYSTEM." International Journal of Bifurcation and Chaos 14, no. 08 (August 2004): 2825–42. http://dx.doi.org/10.1142/s0218127404010862.

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This paper investigates periodic bifurcation solutions of a mechanical system which involves a van der Pol type damping and a hysteretic damper representing restoring force. This system has recently been studied based on the singularity theory for bifurcations of smooth functions. However, the results do not actually take into account the property of nonsmoothness involved in the system. In particular, the transition varieties due to constraint boundaries were ignored, resulting in failure in finding some important bifurcation solutions. To reveal all possible bifurcation patterns for such systems, a new method is developed in this paper. With this method, a continuous, piecewise smooth bifurcation problem can be transformed into several subbifurcation problems with either single-sided or double-sided constraints. Further, the constrained bifurcation problems are converted to unconstrained problems and then singularity theory is employed to find transition varieties. Explicit formulas are applied to reconsider the mechanical system. Numerical simulations are carried out to verify analytical predictions. Moreover, symbolic notation for a sequence of bifurcations is introduced to easily show the characteristics of bifurcations, and also the comparison of different bifurcations. The method developed in this paper can be easily extended to study bifurcation problems with other types of nonsmoothness.

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Cliffe, K. A., A. Spence, and S. J. Tavener. "The numerical analysis of bifurcation problems with application to fluid mechanics." Acta Numerica 9 (January 2000): 39–131. http://dx.doi.org/10.1017/s0962492900000398.

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In this review we discuss bifurcation theory in a Banach space setting using the singularity theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical analysis of bifurcation problems is discussed and the convergence theory for several important bifurcations is described for both projection and finite difference methods. These results are used to provide a convergence theory for the mixed finite element method applied to the steady incompressible Navier–Stokes equations. Numerical methods for the calculation of several common bifurcations are described and the performance of these methods is illustrated by application to several problems in fluid mechanics. A detailed description of the Taylor–Couette problem is given, and extensive numerical and experimental results are provided for comparison and discussion.

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Aydin Akgun, Fatma. "Global Bifurcation of Fourth-Order Nonlinear Eigenvalue Problems’ Solution." International Journal of Differential Equations 2021 (November 26, 2021): 1–6. http://dx.doi.org/10.1155/2021/7516324.

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In this paper, we study the global bifurcation of infinity of a class of nonlinear eigenvalue problems for fourth-order ordinary differential equations with nondifferentiable nonlinearity. We prove the existence of two families of unbounded continuance of solutions bifurcating at infinity and corresponding to the usual nodal properties near bifurcation intervals.

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Deng, Baoyang, Michael O'Connor, and Bill Goodwine. "Bifurcations and symmetry in two optimal formation control problems for mobile robotic systems." Robotica 35, no. 8 (July 14, 2016): 1712–31. http://dx.doi.org/10.1017/s026357471600045x.

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SUMMARYThis paper studies bifurcations in the solution structure of an optimal control problem for mobile robotic formation control. In particular, this paper studies a group of mobile robots operating in a two-dimensional environment. Each robot has a predefined initial state and final state and we compute an optimal path between the two states for every robot. The path is optimized with respect to two factors, the control effort and the deviation from a desired “formation,” and a bifurcation parameter gives the relative weight given to each factor. Using an asymptotic analysis, we show that for small values of the bifurcation parameter (corresponding to heavily weighting the control effort) a single unique solution is expected, and that as the bifurcation parameter becomes large (corresponding to heavily weighting maintaining the formation) a large number of solutions is expected. Between the asymptotic extremes, a numerical investigation indicates a solution bifurcation structure with a cascade of increasing numbers of solutions, reminiscent, but not the same as, period-doubling bifurcations leading to chaos in dynamical systems. Furthermore, we show that if the system is symmetric, the bifurcation structure possesses symmetries, and also present a symmetry-breaking example of a non-holonomic system. Knowledge and understanding of the existence and structure of bifurcations in the solutions of this type of formation control problem are important for robotics engineers because common optimization approaches based on gradient-descent are only likely to converge to the single nearest solution, and a more global study provides a deeper and more comprehensive understanding of the nature of this important problem in robotics.

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AMDJADI, FARIDON. "MULTIPLE HOPF BIFURCATION AND CHAOTIC REVERSING WAVES IN PROBLEMS WITH O(2) SYMMETRY." International Journal of Bifurcation and Chaos 14, no. 05 (May 2004): 1831–38. http://dx.doi.org/10.1142/s0218127404010199.

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Multiple Hopf bifurcation in problems with O(2) symmetry leads to the standing and the traveling wave solutions. Swapping the branches at this point is considered by studying an O(2) symmetric problem on [Formula: see text]. The torus-doubling cascade bifurcations are investigated using canonical coordinate transformation. It is shown that direction reversing chaos can be obtained through a symmetry-increasing bifurcation.

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Pla, Francisco, and Henar Herrero. "Reduced Basis Method Applied to Eigenvalue Problems from Convection." International Journal of Bifurcation and Chaos 29, no. 03 (March 2019): 1950028. http://dx.doi.org/10.1142/s0218127419500287.

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The reduced basis method is a suitable technique for finding numerical solutions to partial differential equations that must be obtained for many values of parameters. This method is suitable when researching bifurcations and instabilities of stationary solutions for partial differential equations. It is necessary to solve numerically the partial differential equations along with the corresponding eigenvalue problems of the linear stability analysis of stationary solutions for a large number of bifurcation parameter values. In this paper, the reduced basis method has been used to solve eigenvalue problems derived from the linear stability analysis of stationary solutions in a two-dimensional Rayleigh–Bénard convection problem. The bifurcation parameter is the Rayleigh number, which measures buoyancy. The reduced basis considered belongs to the eigenfunction spaces derived from the eigenvalue problems for different types of solutions in the bifurcation diagram depending on the Rayleigh number. The eigenvalue with the largest real part and its corresponding eigenfunction are easily calculated and the bifurcation points are correctly captured. The resulting matrices are small, which enables a drastic reduction in the computational cost of solving the eigenvalue problems.

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Dissertations / Theses on the topic "Bifurcation problems"

1

Duka, E. D. "Bifurcation problems in finite elasticity." Thesis, University of Nottingham, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384747.

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Melbourne, I. "Bifurcation problems with octahedral symmetry." Thesis, University of Warwick, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383295.

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Park, Jungho. "Bifurcation and stability problems in fluid dynamics." [Bloomington, Ind.] : Indiana University, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3274924.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2007.
Source: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4529. Adviser: Shouhong Wang. Title from dissertation home page (viewed Apr. 22, 2008).

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McGarry, John Kevin. "Application of bifurcation theory to physical problems." Thesis, University of Leeds, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252925.

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Bougherara, Brahim. "Problèmes non-linéaires singuliers et bifurcation." Thesis, Pau, 2014. http://www.theses.fr/2014PAUU3012/document.

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Cette thèse s’inscrit dans le domaine mathématique de l’analyse des équations aux dérivées partielles non linéaires. Précisément, nous nous sommes intéressés à une classe de problèmes elliptiques et paraboliques avec coefficients singuliers. Ce manque de régularité pose un certain nombre de difficultés qui ne permettent pas d’utiliser directement les méthodes classiques de l’analyse non-linéaire fondées entre autres sur des résultats de compacité. Dans les démonstrations des principaux résultats, nous montrons comment pallier ces difficultés. Ceci suppose d’adapter certaines techniques bien connues mais aussi d’introduire de nouvelles méthodes. Dans ce contexte, une étape importante est l’estimation fine du comportement des solutions qui permet d’adapter le principe de comparaison faible, d’utiliser la régularité elliptique et parabolique et d’appliquer dans un nouveau contexte la théorie globale de la bifurcation analytique. La thèse se présente sous forme de deux parties indépendantes. 1- Dans la première partie (chapitre I de la thèse), nous avons étudié un problème quasi-linéaire parabolique fortement singulier faisant intervenir l’opérateur p-Laplacien. On a démontré l’existence locale et la régularité de solutions faibles. Ce résultat repose sur des estimations a priori obtenues via l’utilisation d’inégalités de type log-Sobolev combinées à des inégalités de Gagliardo-Nirenberg. On démontre l’unicité de la solution pour un intervalle de valeurs du paramètre de la singularité en utilisant un principe de comparaison faible fondé sur la monotonie d’un opérateur non linéaire adéquat. 2- Dans la deuxième partie (correspondant aux Chapitres II, III et IV de la thèse), nous sommes intéressés à l’étude de problèmes de bifurcation globale. On a établi pour ces problèmes l’existence de continuas non bornés de solutions qui admettent localement une paramétrisation analytique. Pour établir ces résultats, nous faisons appel à différents outils d’analyse non linéaire. Un outil important est la théorie analytique de la bifurcation globale qui a été introduite par Dancer (voir Chapitre II de la thèse). Pour un problème semi linéaire elliptique avec croissance critique en dimension 2, on montre que les solutions le long de la branche convergent vers une solution singulière (solution non bornée) lorsque la norme des solutions converge vers l’infini. Par ailleurs nous montrons que la branche admet une infinité dénombrable de "points de retournement" correspondant à un changement de l’indice de Morse des solutions qui tend vers l’infini le long de la branche
This thesis is concerned with the mathematical study of nonlinear partial differential equations. Precisely, we have investigated a class of nonlinear elliptic and parabolic problems with singular coefficients. This lack of regularity involves some difficulties which prevent the straight-orward application of classical methods of nonlinear analysis based on compactness results. In the proofs of the main results, we show how to overcome these difficulties. Precisely we adapt some well-known techniques together with the use of new methods. In this framework, an important step is to estimate accurately the solutions in order to apply the weak comparison principle, to use the regularity theory of parabolic and elliptic equations and to develop in a new context the analytic theory of global bifurcation. The thesis presents two independent parts. 1- In the first part (corresponding to Chapter I), we are interested by a nonlinear and singular parabolic equation involving the p-Laplacian operator. We established for this problem that for any non-negative initial datum chosen in a certain Lebeque space, there exists a local positive weak solution. For that we use some a priori bounds based on logarithmic Sobolev inequalities to get ultracontractivity of the associated semi-group. Additionaly, for a range of values of the singular coefficient, we prove the uniqueness of the solution and further regularity results. 2- In the second part (corresponding to Chapters II, III and IV of the thesis), we are concerned with the study of global bifurcation problems involving singular nonlinearities. We establish the existence of a piecewise analytic global path of solutions to these problems. For that we use crucially the analytic bifurcation theory introduced by Dancer (described in Chapter II of the thesis). In the frame of a class of semilinear elliptic problems involving a critical nonlinearity in two dimensions, we further prove that the piecewise analytic path of solutions admits asymptotically a singular solution (i.e. an unbounded solution), whose Morse index is infinite. As a consequence, this path admits a countable infinitely many “turning points” where the Morse index is increasing

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Manoel, Miriam Garcia. "Hidden symmetries in bifurcation problems : the singularity theory." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327556.

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Menon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." Thesis, The University of Sydney, 2008. http://hdl.handle.net/2123/3685.

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A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.

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Menon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." University of Sydney, 2008. http://hdl.handle.net/2123/3685.

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Doctor of Philosophy
A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.

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Sallam, M. H. M. "Aspects of stability and bifurcation theory for multiparameter problems." Thesis, University of Strathclyde, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371969.

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Zhang, Tiansi. "Problems of homoclinic flips bifurcation in four-dimensional systems." Lyon, École normale supérieure (sciences), 2007. http://www.theses.fr/2007ENSL0431.

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Books on the topic "Bifurcation problems"

1

Melbourne, Ian. Bifurcation problems with octahedral symmetry. [s.l.]: typescript, 1987.

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2

Mittelmann, Hans D., and Dirk Roose, eds. Continuation Techniques and Bifurcation Problems. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-5681-2.

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1945-, Mittelmann H. D., and Roose Dirk, eds. Continuation techniques and bifurcation problems. Basel: Birkhäuser Verlag, 1990.

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Fečkan, Michal. Topological Degree Approach to Bifurcation Problems. Dordrecht: Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-8724-0.

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Topological Degree Approach to Bifurcation Problems. Berlin: Springer Netherland, 2008.

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Manoel, Míriam Garcia. Hidden symmetries in bifurcation problems: The singularity theory. [s.l.]: typescript, 1997.

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Center, Langley Research, ed. Multigrid methods for bifurcation problems: The self adjoint case. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1987.

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Doedel, Eusebius, and Laurette S. Tuckerman, eds. Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1208-9.

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Doedel, Eusebius. Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems. New York, NY: Springer New York, 2000.

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Le, Vy Khoi. Global bifurcation invariational inequalities: Applications to obstacle and unilateral problems. New York: Springer, 1997.

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Book chapters on the topic "Bifurcation problems"

1

Gaeta, Giuseppe. "Bifurcation problems." In Nonlinear Symmetries and Nonlinear Equations, 97–121. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1018-1_6.

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Salvadori, L., and F. Visentin. "Stability and Bifurcation Problems." In Modern Methods of Analytical Mechanics and their Applications, 103–51. Vienna: Springer Vienna, 1998. http://dx.doi.org/10.1007/978-3-7091-2520-5_3.

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Mei, Zhen. "Bifurcation Problems with Symmetry." In Numerical Bifurcation Analysis for Reaction-Diffusion Equations, 85–100. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04177-2_5.

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Ambrosetti, Antonio, and David Arcoya. "Bifurcation Theory." In An Introduction to Nonlinear Functional Analysis and Elliptic Problems, 61–72. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8114-2_6.

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Motreanu, Dumitru, Viorica Venera Motreanu, and Nikolaos Papageorgiou. "Bifurcation Theory." In Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 181–200. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9323-5_7.

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Allgower, E. L., C. S. Chien, and K. Georg. "Large sparse continuation problems." In Continuation Techniques and Bifurcation Problems, 3–21. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-5681-2_1.

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True, Hans. "Bifurcation Problems in Railway Vehicle Dynamics." In Bifurcation: Analysis, Algorithms, Applications, 319–33. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7241-6_33.

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Chow, Shui-Nee, and Reiner Lauterbach. "On Bifurcation for Variational Problems." In Dynamics of Infinite Dimensional Systems, 57–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-86458-2_7.

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Mandel, Paul. "Bifurcation Problems in Nonlinear Optics." In Instabilities and Chaos in Quantum Optics II, 321–34. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2548-0_21.

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Tuckerman, Laurette S., Cristian Huepe, and Marc-Etienne Brachet. "Numerical methods for bifurcation problems." In Instabilities and Nonequilibrium Structures IX, 75–83. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-94-007-0991-1_3.

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Conference papers on the topic "Bifurcation problems"

1

LUCIA, MARCELLO, and MYTHILY RAMASWAMY. "GLOBAL BIFURCATION FOR SEMILINEAR ELLIPTIC PROBLEMS." In Proceedings of the International Conference on Nonlinear Analysis. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812709257_0013.

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Ji, Quanbao, Qishao Lu, and Xia Gu. "Computation of D10-Equivariant Nonlinear Bifurcation Problems." In 2009 Fifth International Conference on Natural Computation. IEEE, 2009. http://dx.doi.org/10.1109/icnc.2009.250.

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CHENG, YUANJI, and LINA WANG. "REMARKS ON BIFURCATION IN ELLIPTIC BOUNDARY VALUE PROBLEMS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0178.

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Mohammadi, Aliakbar. "Detection of hopf bifurcation using eigenvalue identification." In 2012 IV International Conference "Problems of Cybernetics and Informatics" (PCI). IEEE, 2012. http://dx.doi.org/10.1109/icpci.2012.6486386.

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Ramuzat, A., H. Richard, and M. L. Riethmuller. "Unsteady Flows Within a 2D Model of Multiple Lung Bifurcations." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0363.

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Abstract In our environment, chronic pulmonary illness due to pollution effects or asthmatic problems are increasing. To identify the contribution of pollution effect on the alterations in breath patterns, a better understanding of the human pulmonary system is needed. As a result, fields to be investigated are mostly flows in the lungs at high breathing frequency and aerosol deposition in lung bifurcations under unsteady conditions. The respiration pattern has to be better understood and investigated, to have the possibility to get the most appropriate palliative treatment. Most of the medical treatments are based on aerosol deposition in the bronchial tree. The lung is a complex network of 23 successive generations of bifurcation (Weibel, 1963). The airways, from the trachea to the alveolar zone, divide by dichotomy and become shorter and narrower as they penetrate deeper into the lung. As a result, in vivo investigations of pulmonary flows are not possible, and in vitro experiments in models have to be performed. Flows in the bifurcating airways of the lung are modeled to determine velocities and pressure fields. A complete description of steady flow in a single 3D bifurcation has been previously performed by experimental and numerical modeling. As a result of this study, it has been shown that the first bifurcation influences the flow in the second and in the third bifurcation when the length of the second bifurcation is not sufficiently long. To extend the investigations to a system of three generations, an experimental study of steady and unsteady flows has been carried out on a 2D multiple bifurcations model.

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Rezgui, Djamel, Mark Lowenberg, Mark Jones, and Claudio Monteggia. "Towards Industrialisation of Bifurcation Analysis in Rotorcraft Aeroelastic Problems." In AIAA Atmospheric Flight Mechanics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2012. http://dx.doi.org/10.2514/6.2012-4732.

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García-Huidobro, M., R. Manásevich, and J. R. Ward. "Bifurcation through higher order terms for problems at resonance." In The First 60 Years of Nonlinear Analysis of Jean Mawhin. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702906_0007.

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Liu, Shiqi, Jiongman Huang, Yingxin Liu, Zhibin Li, and Lidong Wang. "A class of inverse eigenvalue problems for bifurcation matrices." In 2022 Global Conference on Robotics, Artificial Intelligence and Information Technology (GCRAIT). IEEE, 2022. http://dx.doi.org/10.1109/gcrait55928.2022.00132.

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Riabinin, A., and A. Suleymanov. "BIFURCATION OF TRANSONIC FLOW IN A CHANNEL WITH A CENTRAL BODY." In Topical Problems of Fluid Mechanics 2016. Institute of Thermomechanics, AS CR, v.v.i., 2016. http://dx.doi.org/10.14311/tpfm.2016.025.

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Hetzler, Hartmut. "Bifurcation Analysis for Brake Squeal." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24814.

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Abstract:

This article presents a perturbation approach for the bifurcation analysis of MDoF vibration systems with gyroscopic and circulatory contributions, as they naturally arise from problems involving moving continua and sliding friction. Based on modal data of the underlying linear system, a multiple scales technique is utilized in order to find equations for the nonlinear amplitudes of the critical mode. The presented method is suited for an algorithmic implementation using commercial software and does not involve costly time-integration. As an engineering example, the bifurcation behaviour of a MDoF disk brake model is investigated. Sub- and supercritical Hopf-bifurcations are found and stationary nonlinear amplitudes are presented depending on operating parameters of the brake as well as of tribological parameters of the contact.

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Reports on the topic "Bifurcation problems"

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Mittelmann, Hans D. Continuation and Multi-Grid for Bifurcation Problems. Fort Belvoir, VA: Defense Technical Information Center, December 1993. http://dx.doi.org/10.21236/ada274965.

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Mittelmann, Hans D. Continuation and Multi-Grid Methods for Bifurcation Problems. Fort Belvoir, VA: Defense Technical Information Center, January 1990. http://dx.doi.org/10.21236/ada218904.

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Hong, Bin. Computational Methods for Bifurcation Problems with Symmetries on the Manifold. Fort Belvoir, VA: Defense Technical Information Center, June 1991. http://dx.doi.org/10.21236/ada237146.

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Chan, Tony F. Numerical Methods for Solving Large Sparse Eigenvalue Problems and for the Analysis of Bifurcation Phenomena. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada244273.

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Chan, Tony F. Numerical Methods for Solving Large Sparse Eigenvalue Problems and for the Analysis of Bifurcation Phenomena. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada246470.

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