Energy Technology Data Exchange (ETDEWEB)
Luo, Kang; Yi, Hong-Liang, E-mail: yihongliang@hit.edu.cn; Tan, He-Ping, E-mail: tanheping@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001 (China)
2014-05-15
Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.
Bifurcation and stability of forced convection in tightly coiled ducts: multiplicity
International Nuclear Information System (INIS)
Wang Liqiu; Pang, Ophelia; Cheng Lin
2005-01-01
A numerical study is made on the fully developed bifurcation structure of the forced convection in tightly coiled ducts of square cross-section. In addition to the examination of structural changes of three known solution branches found in loosely coiled ducts, three new solution branches are found. These new branches are isolated from the three known branches. The flows on these new branches are in a symmetric 4-cell state, a symmetric 8-cell state, an asymmetric 2-cell state, an asymmetric 5-cell state, an asymmetric 7-cell state, or an asymmetric 8-cell structure
Bifurcations and chaos in convection taking non-Fourier heat-flux
Layek, G. C.; Pati, N. C.
2017-11-01
In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.
Energy Technology Data Exchange (ETDEWEB)
Li, K., E-mail: likai@imech.ac.cn [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China); University of Chinese Academy of Sciences, Beijing 100190 (China); Xun, B.; Hu, W. R. [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China)
2016-05-15
As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.
International Nuclear Information System (INIS)
Li, K.; Xun, B.; Hu, W. R.
2016-01-01
As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.
Forced convection heat transfer in He II
International Nuclear Information System (INIS)
Kashani, A.
1986-01-01
An investigation of forced convection heat transfer in He II is conducted. The study includes both experimental and theoretical treatments of the problem. The experiment consists of a hydraulic pump and a copper flow tube, 3 mm in ID and 2m long. The system allows measurements of one-dimensional heat and mass transfer in He II. The heat transfer experiments are performed by applying heat at the midpoint along the length of the flow tube. Two modes of heat input are employed, i.e., step function heat input and square pulse heat input. The heat transfer results are discussed in terms of temperature distribution in the tube. The experimental temperature profiles are compared with numerical solutions of an analytical model developed from the He II energy equation. The bath temperature is set at three different values of 1.65, 1.80, and 1.95 K. The He II flow velocity is varied up to 90 cm/s. Pressure is monitored at each end of the flow tube, and the He II pressure drop is obtained for different flow velocities. Results indicate that He II heat transfer by forced convention is considerably higher than that by internal convection. The theoretical model is in close agreement with the experiment. He II pressure drop and friction factor are very similar to those of an ordinary fluid
Topological bifurcations in the evolution of coherent structures in a convection model
DEFF Research Database (Denmark)
Dam, Magnus; Rasmussen, Jens Juul; Naulin, Volker
2017-01-01
Blob filaments are coherent structures in a turbulent plasma flow. Understanding the evolution of these structures is important to improve magnetic plasma confinement. Three state variables describe blob filaments in a plasma convection model. A dynamical systems approach analyzes the evolution...
Bifurcation Tools for Flight Dynamics Analysis and Control System Design, Phase II
National Aeronautics and Space Administration — The purpose of the project is the development of a computational package for bifurcation analysis and advanced flight control of aircraft. The development of...
Tides in differentially rotating convective envelopes. II. The tidal coupling
International Nuclear Information System (INIS)
Scharlemann, E.T.
1982-01-01
The tidal coupling between a star with an extended, differentially rotating convective envelope, and its companion in a close binary system, is calculated from the tidal velocity field derived in Paper I. The derived coupling torque can be tested using observations of RS Canum Venaticorum systems, for which a photometric wave in the light curve provides an accurate stellar rotation rate, and for which observed orbital period changes require the stars in the systems to be coupled. The coupling torque is sufficient to explain the nearly synchronous rotation of the active star in RS CVn systems, despite the observed orbital period changes, but may not be able to explain the extreme tightness of the coupling implied by the very long periods for the migration of the photometric waves in the systems. This conclusion depends on the origin of the orbital period changes, but not on the nature of the wave or the wave migration. When the coupling torque vanishes, a specific latitude at the surface of the convective star will exactly corotate with the binary system: this corotation latitude is calculated. Finally, it is shown that the additional viscous terms introduced by tides should not suppress differential rotation in binary systems with RS Cvn parameters
Investigation of the transition from forced to natural convection in the research reactor Munich II
International Nuclear Information System (INIS)
Skreba, S.; Adamek, J.; Unger, H.
1999-01-01
The new research reactor Munich II (FRM-II), which is under construction at the Technical University Munich, Germany, makes use of a newly developed compact reactor core consisting of a single fuel element, which is assembled of two concentric pipes. Between the fuel element's inner and outer pipe 113 involutely bent fuel plates are placed rotationally symmetric, forming 113 cooling channels of a constant width of 2.2 mm. After a shut down of the reactor, battery supported cooling pumps are started by the reactor safety system in order to remove the decay heat by a downwards directed forced flow. Three hours after they have been started, the cooling pumps are shut down and so-called 'natural convection flaps' are opened by their own weight. Through a flow path, which is provided by the opening of the natural convection flaps, the decay heat is given off to the water in the reactor pool after the direction of the flow has changed and an upwards directed natural convection flow has developed. At the Department for Nuclear and New Energy Systems of the Ruhr-University Bochum, Germany, a test facility has been built in order to confirm the concept of the decay heat removal in the FRM-II, to acquire data of single and two phase natural convection flows and to detect the dry out in a narrow channel. The thermohydraulics of the FRM-II are simulated by an electrically heated test section, which represents one cooling channel of the fuel element. At first experiments have been performed, which simulated the transition from forced to natural convection in the core of the FRM-II, both at normal operation and at a complete loss of the decay heat removal pumps. In case of normal operation, the transition from forced to natural convection takes place single phased. If a complete loss of the active decay heat removal system occurs, the decay heat removal is ensured by a quasi-steady two phase flow. In a second test series minimum heat flux densities leading to pressure pulsations
1991-01-01
Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambe...
Two-dimensional numerical modeling and solution of convection heat transfer in turbulent He II
Zhang, Burt X.; Karr, Gerald R.
1991-01-01
Numerical schemes are employed to investigate heat transfer in the turbulent flow of He II. FEM is used to solve a set of equations governing the heat transfer and hydrodynamics of He II in the turbulent regime. Numerical results are compared with available experimental data and interpreted in terms of conventional heat transfer parameters such as the Prandtl number, the Peclet number, and the Nusselt number. Within the prescribed Reynolds number domain, the Gorter-Mellink thermal counterflow mechanism becomes less significant, and He II acts like an ordinary fluid. The convection heat transfer characteristics of He II in the highly turbulent regime can be successfully described by using the conventional turbulence and heat transfer theories.
Directory of Open Access Journals (Sweden)
Alexander S. Mikherdov
2018-02-01
Full Text Available The coupling of cis-[PdCl2(CNXyl2] (Xyl = 2,6-Me2C6H3 with 4-phenylthiazol-2-amine in molar ratio 2:3 at RT in CH2Cl2 leads to binuclear (diaminocarbenePdII complex 3c. The complex was characterized by HRESI+-MS, 1H NMR spectroscopy, and its structure was elucidated by single-crystal XRD. Inspection of the XRD data for 3c and for three relevant earlier obtained thiazole/thiadiazole derived binuclear diaminocarbene complexes (3a EYOVIZ; 3b: EYOWAS; 3d: EYOVOF suggests that the structures of all these species exhibit intra-/intermolecular bifurcated chalcogen bonding (BCB. The obtained data indicate the presence of intramolecular S•••Cl chalcogen bonds in all of the structures, whereas varying of substituent in the 4th and 5th positions of the thiazaheterocyclic fragment leads to changes of the intermolecular chalcogen bonding type, viz. S•••π in 3a,b, S•••S in 3c, and S•••O in 3d. At the same time, the change of heterocyclic system (from 1,3-thiazole to 1,3,4-thiadiazole does not affect the pattern of non-covalent interactions. Presence of such intermolecular chalcogen bonding leads to the formation of one-dimensional (1D polymeric chains (for 3a,b, dimeric associates (for 3c, or the fixation of an acetone molecule in the hollow between two diaminocarbene complexes (for 3d in the solid state. The Hirshfeld surface analysis for the studied X-ray structures estimated the contributions of intermolecular chalcogen bonds in crystal packing of 3a–d: S•••π (3a: 2.4%; 3b: 2.4%, S•••S (3c: less 1%, S•••O (3d: less 1%. The additionally performed DFT calculations, followed by the topological analysis of the electron density distribution within the framework of Bader’s theory (AIM method, confirm the presence of intra-/intermolecular BCB S•••Cl/S•••S in dimer of 3c taken as a model system (solid state geometry. The AIM analysis demonstrates the presence of appropriate bond critical points for these
Energy Technology Data Exchange (ETDEWEB)
Feiden, Gregory A. [Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala (Sweden); Chaboyer, Brian, E-mail: gregory.a.feiden@gmail.com, E-mail: brian.chaboyer@dartmouth.edu [Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, NH 03755 (United States)
2014-07-01
We examine the hypothesis that magnetic fields are inflating the radii of fully convective main-sequence stars in detached eclipsing binaries (DEBs). The magnetic Dartmouth stellar evolution code is used to analyze two systems in particular: Kepler-16 and CM Draconis. Magneto-convection is treated assuming stabilization of convection and also by assuming reductions in convective efficiency due to a turbulent dynamo. We find that magnetic stellar models are unable to reproduce the properties of inflated fully convective main-sequence stars, unless strong interior magnetic fields in excess of 10 MG are present. Validation of the magnetic field hypothesis given the current generation of magnetic stellar evolution models therefore depends critically on whether the generation and maintenance of strong interior magnetic fields is physically possible. An examination of this requirement is provided. Additionally, an analysis of previous studies invoking the influence of star spots is presented to assess the suggestion that star spots are inflating stars and biasing light curve analyses toward larger radii. From our analysis, we find that there is not yet sufficient evidence to definitively support the hypothesis that magnetic fields are responsible for the observed inflation among fully convective main-sequence stars in DEBs.
Bifurcation of the spin-wave equations
International Nuclear Information System (INIS)
Cascon, A.; Koiller, J.; Rezende, S.M.
1990-01-01
We study the bifurcations of the spin-wave equations that describe the parametric pumping of collective modes in magnetic media. Mechanisms describing the following dynamical phenomena are proposed: (i) sequential excitation of modes via zero eigenvalue bifurcations; (ii) Hopf bifurcations followed (or not) by Feingenbaum cascades of period doubling; (iii) local and global homoclinic phenomena. Two new organizing center for routes to chaos are identified; in the classification given by Guckenheimer and Holmes [GH], one is a codimension-two local bifurcation, with one pair of imaginary eigenvalues and a zero eigenvalue, to which many dynamical consequences are known; secondly, global homoclinic bifurcations associated to splitting of separatrices, in the limit where the system can be considered a Hamiltonian subjected to weak dissipation and forcing. We outline what further numerical and algebraic work is necessary for the detailed study following this program. (author)
Unfolding the Riddling Bifurcation
DEFF Research Database (Denmark)
Maistrenko, Yu.; Popovych, O.; Mosekilde, Erik
1999-01-01
We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation.......We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation....
International Nuclear Information System (INIS)
Cheng, S.K.; Todreas, N.E.
1984-08-01
A new version of the ENERGY series code, ENERGY-IV, was written for predicting coolant temperature distributions in wire-wrapped rod assemblies used in the Liquid Metal Fast Breeder Reactor. The ENERGY-IV Code is applicable to both steady-state forced and mixed convection operation for a single isolated assembly. (The SUPERENERGY Code, [Basehore (1980)] is applicable to core wide forced convection analysis.) ENERGY-IV is an empirical code designed to be fast running. Hence the core designer can use it as an inexpensive thermal hydraulic design or diagnosis tool
Compressible convection in a rotating spherical shell. II. A linear anelastic model
International Nuclear Information System (INIS)
Glatzmaier, G.A.; Gilman, P.A.
1981-01-01
We study the onset of convection for a compressible fluid in a rotating spherical shell via linear anelastic fluid equations for a depth of 40% of the radius, constant kinematic viscosity and thermometric diffusivity, Taylor numbers up to 10 5 , and density stratifications up to seven e-folds across the zone. The perturbations are expanded in spherical harmonics, and the radially dependent equations are solved with a Newton-Raphson relaxation method
Burnout in boiling heat transfer. Part II: subcooled and low quality forced-convection systems
International Nuclear Information System (INIS)
Bergles, A.E.
1977-01-01
Recent experimental and analytical developments regrading burnout in subcooled and low quality forced-convection systems are reviewed. Much data have been accumulated which clarify the parametric trends and lead to new design correlations for water and a variety of other coolants in both simple and complex geometries. A number of critical experiments and models have been developed to attempt to clarify the burnout mechanism(s) in simpler geometries and power transients
Effect of nature convection on heat transfer in the liquid LiPb blanket for FDS-II
Energy Technology Data Exchange (ETDEWEB)
Wang Hongyan; Chen Hongli [Huaibei Coal Industry Teachers Coll. (China). Dept. of Physics; Zhou Tao [Chinese Academy of Sciences, Hefei (China). Inst. of Plasma Physics
2007-07-01
The He-cooled liquid LiPb tritium breeder (SLL) blanket concept is one of options of the blanket design of the fusion power reactor (FDS-II). The SLL blanket could be developed relatively easily with lower LiPb outlet temperature and slower LiPb flow velocity that allows the utilization of relatively mature material technology. The velocity of the liquid LiPb in the blanket is very slowly only in order to extract tritium. The magnetohydrodynamic (MHD) flow and heat transfer become very complex resulting from the differential heating of walls of the channels, especially adjacent to the First Wall (FW), and internal heat sources inside of the liquid LiPb. It is necessary to analyse the effect of the buoyancy-driven LiPb MHD flow on heat transfer in the channels with electrically and thermally conducting walls adjacent to the FW. The nature convection of the liquid LiPb, due to thermal diffusion, in the poloidal channel adjacent to the FW in the presence of the strong magnetic field of the SLL blanket has been considered and studied. The specially numerical MHD code based on the computational fluid dynamic software has been developed for analysis of the buoyancy-driven MHD flow. The properties of buoyantly convective flows have been investigated for various thermal boundary conditions. The numerical analysis was performed for the effect of nature convection on heat transfer of the liquid LiPb MHD flow in the poloidal channel in the SLL blanket. For the strong temperature gradient in the blanket and internal heat flux of Liquid LiPb, the three-dimensional temperature distributions of the LiPb, the FW and other walls have been given. Finally, The effect of the ratio of MHD buoyancy on the heat transfer characteristics of the LiPb flow have been calculated and presented. (orig.)
Decoupled Scheme for Time-Dependent Natural Convection Problem II: Time Semidiscreteness
Directory of Open Access Journals (Sweden)
Tong Zhang
2014-01-01
stability and the corresponding optimal error estimates are presented. Furthermore, a decoupled numerical scheme is proposed by decoupling the nonlinear terms via temporal extrapolation; optimal error estimates are established. Finally, some numerical results are provided to verify the performances of the developed algorithms. Compared with the coupled numerical scheme, the decoupled algorithm not only keeps good accuracy but also saves a lot of computational cost. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled method for time-dependent natural convection problem.
Burnout in boiling heat transfer. II. Subcooled and low-quality forced-convection systems
International Nuclear Information System (INIS)
Bergles, A.E.
1977-01-01
Recent experimental and analytical developments regarding burnout in subcooled and low-quality forced-convection systems are reviewed. Many data have been accumulated which clarify the parametric trends and lead to new design correlations for water and a variety of other coolants in both simple and complex geometries. A number of critical experiments and models have been developed to attempt to clarify the burnout mechanism(s) in simpler geometries. Other topics discussed include burnout with power transients and techniques to augment burnout. 86 references
Relative Lyapunov Center Bifurcations
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2014-01-01
Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....
Zhang, Yao-Jun; Zhu, Hao; Shi, Shun-Yi; Muramatsu, Takashi; Pan, Dao-Rong; Ye, Fei; Zhang, Jun-Jie; Tian, Nai-Liang; Bourantas, Christos V; Chen, Shao-Liang
2016-03-01
This study investigated the diagnostic accuracy of three-dimensional quantitative coronary angiography (3D-QCA) compared with conventional 2D-QCA for predicting functional severity assessed by fractional flow reserve (FFR) for true bifurcation lesions. Based on pooled data from the randomized DK-CRUSH II, III, and IV trials, we evaluated the patients with true bifurcation lesions who underwent coronary angiography together with functional evaluations using FFR in both the main vessel and the side branch. Off-line 2D- and 3D-QCA analyses were conducted using dedicated bifurcation QCA analysis software. Measurements of minimum lumen diameter (MLD), percentage diameter stenosis (% DS), and minimum lumen area (MLA) were compared between 2D- and 3D-QCA, and we evaluated their predictive values of functionally significant FFR. Ninety patients were eligible for enrollment in the present study. In the main vessel, MLA measured by 3D-QCA was the most accurate predictor of FFR <0.75 (C statistic 0.85, P < 0.001), while MLD measured by 2D-QCA was a similarly accurate predictor (C statistic 0.85, P < 0.001). In the side branch, the best metrics for predicting FFR <0.75 were % DS measured by 2D-QCA with a C statistic value of 0.91 (P < 0.001) and MLA measured by 3D-QCA with a C statistic value of 0.81 (P < 0.001). However, both 2D- and 3D-QCA metrics exhibited low accuracies for predicting FFR <0.75 in intermediate bifurcation lesions. 3D-QCA analysis for true bifurcation lesions did not improve the predictive accuracy of functionally significant FFR compared with 2D-QCA analysis. In lesions with intermediate stenosis, the diagnostic performance of both 2D- and 3D-QCA-derived measurements in differentiating functional severity is limited. © 2016 Wiley Periodicals, Inc.
Energy Technology Data Exchange (ETDEWEB)
Bau, H.H. [Univ. of Pennsylvania, Philadelphia, PA (United States)
1995-12-31
Using stability theory, numerical simulations, and in some instances experiments, it is demonstrated that the critical Rayleigh number for the bifurcation (1) from the no-motion (conduction) state to the motion state and (2) from time-independent convection to time-dependent, oscillatory convection in the thermal convection loop and Rayleigh-Benard problems can be significantly increased or decreased. This is accomplished through the use of a feedback controller effectuating small perturbations in the boundary data. The controller consists of sensors which detect deviations in the fluid`s temperature from the motionless, conductive values and then direct actuators to respond to these deviations in such a way as to suppress the naturally occurring flow instabilities. Actuators which modify the boundary`s temperature/heat flux are considered. The feedback controller can also be used to control flow patterns and generate complex dynamic behavior at relatively low Rayleigh numbers.
Bifurcations of transition states: Morse bifurcations
International Nuclear Information System (INIS)
MacKay, R S; Strub, D C
2014-01-01
A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy level that can be spanned by two compact codimension-1 surfaces of unidirectional flux whose union, called a dividing surface, locally separates the energy level into two components and has no local recrossings. For this to happen robustly to all smooth perturbations, the transition state must be normally hyperbolic. The dividing surface then has locally minimal geometric flux through it, giving an upper bound on the rate of transport in either direction. Transition states diffeomorphic to S 2m−3 are known to exist for energies just above any index-1 critical point of a Hamiltonian of m degrees of freedom, with dividing surfaces S 2m−2 . The question addressed here is what qualitative changes in the transition state, and consequently the dividing surface, may occur as the energy or other parameters are varied? We find that there is a class of systems for which the transition state becomes singular and then regains normal hyperbolicity with a change in diffeomorphism class. These are Morse bifurcations. Various examples are considered. Firstly, some simple examples in which transition states connect or disconnect, and the dividing surface may become a torus or other. Then, we show how sequences of Morse bifurcations producing various interesting forms of transition state and dividing surface are present in reacting systems, by considering a hypothetical class of bimolecular reactions in gas phase. (paper)
International Nuclear Information System (INIS)
Olmstead, W.E.; Davis, S.H.; Rosenblat, S.; Kath, W.L.
1986-01-01
A model equation containing a memory integral is posed. The extent of the memory, the relaxation time lambda, controls the bifurcation behavior as the control parameter R is increased. Small (large) lambda gives steady (periodic) bifurcation. There is a double eigenvalue at lambda = lambda 1 , separating purely steady (lambda 1 ) from combined steady/T-periodic (lambda > lambda 1 ) states with T → infinity as lambda → lambda + 1 . Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from lambda = lambda 1
Convective excitation of quasistatic waves in an inhomogeneous anisothermic plasma. II
International Nuclear Information System (INIS)
Jungwirth, K.; Sizonenko, V.L.
1977-01-01
Nonlinear effects stabilizing the convective instabilities excited in an anisothermic plasma (Tsub(e)>>Tsub(i)) at the plasma boundary (a >ωsub(Bi)) saturate at first. Being excited by a small part of slow plasma electrons (vsub(z)<< vsub(Te)) only, they saturate at a relatively low level. Further, surface waves with lower frequencies and higher phase velocities (vsub(ph)=ω/ksub(z)) become dominant and a broadening of the plasma boundary occurs. For their saturation nonlinear interaction is more important than the quasilinear effects. During the time interval of several ωsub(Bi)sup(-1) the longest surface waves with ksub(y) approximately ωsub(Bi)/Vsub(s), γ approximately ω approximately ωsub(Bi) approximately ksub(y)Vsub(s) and vsub(ph) approximately vsub(Te) saturate at the absolutely highest level. The plasma boundary broadens in the meanwhile up to a approximately Vsub(s)/ωsub(Bi). The wave energy is comparable to the total energy connected with the longitudinal motion of the initially thermal electrons inside this boundary layer. The wave amplitude is large enough to trap the initially cold ions belonging to this layer and 'heat' them up to energies comparable to those of the electron component. The heating process again occurs within several ωsub(Bi)sup(-1) and the Larmor radius of the ions is then comparable to Vsub(s)/ωsub(Bi). Further evolution of the system is governed by the unstable local perturbations. (author)
Bifurcations and Patterns in Nonlinear Dissipative Systems
Energy Technology Data Exchange (ETDEWEB)
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
Flow Topology Transition via Global Bifurcation in Thermally Driven Turbulence
Xie, Yi-Chao; Ding, Guang-Yu; Xia, Ke-Qing
2018-05-01
We report an experimental observation of a flow topology transition via global bifurcation in a turbulent Rayleigh-Bénard convection. This transition corresponds to a spontaneous symmetry breaking with the flow becomes more turbulent. Simultaneous measurements of the large-scale flow (LSF) structure and the heat transport show that the LSF bifurcates from a high heat transport efficiency quadrupole state to a less symmetric dipole state with a lower heat transport efficiency. In the transition zone, the system switches spontaneously and stochastically between the two long-lived metastable states.
Energetics and monsoon bifurcations
Seshadri, Ashwin K.
2017-01-01
Monsoons involve increases in dry static energy (DSE), with primary contributions from increased shortwave radiation and condensation of water vapor, compensated by DSE export via horizontal fluxes in monsoonal circulations. We introduce a simple box-model characterizing evolution of the DSE budget to study nonlinear dynamics of steady-state monsoons. Horizontal fluxes of DSE are stabilizing during monsoons, exporting DSE and hence weakening the monsoonal circulation. By contrast latent heat addition (LHA) due to condensation of water vapor destabilizes, by increasing the DSE budget. These two factors, horizontal DSE fluxes and LHA, are most strongly dependent on the contrast in tropospheric mean temperature between land and ocean. For the steady-state DSE in the box-model to be stable, the DSE flux should depend more strongly on the temperature contrast than LHA; stronger circulation then reduces DSE and thereby restores equilibrium. We present conditions for this to occur. The main focus of the paper is describing conditions for bifurcation behavior of simple models. Previous authors presented a minimal model of abrupt monsoon transitions and argued that such behavior can be related to a positive feedback called the `moisture advection feedback'. However, by accounting for the effect of vertical lapse rate of temperature on the DSE flux, we show that bifurcations are not a generic property of such models despite these fluxes being nonlinear in the temperature contrast. We explain the origin of this behavior and describe conditions for a bifurcation to occur. This is illustrated for the case of the July-mean monsoon over India. The default model with mean parameter estimates does not contain a bifurcation, but the model admits bifurcation as parameters are varied.
Systematic parameter study of dynamo bifurcations in geodynamo simulations
Petitdemange, Ludovic
2018-04-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike in previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition disappears and is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the geostrophic zonal flow can develop and participate to the dynamo mechanism for non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently. The following three regimes are distinguished: (i) Close to the onset of convection (Rac) with only the most critical convective mode (wave number) being present, dynamos set in supercritically in the Ekman number regime explored here and are dipole-dominated. Larger critical magnetic Reynolds numbers indicate that they are particularly inefficient. (ii) in the range 3 10) , the relative importance of zonal flows increases with Ra in non-magnetic models. The field topology depends on the magnitude of the initial magnetic field. The dipolar branch has a subcritical behavior whereas the multipolar branch has a supercritical behavior. By approaching more realistic parameters, the extension of this bistable regime increases. A hysteretic behavior questions the common interpretation for geomagnetic reversals. Far above the dynamo threshold (by increasing the magnetic Prandtl number), Lorentz forces contribute to the first order force balance, as predicted for planetary dynamos. When
Directory of Open Access Journals (Sweden)
Ajith Ananthakrishna Pillai
2012-03-01
Full Text Available Bifurcation percutaneous coronary intervention (PCI is still a difficult call for the interventionist despite advancements in the instrumentation, technical skill and the imaging modalities. With major cardiac events relate to the side-branch (SB compromise, the concept and practice of dedicated bifurcation stents seems exciting. Several designs of such dedicated stents are currently undergoing trials. This novel concept and pristine technology offers new hope notwithstanding the fact that we need to go a long way in widespread acceptance and practice of these gadgets. Some of these designs even though looks enterprising, the mere complex delivering technique and the demanding knowledge of the exact coronary anatomy makes their routine use challenging.
Bifurcation and Nonlinear Oscillations.
1980-09-28
Structural stability and bifurcation theory. pp. 549-560 in Dinamical Systems (Ed. MI. Peixoto), Academic Press, 1973. [211 J. Sotomayor, Generic one...Dynamical Systems Brown University ELECTP" 71, Providence, R. I. 02912 1EC 2 4 1980j //C -*)’ Septabe-4., 1980 / -A + This research was supported in...problems are discussed. The first one deals with the characterization of the flow for a periodic planar system which is the perturbation of an autonomous
Numerical analysis of bifurcations
International Nuclear Information System (INIS)
Guckenheimer, J.
1996-01-01
This paper is a brief survey of numerical methods for computing bifurcations of generic families of dynamical systems. Emphasis is placed upon algorithms that reflect the structure of the underlying mathematical theory while retaining numerical efficiency. Significant improvements in the computational analysis of dynamical systems are to be expected from more reliance of geometric insight coming from dynamical systems theory. copyright 1996 American Institute of Physics
Bifurcation of solutions to Hamiltonian boundary value problems
McLachlan, R. I.; Offen, C.
2018-06-01
A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples.
Modulated convection at high frequencies and large modulation amplitudes
International Nuclear Information System (INIS)
Swift, J.B.; Hohenberg, P.C.
1987-01-01
Modulated Rayleigh-Benard convection is analyzed for high frequencies and large modulation amplitudes. The linear theory of Gershuni and Zhukhovitskii is generalized to the nonlinear domain, and a subcritical bifurcation to convection is found in agreement with the experiments of Niemela and Donnelly. The crossover between the high-frequency (''Stokes layer'') regime and the low-frequency regime studied previously is analyzed
Futterer, Birgit; Egbers, Christoph; Chossat, Pascal; Hollerbach, Rainer; Breuer, Doris; Feudel, Fred; Mutabazi, Innocent; Tuckerman, Laurette
modes, with a strong influence of initial conditions leading to axisymmetric, octahedral/cubic or pentagonal solutions. Transition to chaos is in form of a sudden onset. Experimental data supports the numerically validated influence of initial conditions in showing the octahedral mode as most preferred stable state. Well-known issue of rapid rotation is the alignment of convective cells at the tangent cylinder due to the domination of centrifugal forces against the self-gravitating buoyancy field. The system shows very clearly the centrifugal effects by patterns in form of columnar cells. For the planned second mission `GeoFlow II' (on orbit 2010) working fluid shall be an alcanole having a temperature dependent viscosity, i.e. nonanol. Herewith experimental modelling of mantle convection is going to spotlight.
Bubble transport in bifurcations
Bull, Joseph; Qamar, Adnan
2017-11-01
Motivated by a developmental gas embolotherapy technique for cancer treatment, we examine the transport of bubbles entrained in liquid. In gas embolotherapy, infarction of tumors is induced by selectively formed vascular gas bubbles that originate from acoustic vaporization of vascular droplets. In the case of non-functionalized droplets with the objective of vessel occlusion, the bubbles are transported by flow through vessel bifurcations, where they may split prior to eventually reach vessels small enough that they become lodged. This splitting behavior affects the distribution of bubbles and the efficacy of flow occlusion and the treatment. In these studies, we investigated bubble transport in bifurcations using computational and theoretical modeling. The model reproduces the variety of experimentally observed splitting behaviors. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Maximum shear stresses were found to decrease with increasing Reynolds number. The initial bubble length was found to affect the splitting behavior in the presence of gravitational asymmetry. This work was supported by NIH Grant R01EB006476.
Thermal convection in a toroidal duct of a liquid metal blanket. Part II. Effect of axial mean flow
Energy Technology Data Exchange (ETDEWEB)
Zhang, Xuan, E-mail: xuanz@umich.edu; Zikanov, Oleg
2017-03-15
Highlights: • 2D convection flow develops with internal heating and strong axial magnetic field. • The flow is strongly modified by the buoyancy force associated with growing T{sub m}. • Thermal convection is suppressed at high Gr. • High temperature difference between top and bottom walls is expected at high Gr. - Abstract: The work continues the exploration of the effect of thermal convection on flows in toroidal ducts of a liquid metal blanket. This time we consider the effect of the mean flow along the duct and of the associated heat transfer diverting the heat deposited by captured neutrons. Numerical simulations are conducted for a model system with two-dimensional (streamwise-uniform) fully developed flow, purely toroidal magnetic field, and perfectly electrically and thermally insulating walls. Realistically high Grashof (up to 10{sup 11}) and Reynolds (up to 10{sup 6}) numbers are used. It is found that the flow develops thermal convection in the transverse plane at moderate Grashof numbers. At large Grashof numbers, the flow is dominated by the top-bottom asymmetry of the streamwise velocity and stable stratification of temperature, which are caused by the buoyancy force due to the mean temperature growing along the duct. This leads to suppression of thermal convection, weak mixing, and substantial gradients of wall temperature. Further analysis based on more realistic models is suggested.
International Nuclear Information System (INIS)
Kalkofen, W.
1985-01-01
The assumptions of Ayres' model of the upper solar atmosphere are examined. It is found that the bistable character of his model is postulated - through the assumptions concerning the opacity sources and the effect of mechanical waves, which are allowed to destroy the CO molecules but not to heat the gas. The neglect of cooling by metal lines is based on their reduced local cooling rate, but it ignores the increased depth over which this cooling occurs. Thus, the bifurcated model of the upper solar atmosphere consists of two models, one cold at the temperature minimum, with a kinetic temperature of 2900 K, and the other hot, with a temperature of 4900 K. 8 references
Kesseli, Aurora Y.; Muirhead, Philip S.; Mann, Andrew W.; Mace, Greg
2018-06-01
Main-sequence, fully convective M dwarfs in eclipsing binaries are observed to be larger than stellar evolutionary models predict by as much as 10%–15%. A proposed explanation for this discrepancy involves effects from strong magnetic fields, induced by rapid rotation via the dynamo process. Although, a handful of single, slowly rotating M dwarfs with radius measurements from interferometry also appear to be larger than models predict, suggesting that rotation or binarity specifically may not be the sole cause of the discrepancy. We test whether single, rapidly rotating, fully convective stars are also larger than expected by measuring their R\\sin i distribution. We combine photometric rotation periods from the literature with rotational broadening (v\\sin i) measurements reported in this work for a sample of 88 rapidly rotating M dwarf stars. Using a Bayesian framework, we find that stellar evolutionary models underestimate the radii by 10 % {--}15{ % }-2.5+3, but that at higher masses (0.18 theory is 13%–18%, and we argue that the discrepancy is unlikely to be due to effects from age. Furthermore, we find no statistically significant radius discrepancy between our sample and the handful of M dwarfs with interferometric radii. We conclude that neither rotation nor binarity are responsible for the inflated radii of fully convective M dwarfs, and that all fully convective M dwarfs are larger than models predict.
Bifurcations sights, sounds, and mathematics
Matsumoto, Takashi; Kokubu, Hiroshi; Tokunaga, Ryuji
1993-01-01
Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, howev...
Riddling bifurcation and interstellar journeys
International Nuclear Information System (INIS)
Kapitaniak, Tomasz
2005-01-01
We show that riddling bifurcation which is characteristic for low-dimensional attractors embedded in higher-dimensional phase space can give physical mechanism explaining interstellar journeys described in science-fiction literature
Dynamic bifurcations on financial markets
International Nuclear Information System (INIS)
Kozłowska, M.; Denys, M.; Wiliński, M.; Link, G.; Gubiec, T.; Werner, T.R.; Kutner, R.; Struzik, Z.R.
2016-01-01
We provide evidence that catastrophic bifurcation breakdowns or transitions, preceded by early warning signs such as flickering phenomena, are present on notoriously unpredictable financial markets. For this we construct robust indicators of catastrophic dynamical slowing down and apply these to identify hallmarks of dynamical catastrophic bifurcation transitions. This is done using daily closing index records for the representative examples of financial markets of small and mid to large capitalisations experiencing a speculative bubble induced by the worldwide financial crisis of 2007-08.
Rattez, Hadrien; Stefanou, Ioannis; Sulem, Jean; Veveakis, Manolis; Poulet, Thomas
2018-06-01
In this paper we study the phenomenon of localization of deformation in fault gouges during seismic slip. This process is of key importance to understand frictional heating and energy budget during an earthquake. A infinite layer of fault gouge is modeled as a Cosserat continuum taking into account Thermo-Hydro-Mechanical (THM) couplings. The theoretical aspects of the problem are presented in the companion paper (Rattez et al., 2017a), together with a linear stability analysis to determine the conditions of localization and estimate the shear band thickness. In this Part II of the study, we investigate the post-bifurcation evolution of the system by integrating numerically the full system of non-linear equations using the method of Finite Elements. The problem is formulated in the framework of Cosserat theory. It enables to introduce information about the microstructure of the material in the constitutive equations and to regularize the mathematical problem in the post-localization regime. We emphasize the influence of the size of the microstructure and of the softening law on the material response and the strain localization process. The weakening effect of pore fluid thermal pressurization induced by shear heating is examined and quantified. It enhances the weakening process and contributes to the narrowing of shear band thickness. Moreover, due to THM couplings an apparent rate-dependency is observed, even for rate-independent material behavior. Finally, comparisons show that when the perturbed field of shear deformation dominates, the estimation of the shear band thickness obtained from linear stability analysis differs from the one obtained from the finite element computations, demonstrating the importance of post-localization numerical simulations.
International Nuclear Information System (INIS)
Li, Rui; Min, Qilong; Wu, Xiaoqing; Fu, Yunfei
2013-01-01
An exploratory study on physical based latent heat (LH) retrieval algorithm is conducted by parameterizing the physical linkages between observed cloud and precipitation profiles to the major processes of phase change of atmospheric water. Specifically, rain is segregated into three rain types: warm, convective, and stratiform rain, based on their dynamical and thermodynamical characteristics. As the second of series, both convective and stratiform rain LH algorithms are presented and evaluated here. For convective and stratiform rain, the major LH-related microphysical processes including condensation, deposition, evaporation, sublimation, and freezing–melting are parameterized with the aid of Cloud Resolving Model (CRM) simulations. The condensation and deposition processes are parameterized in terms of rain formation processes through the precipitation formation theory. LH associated with the freezing–melting process is relatively small and is assumed to be a fraction of total condensation and deposition LH. The evaporation and sublimation processes are parameterized for three unsaturated scenarios: rain out of the cloud body, clouds at cloud boundary and clouds and rain in downdraft region. The evaluation or self-consistency test indicates the retrievals capture the major features of LH profiles and reproduce the double peaks at right altitudes. The LH products are applicable at various stages of cloud system life cycle for high-resolution models, as well as for large-scale climate models. -- Highlights: ► An exploratory study on physics-based cold rain latent heat retrieval algorithm. ► Utilize the full information of the vertical structures of cloud and rainfall. ► Include all major LH-related microphysical processes (in ice and liquid phase). ► Directly link water mass measurements to latent heat at instantaneous pixel level. ► Applicable at various stages of cloud system life cycle
The charge effect on the hindrance factors for diffusion and convection of a solute in pores: II
Energy Technology Data Exchange (ETDEWEB)
Akinaga, Takeshi; O-tani, Hideyuki; Sugihara-Seki, Masako, E-mail: r091077@kansai-u.ac.jp [Department of Pure and Applied Physics, Kansai University, Yamate-cho, Suita, Osaka 564-8680 (Japan)
2012-10-15
The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e. the Debye-Hueckel equation. (paper)
Quantitative angiography methods for bifurcation lesions
DEFF Research Database (Denmark)
Collet, Carlos; Onuma, Yoshinobu; Cavalcante, Rafael
2017-01-01
Bifurcation lesions represent one of the most challenging lesion subsets in interventional cardiology. The European Bifurcation Club (EBC) is an academic consortium whose goal has been to assess and recommend the appropriate strategies to manage bifurcation lesions. The quantitative coronary...... angiography (QCA) methods for the evaluation of bifurcation lesions have been subject to extensive research. Single-vessel QCA has been shown to be inaccurate for the assessment of bifurcation lesion dimensions. For this reason, dedicated bifurcation software has been developed and validated. These software...
Subcritical thermal convection of liquid metals in a rotating sphere using a quasi-geostrophic model
Cardin, P.; Guervilly, C.
2016-12-01
We study non-linear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals (10-2-1). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than 10-6, which is continuous at the onset (supercritical bifurcation) and consists of the interaction of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of 10-8. On the strong branch, the Reynolds number of the flow is greater than 1000, and a strong zonal flow with multiple jets develops, even close to the non-linear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis (E = 10-6, Pr =10-2). Non-linear oscillations are observed near the onset of convection for E = 10-7 and Pr = 10-1.
Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model
Guervilly, Céline; Cardin, Philippe
2016-12-01
We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals ($Pr\\in[10^{-2},10^{-1}]$). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$, which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of $10^{-8}$. On the strong branch, the Reynolds number of the flow is greater than $10^3$, and a strong zonal flow with multiple jets develops, even close to the nonlinear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis ($Ek=10^{-6}$, $Pr=10^{-2}$). Nonlinear oscillations are observed near the onset of convection for $Ek=10^{-7}$ and $Pr=10^{-1}$.
Pierce instability and bifurcating equilibria
International Nuclear Information System (INIS)
Godfrey, B.B.
1981-01-01
The report investigates the connection between equilibrium bifurcations and occurrence of the Pierce instability. Electrons flowing from one ground plane to a second through an ion background possess a countable infinity of static equilibria, of which only one is uniform and force-free. Degeneracy of the uniform and simplest non-uniform equilibria at a certain ground plan separation marks the onset of the Pierce instability, based on a newly derived dispersion relation appropriate to all the equilibria. For large ground plane separations the uniform equilibrium is unstable and the non-uniform equilibrium is stable, the reverse of their stability properties at small separations. Onset of the Pierce instability at the first bifurcation of equilibria persists in more complicated geometries, providing a general criterion for marginal stability. It seems probable that bifurcation analysis can be a useful tool in the overall study of stable beam generation in diodes and transport in finite cavities
Convection in a nematic liquid crystal with homeotropic alignment and heated from below
Energy Technology Data Exchange (ETDEWEB)
Ahlers, G. [Univ. of California, Santa Barbara, CA (United States)
1995-12-31
Experimental results for convection in a thin horizontal layer of a homeotropically aligned nematic liquid crystal heated from below and in a vertical magnetic field are presented. A subcritical Hopf bifurcation leads to the convecting state. There is quantitative agreement between the measured and the predicted bifurcation line as a function of magnetic field. The nonlinear state near the bifurcation is one of spatio-temporal chaos which seems to be the result of a zig-zag instability of the straight-roll state.
Homoclinic bifurcation in Chua's circuit
Indian Academy of Sciences (India)
spiking and bursting behaviors of neurons. Recent experiments ... a limit cycle increases in a wiggle with alternate sequences of stable and unstable orbits via ... further changes in parameter, the system shows period-adding bifurcation when .... [21–23] transition from limit cycle to single scroll chaos via PD and then to alter-.
Bifurcation scenarios for bubbling transition.
Zimin, Aleksey V; Hunt, Brian R; Ott, Edward
2003-01-01
Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations transverse to the invariant manifold. Generically the periodic orbit can become transversely unstable through a pitchfork, transcritical, period-doubling, or Hopf bifurcation. In this paper a unified treatment of the four types of bubbling bifurcation is presented. Conditions are obtained determining whether the transition to bubbling is soft or hard; that is, whether the maximum burst amplitude varies continuously or discontinuously with variation of the parameter through its critical value. For soft bubbling transitions, the scaling of the maximum burst amplitude with the parameter is derived. For both hard and soft transitions the scaling of the average interburst time with the bifurcation parameter is deduced. Both random (noise) and fixed (mismatch) perturbations are considered. Results of numerical experiments testing our theoretical predictions are presented.
Bifurcation of steady tearing states
International Nuclear Information System (INIS)
Saramito, B.; Maschke, E.K.
1985-10-01
We apply the bifurcation theory for compact operators to the problem of the nonlinear solutions of the 3-dimensional incompressible visco-resistive MHD equations. For the plane plasma slab model we compute branches of nonlinear tearing modes, which are stationary for the range of parameters investigated up to now
Energy Technology Data Exchange (ETDEWEB)
Bierwage, Andreas [National Institutes for Quantum and Radiological Science and Technology, Rokkasho Fusion Institute, Aomori 039-3212 (Japan); Shinohara, Kouji [National Institutes for Quantum and Radiological Science and Technology, Naka Fusion Institute, Ibaraki 311-0193 Japan (Japan)
2016-04-15
The nonlinear interactions between shear Alfvén modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in realistic geometry for a JT-60U tokamak scenario. In Paper I, which was reported in the companion paper, the recently developed orbit-based resonance analysis method was used to track the resonant frequency of fast ions during their nonlinear evolution subject to large magnetic and electric drifts. Here, that method is applied to map the wave-particle power transfer from the canonical guiding center phase space into the frequency-radius plane, where it can be directly compared with the evolution of the fluctuation spectra of fast-ion-driven modes. Using this technique, we study the nonlinear dynamics of strongly driven shear Alfvén modes with low toroidal mode numbers n = 1 and n = 3. In the n = 3 case, both chirping and convective amplification can be attributed to the mode following the resonant frequency of the radially displaced particles, i.e., the usual one-dimensional phase locking process. In the n = 1 case, a new chirping mechanism is found, which involves multiple dimensions, namely, wave-particle trapping in the radial direction and phase mixing across velocity coordinates.
Bifurcation in a buoyant horizontal laminar jet
Arakeri, Jaywant H.; Das, Debopam; Srinivasan, J.
2000-06-01
The trajectory of a laminar buoyant jet discharged horizontally has been studied. The experimental observations were based on the injection of pure water into a brine solution. Under certain conditions the jet has been found to undergo bifurcation. The bifurcation of the jet occurs in a limited domain of Grashof number and Reynolds number. The regions in which the bifurcation occurs has been mapped in the Reynolds number Grashof number plane. There are three regions where bifurcation does not occur. The various mechanisms that prevent bifurcation have been proposed.
Bifurcation routes and economic stability
Czech Academy of Sciences Publication Activity Database
Vošvrda, Miloslav
2001-01-01
Roč. 8, č. 14 (2001), s. 43-59 ISSN 1212-074X R&D Projects: GA ČR GA402/00/0439; GA ČR GA402/01/0034; GA ČR GA402/01/0539 Institutional research plan: AV0Z1075907 Keywords : macroeconomic stability * foreign investment phenomenon * the Hopf bifurcation Subject RIV: AH - Economics
Bifurcations of Fibonacci generating functions
Energy Technology Data Exchange (ETDEWEB)
Ozer, Mehmet [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey) and Semiconductor Physics Institute, LT-01108 and Vilnius Gediminas Technical University, Sauletekio 11, LT-10223 (Lithuania)]. E-mail: m.ozer@iku.edu.tr; Cenys, Antanas [Semiconductor Physics Institute, LT-01108 and Vilnius Gediminas Technical University, Sauletekio 11, LT-10223 (Lithuania); Polatoglu, Yasar [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey); Hacibekiroglu, Guersel [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey); Akat, Ercument [Yeditepe University, 26 Agustos Campus Kayisdagi Street, Kayisdagi 81120, Istanbul (Turkey); Valaristos, A. [Aristotle University of Thessaloniki, GR-54124, Thessaloniki (Greece); Anagnostopoulos, A.N. [Aristotle University of Thessaloniki, GR-54124, Thessaloniki (Greece)
2007-08-15
In this work the dynamic behaviour of the one-dimensional family of maps F{sub p,q}(x) = 1/(1 - px - qx {sup 2}) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean.
Bifurcations of Fibonacci generating functions
International Nuclear Information System (INIS)
Ozer, Mehmet; Cenys, Antanas; Polatoglu, Yasar; Hacibekiroglu, Guersel; Akat, Ercument; Valaristos, A.; Anagnostopoulos, A.N.
2007-01-01
In this work the dynamic behaviour of the one-dimensional family of maps F p,q (x) = 1/(1 - px - qx 2 ) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean
Jiji, Latif M.
Professor Jiji's broad teaching experience lead him to select the topics for this book to provide a firm foundation for convection heat transfer with emphasis on fundamentals, physical phenomena, and mathematical modelling of a wide range of engineering applications. Reflecting recent developments, this textbook is the first to include an introduction to the challenging topic of microchannels. The strong pedagogic potential of Heat Convection is enhanced by the follow ing ancillary materials: (1) Power Point lectures, (2) Problem Solutions, (3) Homework Facilitator, and, (4) Summary of Sections and Chapters.
Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Directory of Open Access Journals (Sweden)
Tiansi Zhang
2013-01-01
Full Text Available A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the Poincaré return map and the bifurcation equation. A detailed investigation produces the number and the existence of 1-homoclinic orbit, 1-periodic orbit, and double 1-periodic orbits. We also locate their bifurcation surfaces in certain regions.
Bifurcation software in Matlab with applications in neuronal modeling.
Govaerts, Willy; Sautois, Bart
2005-02-01
Many biological phenomena, notably in neuroscience, can be modeled by dynamical systems. We describe a recent improvement of a Matlab software package for dynamical systems with applications to modeling single neurons and all-to-all connected networks of neurons. The new software features consist of an object-oriented approach to bifurcation computations and the partial inclusion of C-code to speed up the computation. As an application, we study the origin of the spiking behaviour of neurons when the equilibrium state is destabilized by an incoming current. We show that Class II behaviour, i.e. firing with a finite frequency, is possible even if the destabilization occurs through a saddle-node bifurcation. Furthermore, we show that synchronization of an all-to-all connected network of such neurons with only excitatory connections is also possible in this case.
Energy Technology Data Exchange (ETDEWEB)
Jacobs, A. M.; Zingale, M. [Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800 (United States); Nonaka, A.; Almgren, A. S.; Bell, J. B. [Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
2016-08-10
The dynamics of helium shell convection driven by nuclear burning establish the conditions for runaway in the sub-Chandrasekhar-mass, double-detonation model for SNe Ia, as well as for a variety of other explosive phenomena. We explore these convection dynamics for a range of white dwarf core and helium shell masses in three dimensions using the low Mach number hydrodynamics code MAESTRO. We present calculations of the bulk properties of this evolution, including time-series evolution of global diagnostics, lateral averages of the 3D state, and the global 3D state. We find a variety of outcomes, including quasi-equilibrium, localized runaway, and convective runaway. Our results suggest that the double-detonation progenitor model is promising and that 3D dynamic convection plays a key role.
Bifurcations of optimal vector fields: an overview
Kiseleva, T.; Wagener, F.; Rodellar, J.; Reithmeier, E.
2009-01-01
We develop a bifurcation theory for the solution structure of infinite horizon optimal control problems with one state variable. It turns out that qualitative changes of this structure are connected to local and global bifurcations in the state-costate system. We apply the theory to investigate an
Dynamical Regimes and the Dynamo Bifurcation in Geodynamo Simulations
Petitdemange, L.
2017-12-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core : in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the strong shear of geostrophic zonal flows can develop and gives rise to non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently.Close to the onset of convection (Rac), the axial dipole grows exponentially in the kinematic phase and saturation occurs by marginally changing the flow structure close to the dynamo threshold Rmc. The resulting bifurcation is then supercritical.In the range 3RacIf (Ra/Ra_c>10), important zonal flows develop in non-magnetic models with low viscosity. The field topology depends on the initial magnetic field. The dipolar branch has a subcritical behaviour whereas the multipolar branch is supercritical. By approaching more realistic parameters, the extension of this bistable regime increases (lower Rossby numbers). An hysteretic behaviour questions the common interpretation for geomagnetic reversals. Far above Rm_c$, the Lorentz force becomes dominant, as it is expected in planetary cores.
Voltage stability, bifurcation parameters and continuation methods
Energy Technology Data Exchange (ETDEWEB)
Alvarado, F L [Wisconsin Univ., Madison, WI (United States)
1994-12-31
This paper considers the importance of the choice of bifurcation parameter in the determination of the voltage stability limit and the maximum power load ability of a system. When the bifurcation parameter is power demand, the two limits are equivalent. However, when other types of load models and bifurcation parameters are considered, the two concepts differ. The continuation method is considered as a method for determination of voltage stability margins. Three variants of the continuation method are described: the continuation parameter is the bifurcation parameter the continuation parameter is initially the bifurcation parameter, but is free to change, and the continuation parameter is a new `arc length` parameter. Implementations of voltage stability software using continuation methods are described. (author) 23 refs., 9 figs.
Bifurcation and chaos in neural excitable system
International Nuclear Information System (INIS)
Jing Zhujun; Yang Jianping; Feng Wei
2006-01-01
In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained
National Convective Weather Diagnostic
National Oceanic and Atmospheric Administration, Department of Commerce — Current convective hazards identified by the National Convective Weather Detection algorithm. The National Convective Weather Diagnostic (NCWD) is an automatically...
Nonlinear stability control and λ-bifurcation
International Nuclear Information System (INIS)
Erneux, T.; Reiss, E.L.; Magnan, J.F.; Jayakumar, P.K.
1987-01-01
Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed
Recent perspective on coronary artery bifurcation interventions.
Dash, Debabrata
2014-01-01
Coronary bifurcation lesions are frequent in routine practice, accounting for 15-20% of all lesions undergoing percutaneous coronary intervention (PCI). PCI of this subset of lesions is technically challenging and historically has been associated with lower procedural success rates and worse clinical outcomes compared with non-bifurcation lesions. The introduction of drug-eluting stents has dramatically improved the outcomes. The provisional technique of implanting one stent in the main branch remains the default approach in most bifurcation lesions. Selection of the most effective technique for an individual bifurcation is important. The use of two-stent techniques as an intention to treat is an acceptable approach in some bifurcation lesions. However, a large amount of metal is generally left unapposed in the lumen with complex two-stent techniques, which is particularly concerning for the risk of stent thrombosis. New technology and dedicated bifurcation stents may overcome some of the limitations of two-stent techniques and revolutionise the management of bifurcation PCI in the future.
Energy Technology Data Exchange (ETDEWEB)
Hotta, H.; Rempel, M. [High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO (United States); Yokoyama, T., E-mail: hotta@ucar.edu [Department of Earth and Planetary Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)
2015-01-01
We present a high-resolution, highly stratified numerical simulation of rotating thermal convection in a spherical shell. Our aim is to study in detail the processes that can maintain a near surface shear layer (NSSL) as inferred from helioseismology. Using the reduced speed of sound technique, we can extend our global convection simulation to 0.99 R {sub ☉} and include, near the top of our domain, small-scale convection with short timescales that is only weakly influenced by rotation. We find the formation of an NSSL preferentially in high latitudes in the depth range of r = 0.95-0.975 R {sub ☉}. The maintenance mechanisms are summarized as follows. Convection under the weak influence of rotation leads to Reynolds stresses that transport angular momentum radially inward in all latitudes. This leads to the formation of a strong poleward-directed meridional flow and an NSSL, which is balanced in the meridional plane by forces resulting from the 〈v{sub r}{sup ′}v{sub θ}{sup ′}〉 correlation of turbulent velocities. The origin of the required correlations depends to some degree on latitude. In high latitudes, a positive correlation 〈v{sub r}{sup ′}v{sub θ}{sup ′}〉 is induced in the NSSL by the poleward meridional flow whose amplitude increases with the radius, while a negative correlation is generated by the Coriolis force in bulk of the convection zone. In low latitudes, a positive correlation 〈v{sub r}{sup ′}v{sub θ}{sup ′}〉 results from rotationally aligned convection cells ({sup b}anana cells{sup )}. The force caused by these Reynolds stresses is in balance with the Coriolis force in the NSSL.
Quantum entanglement and fixed-point bifurcations
International Nuclear Information System (INIS)
Hines, Andrew P.; McKenzie, Ross H.; Milburn, G.J.
2005-01-01
How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state--the ground state--achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation
A case study in bifurcation theory
Khmou, Youssef
This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.
Bifurcations of non-smooth systems
Angulo, Fabiola; Olivar, Gerard; Osorio, Gustavo A.; Escobar, Carlos M.; Ferreira, Jocirei D.; Redondo, Johan M.
2012-12-01
Non-smooth systems (namely piecewise-smooth systems) have received much attention in the last decade. Many contributions in this area show that theory and applications (to electronic circuits, mechanical systems, …) are relevant to problems in science and engineering. Specially, new bifurcations have been reported in the literature, and this was the topic of this minisymposium. Thus both bifurcation theory and its applications were included. Several contributions from different fields show that non-smooth bifurcations are a hot topic in research. Thus in this paper the reader can find contributions from electronics, energy markets and population dynamics. Also, a carefully-written specific algebraic software tool is presented.
Bifurcation Control of Chaotic Dynamical Systems
National Research Council Canada - National Science Library
Wang, Hua O; Abed, Eyad H
1992-01-01
A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems...
Bifurcation and instability problems in vortex wakes
DEFF Research Database (Denmark)
Aref, Hassan; Brøns, Morten; Stremler, Mark A.
2007-01-01
A number of instability and bifurcation problems related to the dynamics of vortex wake flows are addressed using various analytical tools and approaches. We discuss the bifurcations of the streamline pattern behind a bluff body as a vortex wake is produced, a theory of the universal Strouhal......-Reynolds number relation for vortex wakes, the bifurcation diagram for "exotic" wake patterns behind an oscillating cylinder first determined experimentally by Williamson & Roshko, and the bifurcations in topology of the streamlines pattern in point vortex streets. The Hamiltonian dynamics of point vortices...... in a periodic strip is considered. The classical results of von Kármán concerning the structure of the vortex street follow from the two-vortices-in-a-strip problem, while the stability results follow largely from a four-vortices-in-a-strip analysis. The three-vortices-in-a-strip problem is argued...
Bifurcation structure of successive torus doubling
International Nuclear Information System (INIS)
Sekikawa, Munehisa; Inaba, Naohiko; Yoshinaga, Tetsuya; Tsubouchi, Takashi
2006-01-01
The authors discuss the 'embryology' of successive torus doubling via the bifurcation theory, and assert that the coupled map of a logistic map and a circle map has a structure capable of generating infinite number of torus doublings
Convective flows of colloidal suspension in an inclined closed cell
Energy Technology Data Exchange (ETDEWEB)
Smorodin, Boris; Ishutov, Sergey [Department of Physics of Phase Transitions, Perm State University, Perm (Russian Federation); Cherepanov, Ivan, E-mail: bsmorodin@yandex.ru [Department of Radio Electronics and Information Security, Perm State University, Perm (Russian Federation)
2016-12-15
The nonlinear spatiotemporal evolution of convective flows is numerically investigated in the case of colloidal suspension filling an inclined closed cell heated from below. The bifurcation diagram (the dependency of the Nusselt number on the Rayleigh number) is obtained. The characteristics of the wave and steady patterns are investigated depending on heat intensity. The travelling wave changing travel direction and the non-regular oscillatory flow are found to be stable solutions within a certain interval of the Rayleigh number. Temporal Fourier decomposition is used together with other diagnostic tools to analyse the complex bifurcation and spatiotemporal properties caused by the interplay of the gravity-induced gradient of concentration and convective mixing of the fluid. It is shown that a more complex flow structure exists at a lower heating intensity (Rayleigh number). (paper)
Hopf bifurcation in an Internet congestion control model
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong; Liao Xiaofeng; Yu Juebang
2004-01-01
We consider an Internet model with a single link accessed by a single source, which responds to congestion signals from the network, and study bifurcation of such a system. By choosing the gain parameter as a bifurcation parameter, we prove that Hopf bifurcation occurs. The stability of bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, a numerical example is given to verify the theoretical analysis
Discretization analysis of bifurcation based nonlinear amplifiers
Feldkord, Sven; Reit, Marco; Mathis, Wolfgang
2017-09-01
Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.
Geometrically Induced Interactions and Bifurcations
Binder, Bernd
2010-01-01
In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels Ramsing; Curzen, Nicholas P
2011-01-01
Background— Controversy persists regarding the correct strategy for bifurcation lesions. Therefore, we combined the patient-level data from 2 large trials with similar methodology: the NORDIC Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study (BBC ONE). Methods and Results— B...
Directory of Open Access Journals (Sweden)
Randhir Singh Baghel
2012-02-01
Full Text Available In this article, we propose a three dimensional mathematical model of phytoplankton dynamics with the help of reaction-diffusion equations that studies the bifurcation and pattern formation mechanism. We provide an analytical explanation for understanding phytoplankton dynamics with three population classes: susceptible, incubated, and infected. This model has a Holling type II response function for the population transformation from susceptible to incubated class in an aquatic ecosystem. Our main goal is to provide a qualitative analysis of Hopf bifurcation mechanisms, taking death rate of infected phytoplankton as bifurcation parameter, and to study further spatial patterns formation due to spatial diffusion. Here analytical findings are supported by the results of numerical experiments. It is observed that the coexistence of all classes of population depends on the rate of diffusion. Also we obtained the time evaluation pattern formation of the spatial system.
Computing closest saddle node bifurcations in a radial system via conic programming
Energy Technology Data Exchange (ETDEWEB)
Jabr, R.A. [Electrical, Computer and Communication Engineering Department, Notre Dame University, P.O. Box 72, Zouk Mikhael, Zouk Mosbeh (Lebanon); Pal, B.C. [Department of Electrical and Electronic Engineering, Imperial College London, SW7 2BT (United Kingdom)
2009-07-15
This paper considers the problem of computing the loading limits in a radial system which are (i) locally closest to current operating load powers and (ii) at which saddle node bifurcation occurs. The procedure is based on a known technique which requires iterating between two computational steps until convergence. In essence, step 1 produces a vector normal to the real and/or reactive load solution space boundary, whereas step 2 computes the bifurcation point along that vector. The paper shows that each of the above computational steps can be formulated as a second-order cone program for which polynomial time interior-point methods and efficient implementations exist. The proposed conic programming approach is used to compute the closest bifurcation points and the corresponding worst case load power margins of eleven different distribution systems. The approach is validated graphically and the existence of multiple load power margins is investigated. (author)
Bifurcation analysis of a three dimensional system
Directory of Open Access Journals (Sweden)
Yongwen WANG
2018-04-01
Full Text Available In order to enrich the stability and bifurcation theory of the three dimensional chaotic systems, taking a quadratic truncate unfolding system with the triple singularity equilibrium as the research subject, the existence of the equilibrium, the stability and the bifurcation of the system near the equilibrium under different parametric conditions are studied. Using the method of mathematical analysis, the existence of the real roots of the corresponding characteristic equation under the different parametric conditions is analyzed, and the local manifolds of the equilibrium are gotten, then the possible bifurcations are guessed. The parametric conditions under which the equilibrium is saddle-focus are analyzed carefully by the Cardan formula. Moreover, the conditions of codimension-one Hopf bifucation and the prerequisites of the supercritical and subcritical Hopf bifurcation are found by computation. The results show that the system has abundant stability and bifurcation, and can also supply theorical support for the proof of the existence of the homoclinic or heteroclinic loop connecting saddle-focus and the Silnikov's chaos. This method can be extended to study the other higher nonlinear systems.
Bifurcations of Tumor-Immune Competition Systems with Delay
Directory of Open Access Journals (Sweden)
Ping Bi
2014-01-01
Full Text Available A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results.
Attractors near grazing–sliding bifurcations
International Nuclear Information System (INIS)
Glendinning, P; Kowalczyk, P; Nordmark, A B
2012-01-01
In this paper we prove, for the first time, that multistability can occur in three-dimensional Fillipov type flows due to grazing–sliding bifurcations. We do this by reducing the study of the dynamics of Filippov type flows around a grazing–sliding bifurcation to the study of appropriately defined one-dimensional maps. In particular, we prove the presence of three qualitatively different types of multiple attractors born in grazing–sliding bifurcations. Namely, a period-two orbit with a sliding segment may coexist with a chaotic attractor, two stable, period-two and period-three orbits with a segment of sliding each may coexist, or a non-sliding and period-three orbit with two sliding segments may coexist
Clavner, Michal; Grasso, Lewis D.; Cotton, William R.; van den Heever, Susan C.
2018-01-01
Mesoscale Convective Systems (MCS) are important contributors to rainfall as well as producers of severe weather such as hail, tornados, and straight-line wind events known as derechos. In this study, different aerosol concentrations and their effects on a derecho event are examined by simulating a case study, the 8 May 2009 "Super-Derecho", using the Regional Atmospheric Modeling System (RAMS), a cloud-resolving model with sophisticated aerosol and cloud microphysics. Three simulations were conducted that differed in the initial aerosol concentrations, spatial distribution and chemical composition as derived from output of GEOS-Chem, a 3D chemical transport model. In order to understand the impact of changes in aerosol concentrations on the derecho characteristics, the dynamical processes that produced the strong surface wind were determined by performing back-trajectory analysis during two periods of the simulated storm: the development and the onset of dissipation. A time dependent and non-monotonic trend was found between the intensity of the derecho and the increased aerosol concentrations that served as cloud condensation nuclei. During the formation period of the MCS, the non-monotonic trend was attributed to the microphysical impact of aerosol loading on the intensity of the cold pool; that is, the impact of aerosols on both the melting and evaporation rates of hydrometeors. The subsequent intensity changes within the cold pool modified the balance between the horizontal vorticity generated by the cold pool and that of the environment, thereby impacting the orientation of the convective updraft at the leading line. This, in turn, altered the primary flow that contributed to the formation of the derecho-strength surface winds. The simulation with no anthropogenic aerosols exhibited the strongest cold pool and the primary flow was associated with a descending rear inflow jet that produced the derecho winds over a larger region. The simulation with the highest
International Nuclear Information System (INIS)
Sushko, Iryna; Agliari, Anna; Gardini, Laura
2006-01-01
We study the structure of the 2D bifurcation diagram for a two-parameter family of piecewise smooth unimodal maps f with one break point. Analysing the parameters of the normal form for the border-collision bifurcation of an attracting n-cycle of the map f, we describe the possible kinds of dynamics associated with such a bifurcation. Emergence and role of border-collision bifurcation curves in the 2D bifurcation plane are studied. Particular attention is paid also to the curves of homoclinic bifurcations giving rise to the band merging of pieces of cyclic chaotic intervals
Bifurcation of Jovian magnetotail current sheet
Directory of Open Access Journals (Sweden)
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the Bx-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
Bifurcation of Jovian magnetotail current sheet
Directory of Open Access Journals (Sweden)
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the B_{x}-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
Instabilities of convection patterns in a shear-thinning fluid between plates of finite conductivity
Varé, Thomas; Nouar, Chérif; Métivier, Christel
2017-10-01
Rayleigh-Bénard convection in a horizontal layer of a non-Newtonian fluid between slabs of arbitrary thickness and finite thermal conductivity is considered. The first part of the paper deals with the primary bifurcation and the relative stability of convective patterns at threshold. Weakly nonlinear analysis combined with Stuart-Landau equation is used. The competition between squares and rolls, as a function of the shear-thinning degree of the fluid, the slabs' thickness, and the ratio of the thermal conductivity of the slabs to that of the fluid is investigated. Computations of heat transfer coefficients are in agreement with the maximum heat transfer principle. The second part of the paper concerns the stability of the convective patterns toward spatial perturbations and the determination of the band width of the stable wave number in the neighborhood of the critical Rayleigh number. The approach used is based on the Ginzburg-Landau equations. The study of rolls stability shows that: (i) for low shear-thinning effects, the band of stable wave numbers is bounded by zigzag instability and cross-roll instability. Furthermore, the marginal cross-roll stability boundary enlarges with increasing shear-thinning properties; (ii) for high shear-thinning effects, Eckhaus instability becomes more dangerous than cross-roll instability. For square patterns, the wave number selection is always restricted by zigzag instability and by "rectangular Eckhaus" instability. In addition, the width of the stable wave number decreases with increasing shear-thinning effects. Numerical simulations of the planform evolution are also presented to illustrate the different instabilities considered in the paper.
National Convective Weather Forecast
National Oceanic and Atmospheric Administration, Department of Commerce — The NCWF is an automatically generated depiction of: (1) current convection and (2) extrapolated signficant current convection. It is a supplement to, but does NOT...
Sparse identification of a predator-prey system from simulation data of a convection model
DEFF Research Database (Denmark)
Dam, Magnus; Brøns, Morten; Rasmussen, Jens Juul
2017-01-01
of a convection problem. A convection model with a pressure source centered at the inner boundary models the edge dynamics of a magnetically confined plasma. The convection problem undergoes a sequence of bifurcations as the strength of the pressure source increases. The time evolution of the energies......The use of low-dimensional dynamical systems as reduced models for plasma dynamics is useful as solving an initial value problem requires much less computational resources than fluid simulations. We utilize a data-driven modeling approach to identify a reduced model from simulation data...
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Ló czi, Lajos
2015-01-01
© 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions
Bifurcations of a class of singular biological economic models
International Nuclear Information System (INIS)
Zhang Xue; Zhang Qingling; Zhang Yue
2009-01-01
This paper studies systematically a prey-predator singular biological economic model with time delay. It shows that this model exhibits two bifurcation phenomena when the economic profit is zero. One is transcritical bifurcation which changes the stability of the system, and the other is singular induced bifurcation which indicates that zero economic profit brings impulse, i.e., rapid expansion of the population in biological explanation. On the other hand, if the economic profit is positive, at a critical value of bifurcation parameter, the system undergoes a Hopf bifurcation, i.e., the increase of delay destabilizes the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results obtained here. In addition, we study numerically that the system undergoes a saddle-node bifurcation when the bifurcation parameter goes through critical value of positive economic profit.
Bifurcation structure of a model of bursting pancreatic cells
DEFF Research Database (Denmark)
Mosekilde, Erik; Lading, B.; Yanchuk, S.
2001-01-01
One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other. The transit......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other....... The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...
Codimension-2 bifurcations of the Kaldor model of business cycle
International Nuclear Information System (INIS)
Wu, Xiaoqin P.
2011-01-01
Research highlights: → The conditions are given such that the characteristic equation may have purely imaginary roots and double zero roots. → Purely imaginary roots lead us to study Hopf and Bautin bifurcations and to calculate the first and second Lyapunov coefficients. → Double zero roots lead us to study Bogdanov-Takens (BT) bifurcation. → Bifurcation diagrams for Bautin and BT bifurcations are obtained by using the normal form theory. - Abstract: In this paper, complete analysis is presented to study codimension-2 bifurcations for the nonlinear Kaldor model of business cycle. Sufficient conditions are given for the model to demonstrate Bautin and Bogdanov-Takens (BT) bifurcations. By computing the first and second Lyapunov coefficients and performing nonlinear transformation, the normal forms are derived to obtain the bifurcation diagrams such as Hopf, homoclinic and double limit cycle bifurcations. Some examples are given to confirm the theoretical results.
Comments on the Bifurcation Structure of 1D Maps
DEFF Research Database (Denmark)
Belykh, V.N.; Mosekilde, Erik
1997-01-01
-within-a-box structure of the total bifurcation set. This presents a picture in which the homoclinic orbit bifurcations act as a skeleton for the bifurcational set. At the same time, experimental results on continued subharmonic generation for piezoelectrically amplified sound waves, predating the Feigenbaum theory......, are called into attention....
NUMERICAL HOPF BIFURCATION OF DELAY-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper we consider the numerical solution of some delay differential equations undergoing a Hopf bifurcation. We prove that if the delay differential equations have a Hopf bifurcation point atλ=λ*, then the numerical solution of the equation also has a Hopf bifurcation point atλh =λ* + O(h).
Bifurcation of elastic solids with sliding interfaces
Bigoni, D.; Bordignon, N.; Piccolroaz, A.; Stupkiewicz, S.
2018-01-01
Lubricated sliding contact between soft solids is an interesting topic in biomechanics and for the design of small-scale engineering devices. As a model of this mechanical set-up, two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so this formulation is the objective of the present paper. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or `spring-type' interfacial conditions are not able to predict bifurcations in tension, while experiments-one of which, ad hoc designed, is reported-show that these bifurcations are a reality and become possible when the correct sliding interface model is used. The presented results introduce a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact.
Climate bifurcation during the last deglaciation?
Lenton, T.M.; Livina, V.N.; Dakos, V.; Scheffer, M.
2012-01-01
There were two abrupt warming events during the last deglaciation, at the start of the Bolling-Allerod and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state
Bifurcation structure of an optical ring cavity
DEFF Research Database (Denmark)
Kubstrup, C.; Mosekilde, Erik
1996-01-01
One- and two-dimensional continuation techniques are applied to determine the basic bifurcation structure for an optical ring cavity with a nonlinear absorbing element (the Ikeda Map). By virtue of the periodic structure of the map, families of similar solutions develop in parameter space. Within...
Resource competition: a bifurcation theory approach.
Kooi, B.W.; Dutta, P.S.; Feudel, U.
2013-01-01
We develop a framework for analysing the outcome of resource competition based on bifurcation theory. We elaborate our methodology by readdressing the problem of competition of two species for two resources in a chemostat environment. In the case of perfect-essential resources it has been
Digital subtraction angiography of carotid bifurcation
International Nuclear Information System (INIS)
Vries, A.R. de.
1984-01-01
This study demonstrates the reliability of digital subtraction angiography (DSA) by means of intra- and interobserver investigations as well as indicating the possibility of substituting catheterangiography by DSA in the diagnosis of carotid bifurcation. Whenever insufficient information is obtained from the combination of non-invasive investigation and DSA, a catheterangiogram will be necessary. (Auth.)
Percutaneous coronary intervention for coronary bifurcation disease
DEFF Research Database (Denmark)
Lassen, Jens Flensted; Holm, Niels Ramsing; Banning, Adrian
2016-01-01
of combining the opinions of interventional cardiologists with the opinions of a large variety of other scientists on bifurcation management. The present 11th EBC consensus document represents the summary of the up-to-date EBC consensus and recommendations. It points to the fact that there is a multitude...
Bifurcation of self-folded polygonal bilayers
Abdullah, Arif M.; Braun, Paul V.; Hsia, K. Jimmy
2017-09-01
Motivated by the self-assembly of natural systems, researchers have investigated the stimulus-responsive curving of thin-shell structures, which is also known as self-folding. Self-folding strategies not only offer possibilities to realize complicated shapes but also promise actuation at small length scales. Biaxial mismatch strain driven self-folding bilayers demonstrate bifurcation of equilibrium shapes (from quasi-axisymmetric doubly curved to approximately singly curved) during their stimulus-responsive morphing behavior. Being a structurally instable, bifurcation could be used to tune the self-folding behavior, and hence, a detailed understanding of this phenomenon is appealing from both fundamental and practical perspectives. In this work, we investigated the bifurcation behavior of self-folding bilayer polygons. For the mechanistic understanding, we developed finite element models of planar bilayers (consisting of a stimulus-responsive and a passive layer of material) that transform into 3D curved configurations. Our experiments with cross-linked Polydimethylsiloxane samples that change shapes in organic solvents confirmed our model predictions. Finally, we explored a design scheme to generate gripper-like architectures by avoiding the bifurcation of stimulus-responsive bilayers. Our research contributes to the broad field of self-assembly as the findings could motivate functional devices across multiple disciplines such as robotics, artificial muscles, therapeutic cargos, and reconfigurable biomedical devices.
Modified jailed balloon technique for bifurcation lesions.
Saito, Shigeru; Shishido, Koki; Moriyama, Noriaki; Ochiai, Tomoki; Mizuno, Shingo; Yamanaka, Futoshi; Sugitatsu, Kazuya; Tobita, Kazuki; Matsumi, Junya; Tanaka, Yutaka; Murakami, Masato
2017-12-04
We propose a new systematic approach in bifurcation lesions, modified jailed balloon technique (M-JBT), and report the first clinical experience. Side branch occlusion brings with a serious complication and occurs in more than 7.0% of cases during bifurcation stenting. A jailed balloon (JB) is introduced into the side branch (SB), while a stent is placed in the main branch (MB) as crossing SB. The size of the JB is half of the MB stent size. While the proximal end of JB attaching to MB stent, both stent and JB are simultaneously inflated with same pressure. JB is removed and then guidewires are recrossed. Kissing balloon dilatation (KBD) and/or T and protrusion (TAP) stenting are applied as needed. Between February 2015 and February 2016, 233 patients (254 bifurcation lesions including 54 left main trunk disease) underwent percutaneous coronary intervention (PCI) using this technique. Procedure success was achieved in all cases. KBD was performed for 183 lesions and TAP stenting was employed for 31 lesions. Occlusion of SV was not observed in any of the patients. Bench test confirmed less deformity of MB stent in M-JBT compared with conventional-JBT. This is the first report for clinical experiences by using modified jailed balloon technique. This novel M-JBT is safe and effective in the preservation of SB patency during bifurcation stenting. © 2017 Wiley Periodicals, Inc.
On a Five-Dimensional Chaotic System Arising from Double-Diffusive Convection in a Fluid Layer
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R. Idris
2013-01-01
Full Text Available A chaotic system arising from double-diffusive convection in a fluid layer is investigated in this paper based on the theory of dynamical systems. A five-dimensional model of chaotic system is obtained using the Galerkin truncated approximation. The results showed that the transition from steady convection to chaos via a Hopf bifurcation produced a limit cycle which may be associated with a homoclinic explosion at a slightly subcritical value of the Rayleigh number.
Stochastic bifurcation in a model of love with colored noise
Yue, Xiaokui; Dai, Honghua; Yuan, Jianping
2015-07-01
In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.
Bifurcation Behavior Analysis in a Predator-Prey Model
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Nan Wang
2016-01-01
Full Text Available A predator-prey model is studied mathematically and numerically. The aim is to explore how some key factors influence dynamic evolutionary mechanism of steady conversion and bifurcation behavior in predator-prey model. The theoretical works have been pursuing the investigation of the existence and stability of the equilibria, as well as the occurrence of bifurcation behaviors (transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation, which can deduce a standard parameter controlled relationship and in turn provide a theoretical basis for the numerical simulation. Numerical analysis ensures reliability of the theoretical results and illustrates that three stable equilibria will arise simultaneously in the model. It testifies the existence of Bogdanov-Takens bifurcation, too. It should also be stressed that the dynamic evolutionary mechanism of steady conversion and bifurcation behavior mainly depend on a specific key parameter. In a word, all these results are expected to be of use in the study of the dynamic complexity of ecosystems.
Symmetry breaking bifurcations of a current sheet
International Nuclear Information System (INIS)
Parker, R.D.; Dewar, R.L.; Johnson, J.L.
1990-01-01
Using a time evolution code with periodic boundary conditions, the viscoresistive hydromagnetic equations describing an initially static, planar current sheet with large Lundquist number have been evolved for times long enough to reach a steady state. A cosh 2 x resistivity model was used. For long periodicity lengths L p , the resistivity gradient drives flows that cause forced reconnection at X point current sheets. Using L p as a bifurcation parameter, two new symmetry breaking bifurcations were found: a transition to an asymmetric island chain with nonzero, positive, or negative phase velocity, and a transition to a static state with alternating large and small islands. These states are reached after a complex transient behavior, which involves a competition between secondary current sheet instability and coalescence
Symmetry breaking bifurcations of a current sheet
International Nuclear Information System (INIS)
Parker, R.D.; Dewar, R.L.; Johnson, J.L.
1988-08-01
Using a time evolution code with periodic boundary conditions, the viscoresistive hydromagnetic equations describing an initially static, planar current sheet with large Lundquist number have been evolved for times long enough to reach a steady state. A cosh 2 x resistivity model was used. For long periodicity lengths, L p , the resistivity gradient drives flows which cause forced reconnection at X point current sheets. Using L p as a bifurcation parameter, two new symmetry breaking bifurcations were found - a transition to an asymmetric island chain with nonzero, positive or negative phase velocity, and a transition to a static state with alternating large and small islands. These states are reached after a complex transient behavior which involves a competition between secondary current sheet instability and coalescence. 31 refs., 6 figs
Experimental Study of Flow in a Bifurcation
Fresconi, Frank; Prasad, Ajay
2003-11-01
An instability known as the Dean vortex occurs in curved pipes with a longitudinal pressure gradient. A similar effect is manifest in the flow in a converging or diverging bifurcation, such as those found in the human respiratory airways. The goal of this study is to characterize secondary flows in a bifurcation. Particle image velocimetry (PIV) and laser-induced fluorescence (LIF) experiments were performed in a clear, plastic model. Results show the strength and migration of secondary vortices. Primary velocity features are also presented along with dispersion patterns from dye visualization. Unsteadiness, associated with a hairpin vortex, was also found at higher Re. This work can be used to assess the dispersion of particles in the lung. Medical delivery systems and pollution effect studies would profit from such an understanding.
Bifurcations and chaos of DNA solitonic dynamics
International Nuclear Information System (INIS)
Gonzalez, J.A.; Martin-Landrove, M.; Carbo, J.R.; Chacon, M.
1994-09-01
We investigated the nonlinear DNA torsional equations proposed by Yakushevich in the presence of damping and external torques. Analytical expressions for some solutions are obtained in the case of the isolated chain. Special attention is paid to the stability of the solutions and the range of soliton interaction in the general case. The bifurcation analysis is performed and prediction of chaos is obtained for some set of parameters. Some biological implications are suggested. (author). 11 refs, 13 figs
Torus bifurcations in multilevel converter systems
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Yanochkina, Olga O.
2011-01-01
embedded one into the other and with their basins of attraction delineated by intervening repelling tori. The paper illustrates the coexistence of three stable tori with different resonance behaviors and shows how reconstruction of these tori takes place across the borders of different dynamical regimes....... The paper also demonstrates how pairs of attracting and repelling tori emerge through border-collision torus-birth and border-collision torus-fold bifurcations. © 2011 World Scientific Publishing Company....
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
Sex differences in intracranial arterial bifurcations
DEFF Research Database (Denmark)
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K
2010-01-01
Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. T....... The female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor-a local sex difference in the intracranial arteries....
Drift bifurcation detection for dissipative solitons
International Nuclear Information System (INIS)
Liehr, A W; Boedeker, H U; Roettger, M C; Frank, T D; Friedrich, R; Purwins, H-G
2003-01-01
We report on the experimental detection of a drift bifurcation for dissipative solitons, which we observe in the form of current filaments in a planar semiconductor-gas-discharge system. By introducing a new stochastic data analysis technique we find that due to a change of system parameters the dissipative solitons undergo a transition from purely noise-driven objects with Brownian motion to particles with a dynamically stabilized finite velocity
Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain
International Nuclear Information System (INIS)
Wang Fengyan; Pang Guoping
2008-01-01
In this paper, we propose and study a model of a hybrid ratio-dependent three species food chain, which is constituted by a hybrid type subsystem of prey and middle-predator and a middle-top predators' subsystem with Holling type-II functional response. We investigate the persistence and Hopf bifurcation of the system. Computer simulations are carried out to explain the mathematical conclusions. The chaotic attractor is obtained for suitable choice of parametric values
Energized Oxygen : Speiser Current Sheet Bifurcation
George, D. E.; Jahn, J. M.
2017-12-01
A single population of energized Oxygen (O+) is shown to produce a cross-tail bifurcated current sheet in 2.5D PIC simulations of the magnetotail without the influence of magnetic reconnection. Treatment of oxygen in simulations of space plasmas, specifically a magnetotail current sheet, has been limited to thermal energies despite observations of and mechanisms which explain energized ions. We performed simulations of a homogeneous oxygen background, that has been energized in a physically appropriate manner, to study the behavior of current sheets and magnetic reconnection, specifically their bifurcation. This work uses a 2.5D explicit Particle-In-a-Cell (PIC) code to investigate the dynamics of energized heavy ions as they stream Dawn-to-Dusk in the magnetotail current sheet. We present a simulation study dealing with the response of a current sheet system to energized oxygen ions. We establish a, well known and studied, 2-species GEM Challenge Harris current sheet as a starting point. This system is known to eventually evolve and produce magnetic reconnection upon thinning of the current sheet. We added a uniform distribution of thermal O+ to the background. This 3-species system is also known to eventually evolve and produce magnetic reconnection. We add one additional variable to the system by providing an initial duskward velocity to energize the O+. We also traced individual particle motion within the PIC simulation. Three main results are shown. First, energized dawn- dusk streaming ions are clearly seen to exhibit sustained Speiser motion. Second, a single population of heavy ions clearly produces a stable bifurcated current sheet. Third, magnetic reconnection is not required to produce the bifurcated current sheet. Finally a bifurcated current sheet is compatible with the Harris current sheet model. This work is the first step in a series of investigations aimed at studying the effects of energized heavy ions on magnetic reconnection. This work differs
Global Bifurcation of a Novel Computer Virus Propagation Model
Directory of Open Access Journals (Sweden)
Jianguo Ren
2014-01-01
Full Text Available In a recent paper by J. Ren et al. (2012, a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network.
Bifurcation theory for finitely smooth planar autonomous differential systems
Han, Maoan; Sheng, Lijuan; Zhang, Xiang
2018-03-01
In this paper we establish bifurcation theory of limit cycles for planar Ck smooth autonomous differential systems, with k ∈ N. The key point is to study the smoothness of bifurcation functions which are basic and important tool on the study of Hopf bifurcation at a fine focus or a center, and of Poincaré bifurcation in a period annulus. We especially study the smoothness of the first order Melnikov function in degenerate Hopf bifurcation at an elementary center. As we know, the smoothness problem was solved for analytic and C∞ differential systems, but it was not tackled for finitely smooth differential systems. Here, we present their optimal regularity of these bifurcation functions and their asymptotic expressions in the finite smooth case.
Bifurcation structure of a model of bursting pancreatic cells
DEFF Research Database (Denmark)
Mosekilde, Erik; Lading, B.; Yanchuk, S.
2001-01-01
. The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...... behavior is born, slightly overlapping with a subcritical period-doubling bifurcation in which n-spike bursting behavior loses its stability.......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other...
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Stability and bifurcation analysis in a delayed SIR model
International Nuclear Information System (INIS)
Jiang Zhichao; Wei Junjie
2008-01-01
In this paper, a time-delayed SIR model with a nonlinear incidence rate is considered. The existence of Hopf bifurcations at the endemic equilibrium is established by analyzing the distribution of the characteristic values. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out
Bifurcation of rupture path by linear and cubic damping force
Dennis L. C., C.; Chew X., Y.; Lee Y., C.
2014-06-01
Bifurcation of rupture path is studied for the effect of linear and cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the separation of variables. Analytical or exact solutions yielded the bifurcation was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible.
Directory of Open Access Journals (Sweden)
Carlos Mario Escobar Callejas
2011-12-01
Full Text Available En el presente artículo de investigación se caracteriza el tipo de bifurcación de Hopf que se presenta en el fenómeno de la bifurcación de zip para un sistema tridimensional no lineal de ecuaciones diferenciales que satisface las condiciones planteadas por Butler y Farkas, las cuales modelan la competición de dos especies predadoras por una presa singular que se regenera. Se demuestra que en todas las variedades bidimensionales invariantes del sistema considerado se desarrolla una bifurcación de Hopf supercrítica lo cual es una extensión de algunos resultados sobre el tipo de bifurcación de Hopf que se forma en el fenómeno de la bifurcación de zip en sistema con respuesta funcional del predador del tipo Holling II, [1].This research article characterizes the type of Hopf bifurcation occurring in the Zip bifurcation phenomenon for a non-linear 3D system of differential equations which meets the conditions stated by Butler and Farkas to model competition of two predators struggling for a prey. It is shown that a supercritical Hopf bifurcation is developed in all invariant two-dimensional varieties of the system considered, which is an extension of some results about the kind of Hopf bifurcation which is formed in the Zip bifurcation phenomenon in a system with functional response of the Holling-type predator.
A codimension two bifurcation in a railway bogie system
DEFF Research Database (Denmark)
Zhang, Tingting; True, Hans; Dai, Huanyun
2017-01-01
In this paper, a comprehensive analysis is presented to investigate a codimension two bifurcation that exists in a nonlinear railway bogie dynamic system combining theoretical analysis with numerical investigation. By using the running velocity V and the primary longitudinal stiffness (Formula...... coexist in a range of the bifurcation parameters which can lead to jumps in the lateral oscillation amplitude of the railway bogie system. Furthermore, reduce the values of the bifurcation parameters gradually. Firstly, the supercritical Hopf bifurcation turns into a subcritical one with multiple limit...
Hopf bifurcation for tumor-immune competition systems with delay
Directory of Open Access Journals (Sweden)
Ping Bi
2014-01-01
Full Text Available In this article, a immune response system with delay is considered, which consists of two-dimensional nonlinear differential equations. The main purpose of this paper is to explore the Hopf bifurcation of a immune response system with delay. The general formula of the direction, the estimation formula of period and stability of bifurcated periodic solution are also given. Especially, the conditions of the global existence of periodic solutions bifurcating from Hopf bifurcations are given. Numerical simulations are carried out to illustrate the the theoretical analysis and the obtained results.
Predicting bifurcation angle effect on blood flow in the microvasculature.
Yang, Jiho; Pak, Y Eugene; Lee, Tae-Rin
2016-11-01
Since blood viscosity is a basic parameter for understanding hemodynamics in human physiology, great amount of research has been done in order to accurately predict this highly non-Newtonian flow property. However, previous works lacked in consideration of hemodynamic changes induced by heterogeneous vessel networks. In this paper, the effect of bifurcation on hemodynamics in a microvasculature is quantitatively predicted. The flow resistance in a single bifurcation microvessel was calculated by combining a new simple mathematical model with 3-dimensional flow simulation for varying bifurcation angles under physiological flow conditions. Interestingly, the results indicate that flow resistance induced by vessel bifurcation holds a constant value of approximately 0.44 over the whole single bifurcation model below diameter of 60μm regardless of geometric parameters including bifurcation angle. Flow solutions computed from this new model showed substantial decrement in flow velocity relative to other mathematical models, which do not include vessel bifurcation effects, while pressure remained the same. Furthermore, when applying the bifurcation angle effect to the entire microvascular network, the simulation results gave better agreements with recent in vivo experimental measurements. This finding suggests a new paradigm in microvascular blood flow properties, that vessel bifurcation itself, regardless of its angle, holds considerable influence on blood viscosity, and this phenomenon will help to develop new predictive tools in microvascular research. Copyright © 2016 Elsevier Inc. All rights reserved.
Double Hopf bifurcation in delay differential equations
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Redouane Qesmi
2014-07-01
Full Text Available The paper addresses the computation of elements of double Hopf bifurcation for retarded functional differential equations (FDEs with parameters. We present an efficient method for computing, simultaneously, the coefficients of center manifolds and normal forms, in terms of the original FDEs, associated with the double Hopf singularity up to an arbitrary order. Finally, we apply our results to a nonlinear model with periodic delay. This shows the applicability of the methodology in the study of delay models arising in either natural or technological problems.
Bifurcation theory for toroidal MHD instabilities
International Nuclear Information System (INIS)
Maschke, E.K.; Morros Tosas, J.; Urquijo, G.
1992-01-01
Using a general representation of magneto-hydrodynamics in terms of stream functions and potentials, proposed earlier, a set of reduced MHD equations for the case of toroidal geometry had been derived by an appropriate ordering with respect to the inverse aspect ratio. When all dissipative terms are neglected in this reduced system, it has the same linear stability limits as the full ideal MHD equations, to the order considered. When including resistivity, thermal conductivity and viscosity, we can apply bifurcation theory to investigate nonlinear stationary solution branches related to various instabilities. In particular, we show that a stationary solution of the internal kink type can be found
Spijkerboer, T.P.
2017-01-01
The externalization of European migration policy has resulted in a bifurcation of global human mobility, which is divided along a North/South axis. In two judgments, the EU Court of Justice was confronted with cases challenging the exclusion of Syrian refugees from Europe. These cases concern core
Observing Convective Aggregation
Holloway, Christopher E.; Wing, Allison A.; Bony, Sandrine; Muller, Caroline; Masunaga, Hirohiko; L'Ecuyer, Tristan S.; Turner, David D.; Zuidema, Paquita
2017-11-01
Convective self-aggregation, the spontaneous organization of initially scattered convection into isolated convective clusters despite spatially homogeneous boundary conditions and forcing, was first recognized and studied in idealized numerical simulations. While there is a rich history of observational work on convective clustering and organization, there have been only a few studies that have analyzed observations to look specifically for processes related to self-aggregation in models. Here we review observational work in both of these categories and motivate the need for more of this work. We acknowledge that self-aggregation may appear to be far-removed from observed convective organization in terms of time scales, initial conditions, initiation processes, and mean state extremes, but we argue that these differences vary greatly across the diverse range of model simulations in the literature and that these comparisons are already offering important insights into real tropical phenomena. Some preliminary new findings are presented, including results showing that a self-aggregation simulation with square geometry has too broad distribution of humidity and is too dry in the driest regions when compared with radiosonde records from Nauru, while an elongated channel simulation has realistic representations of atmospheric humidity and its variability. We discuss recent work increasing our understanding of how organized convection and climate change may interact, and how model discrepancies related to this question are prompting interest in observational comparisons. We also propose possible future directions for observational work related to convective aggregation, including novel satellite approaches and a ground-based observational network.
A Dynamic Analysis for an Anaerobic Digester: Stability and Bifurcation Branches
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Alejandro Rincón
2014-01-01
Full Text Available This work presents a dynamic analysis for an anaerobic digester, supported on the analytical application of the indirect Lyapunov method. The mass-balance model considered is based on two biological reaction pathways and involves both Monod and Haldane representations of the specific biomass growth rates. The dilution rate, the influent concentration of chemical oxygen demand (COD, and the influent concentration of volatile fatty acids (VFA are considered as stability parameters. Several characteristics are determined analytically for the normal operation equilibrium point: (i equilibrium coordinates, (ii parameter conditions that lead to positive values of the equilibrium state variables, (iii parameter conditions for locally stable nature of the equilibrium, (iv coordinates for the local bifurcation points—fold and transcritical—, and (v coordinates of the crossing between bifurcation points. These factors are computed analytically and explicitly as expressions of the dilution rate and the influent concentrations of COD and VFA.
Bifurcation into functional niches in adaptation.
White, Justin S; Adami, Christoph
2004-01-01
One of the central questions in evolutionary biology concerns the dynamics of adaptation and diversification. This issue can be addressed experimentally if replicate populations adapting to identical environments can be investigated in detail. We have studied 501 such replicas using digital organisms adapting to at least two fundamentally different functional niches (survival strategies) present in the same environment: one in which fast replication is the way to live, and another where exploitation of the environment's complexity leads to complex organisms with longer life spans and smaller replication rates. While these two modes of survival are closely analogous to those expected to emerge in so-called r and K selection scenarios respectively, the bifurcation of evolutionary histories according to these functional niches occurs in identical environments, under identical selective pressures. We find that the branching occurs early, and leads to drastic phenotypic differences (in fitness, sequence length, and gestation time) that are permanent and irreversible. This study confirms an earlier experimental effort using microorganisms, in that diversification can be understood at least in part in terms of bifurcations on saddle points leading to peak shifts, as in the picture drawn by Sewall Wright.
Bifurcation theory of ac electric arcing
International Nuclear Information System (INIS)
Christen, Thomas; Peinke, Emanuel
2012-01-01
The performance of alternating current (ac) electric arcing devices is related to arc extinction or its re-ignition at zero crossings of the current (so-called ‘current zero’, CZ). Theoretical investigations thus usually focus on the transient behaviour of arcs near CZ, e.g. by solving the modelling differential equations in the vicinity of CZ. This paper proposes as an alternative approach to investigate global mathematical properties of the underlying periodically driven dynamic system describing the electric circuit containing the arcing device. For instance, the uniqueness of the trivial solution associated with the insulating state indicates the extinction of any arc. The existence of non-trivial attractors (typically a time-periodic state) points to a re-ignition of certain arcs. The performance regions of arcing devices, such as circuit breakers and arc torches, can thus be identified with the regions of absence and existence, respectively, of non-trivial attractors. Most important for applications, the boundary of a performance region in the model parameter space is then associated with the bifurcation of the non-trivial attractors. The concept is illustrated for simple black-box arc models, such as the Mayr and the Cassie model, by calculating for various cases the performance boundaries associated with the bifurcation of ac arcs. (paper)
Analysis of Vehicle Steering and Driving Bifurcation Characteristics
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Xianbin Wang
2015-01-01
Full Text Available The typical method of vehicle steering bifurcation analysis is based on the nonlinear autonomous vehicle model deriving from the classic two degrees of freedom (2DOF linear vehicle model. This method usually neglects the driving effect on steering bifurcation characteristics. However, in the steering and driving combined conditions, the tyre under different driving conditions can provide different lateral force. The steering bifurcation mechanism without the driving effect is not able to fully reveal the vehicle steering and driving bifurcation characteristics. Aiming at the aforementioned problem, this paper analyzed the vehicle steering and driving bifurcation characteristics with the consideration of driving effect. Based on the 5DOF vehicle system dynamics model with the consideration of driving effect, the 7DOF autonomous system model was established. The vehicle steering and driving bifurcation dynamic characteristics were analyzed with different driving mode and driving torque. Taking the front-wheel-drive system as an example, the dynamic evolution process of steering and driving bifurcation was analyzed by phase space, system state variables, power spectral density, and Lyapunov index. The numerical recognition results of chaos were also provided. The research results show that the driving mode and driving torque have the obvious effect on steering and driving bifurcation characteristics.
Sediment discharge division at two tidally influenced river bifurcations
Sassi, M.G.; Hoitink, A.J.F.; Vermeulen, B.; Hidayat, H.
2013-01-01
[1] We characterize and quantify the sediment discharge division at two tidally influenced river bifurcations in response to mean flow and secondary circulation by employing a boat-mounted acoustic Doppler current profiler (ADCP), to survey transects at bifurcating branches during a semidiurnal
Views on the Hopf bifurcation with respect to voltage instabilities
Energy Technology Data Exchange (ETDEWEB)
Roa-Sepulveda, C A [Universidad de Concepcion, Concepcion (Chile). Dept. de Ingenieria Electrica; Knight, U G [Imperial Coll. of Science and Technology, London (United Kingdom). Dept. of Electrical and Electronic Engineering
1994-12-31
This paper presents a sensitivity study of the Hopf bifurcation phenomenon which can in theory appear in power systems, with reference to the dynamics of the process and the impact of demand characteristics. Conclusions are drawn regarding power levels at which these bifurcations could appear and concern the concept of the imaginary axis as a `hard` limit eigenvalue analyses. (author) 20 refs., 31 figs.
Bifurcations of heterodimensional cycles with two saddle points
Energy Technology Data Exchange (ETDEWEB)
Geng Fengjie [School of Information Technology, China University of Geosciences (Beijing), Beijing 100083 (China)], E-mail: gengfengjie_hbu@163.com; Zhu Deming [Department of Mathematics, East China Normal University, Shanghai 200062 (China)], E-mail: dmzhu@math.ecnu.edu.cn; Xu Yancong [Department of Mathematics, East China Normal University, Shanghai 200062 (China)], E-mail: yancongx@163.com
2009-03-15
The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.
Numerical bifurcation analysis of a class of nonlinear renewal equations
Breda, Dimitri; Diekmann, Odo; Liessi, Davide; Scarabel, Francesca
2016-01-01
We show, by way of an example, that numerical bifurcation tools for ODE yield reliable bifurcation diagrams when applied to the pseudospectral approximation of a one-parameter family of nonlinear renewal equations. The example resembles logistic-and Ricker-type population equations and exhibits
Travelling waves and their bifurcations in the Lorenz-96 model
van Kekem, Dirk L.; Sterk, Alef E.
2018-03-01
In this paper we study the dynamics of the monoscale Lorenz-96 model using both analytical and numerical means. The bifurcations for positive forcing parameter F are investigated. The main analytical result is the existence of Hopf or Hopf-Hopf bifurcations in any dimension n ≥ 4. Exploiting the circulant structure of the Jacobian matrix enables us to reduce the first Lyapunov coefficient to an explicit formula from which it can be determined when the Hopf bifurcation is sub- or supercritical. The first Hopf bifurcation for F > 0 is always supercritical and the periodic orbit born at this bifurcation has the physical interpretation of a travelling wave. Furthermore, by unfolding the codimension two Hopf-Hopf bifurcation it is shown to act as an organising centre, explaining dynamics such as quasi-periodic attractors and multistability, which are observed in the original Lorenz-96 model. Finally, the region of parameter values beyond the first Hopf bifurcation value is investigated numerically and routes to chaos are described using bifurcation diagrams and Lyapunov exponents. The observed routes to chaos are various but without clear pattern as n → ∞.
Bifurcations of heterodimensional cycles with two saddle points
International Nuclear Information System (INIS)
Geng Fengjie; Zhu Deming; Xu Yancong
2009-01-01
The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.
Kakac, Sadik; Pramuanjaroenkij, Anchasa
2014-01-01
Intended for readers who have taken a basic heat transfer course and have a basic knowledge of thermodynamics, heat transfer, fluid mechanics, and differential equations, Convective Heat Transfer, Third Edition provides an overview of phenomenological convective heat transfer. This book combines applications of engineering with the basic concepts of convection. It offers a clear and balanced presentation of essential topics using both traditional and numerical methods. The text addresses emerging science and technology matters, and highlights biomedical applications and energy technologies. What’s New in the Third Edition: Includes updated chapters and two new chapters on heat transfer in microchannels and heat transfer with nanofluids Expands problem sets and introduces new correlations and solved examples Provides more coverage of numerical/computer methods The third edition details the new research areas of heat transfer in microchannels and the enhancement of convective heat transfer with nanofluids....
International Nuclear Information System (INIS)
Cliffe, K.A.; Garratt, T.J.; Spence, A.
1992-03-01
This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalised eigenvalue problems arising from mixed finite element discretisations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and can be used in a scheme to determine the stability of steady state solutions and to detect Hopf bifurcations. We introduce a modified Cayley transform of the generalised eigenvalue problem which overcomes a drawback of the usual Cayley transform applied to such problems. Standard iterative methods are then applied to the transformed eigenvalue problem to compute approximations to the eigenvalue of smallest real part. Numerical experiments are performed using a model of double diffusive convection. (author)
Bifurcation diagram of a cubic three-parameter autonomous system
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Lenka Barakova
2005-07-01
Full Text Available In this paper, we study the cubic three-parameter autonomous planar system $$displaylines{ dot x_1 = k_1 + k_2x_1 - x_1^3 - x_2,cr dot x_2 = k_3 x_1 - x_2, }$$ where $k_2, k_3$ are greater than 0. Our goal is to obtain a bifurcation diagram; i.e., to divide the parameter space into regions within which the system has topologically equivalent phase portraits and to describe how these portraits are transformed at the bifurcation boundaries. Results may be applied to the macroeconomical model IS-LM with Kaldor's assumptions. In this model existence of a stable limit cycles has already been studied (Andronov-Hopf bifurcation. We present the whole bifurcation diagram and among others, we prove existence of more difficult bifurcations and existence of unstable cycles.
Critical bifurcation surfaces of 3D discrete dynamics
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Michael Sonis
2000-01-01
Full Text Available This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.
Bifurcation of transition paths induced by coupled bistable systems.
Tian, Chengzhe; Mitarai, Namiko
2016-06-07
We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.
Hopf Bifurcation of Compound Stochastic van der Pol System
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Shaojuan Ma
2016-01-01
Full Text Available Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strength δ and noise intensity σ on stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increased δ can relocate the critical value of bifurcation parameter forward while increased σ makes it backward and the influence of δ is more sensitive than σ. The results are verified by numerical simulations.
Fully three dimensional simulations of rotating convection at low Prandtl number
Kaplan, E.; Schaeffer, N.; Cardin, P.
2016-12-01
Rotating thermal convection in spheres or spherical shells has been extensively studied for Prandtl number unity.However, planetary cores are made of liquid metals which have low Prandtl numbers Pr ≤ 0.1. Recently, using a quasi-geostrophic approximation, Guervilly & Cardin (2016) have studied nonlinear convection in rotating full sphere with internal heating at low Prandtl (0.01 ≤ Pr ≤ 0.1) and Ekman (10-8 ≤ Ek ≤ 10-5 ) numbers. They have found a bifurcation between a weak branch characterized by thermal Rossby waves and a strong branch characterized by a strong zonal flow with multiple jets. In these quasi-geostrophic simulations, where vorticity is defined to be constant along the axis of rotation, these bifurcations could be super- or sub-critical or exhibit hysteresis depending on the Ek and Prnumbers of the simulations. Here we present fully three dimensional simulations carried out over a portion of the parameter space (down to Ek = 10-6, Pr = 0.01) that confirm the scaling and bifurcations of the weak and strong branches found in the QG models. Additionally, by modeling the full flow we get information about the full meridional circulation of the convective fluid. The vigorous flows of the sub-critical strong branch may help to generate powerful dynamos before an inner-core has been formed, with a heat flux extracted from the mantle very close to the adiabatic flux.
Climate bifurcation during the last deglaciation?
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T. M. Lenton
2012-07-01
Full Text Available There were two abrupt warming events during the last deglaciation, at the start of the Bølling-Allerød and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state loses its stability and the climate tips into an alternative state, providing an early warning signal in the form of slowing responses to perturbations, which may be accompanied by increasing variability. Alternatively, short-term stochastic variability in the climate system can trigger abrupt climate changes, without early warning. Previous work has found signals consistent with slowing down during the last deglaciation as a whole, and during the Younger Dryas, but with conflicting results in the run-up to the Bølling-Allerød. Based on this, we hypothesise that a bifurcation point was approached at the end of the Younger Dryas, in which the cold climate state, with weak Atlantic overturning circulation, lost its stability, and the climate tipped irreversibly into a warm interglacial state. To test the bifurcation hypothesis, we analysed two different climate proxies in three Greenland ice cores, from the Last Glacial Maximum to the end of the Younger Dryas. Prior to the Bølling warming, there was a robust increase in climate variability but no consistent slowing down signal, suggesting this abrupt change was probably triggered by a stochastic fluctuation. The transition to the warm Bølling-Allerød state was accompanied by a slowing down in climate dynamics and an increase in climate variability. We suggest that the Bølling warming excited an internal mode of variability in Atlantic meridional overturning circulation strength, causing multi-centennial climate fluctuations. However, the return to the Younger Dryas cold state increased climate stability. We find no consistent evidence for slowing down during the Younger Dryas, or in a longer
Topological bifurcations of coherent structures and dimension reduction of plasma convection models
DEFF Research Database (Denmark)
Dam, Magnus
in an overall neutral gaseous state of negatively charged free electrons and positively charged ions. This state of matter is called plasma. To achieve and maintain fusion temperatures, the plasma must avoid direct contact with any solid material. Since the plasma consists of charged particles, it can......Research in fusion energy seeks to develop a green, safe, and sustainable energy source. Nuclear fusion can be achieved by heating a hydrogen gas to temperatures of millions of kelvin. At fusion temperatures, some or all the electrons leave the atomic nucleus of the hydrogen atom. This results...... mode (H-mode). H-mode is the preferred operating mode for a fusion reactor. The transition from L-mode to H-mode is called the L–H transition. The conﬁnement properties of a plasma are largely determined by the physics near the edge of the conﬁnement region of the plasma. The edge transport...
The bifurcations of nearly flat origami
Santangelo, Christian
Self-folding origami structures provide one means of fabricating complex, three-dimensional structures from a flat, two-dimensional sheet. Self-folding origami structures have been fabricated on scales ranging from macroscopic to microscopic and can have quite complicated structures with hundreds of folds arranged in complex patterns. I will describe our efforts to understand the mechanics and energetics of self-folding origami structures. Though the dimension of the configuration space of an origami structure scales with the size of the boundary and not with the number of vertices in the interior of the structure, a typical origami structure is also floppy in the sense that there are many possible ways to assign fold angles consistently. I will discuss our theoretical progress in understanding the geometry of the configuration space of origami. For random origami, the number of possible bifurcations grows surprisingly quickly even when the dimension of the configuration space is small. EFRI ODISSEI-1240441, DMR-0846582.
Transport Bifurcation in a Rotating Tokamak Plasma
International Nuclear Information System (INIS)
Highcock, E. G.; Barnes, M.; Schekochihin, A. A.; Parra, F. I.; Roach, C. M.; Cowley, S. C.
2010-01-01
The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.
Bifurcated SEN with Fluid Flow Conditioners
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F. Rivera-Perez
2014-01-01
Full Text Available This work evaluates the performance of a novel design for a bifurcated submerged entry nozzle (SEN used for the continuous casting of steel slabs. The proposed design incorporates fluid flow conditioners attached on SEN external wall. The fluid flow conditioners impose a pseudosymmetric pattern in the upper zone of the mold by inhibiting the fluid exchange between the zones created by conditioners. The performance of the SEN with fluid flow conditioners is analyzed through numerical simulations using the CFD technique. Numerical results were validated by means of physical simulations conducted on a scaled cold water model. Numerical and physical simulations confirmed that the performance of the proposed SEN is superior to a traditional one. Fluid flow conditioners reduce the liquid free surface fluctuations and minimize the occurrence of vortexes at the free surface.
Oscillatory bifurcation for semilinear ordinary differential equations
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Tetsutaro Shibata
2016-06-01
\\] where $f(u = u + (1/2\\sin^k u$ ($k \\ge 2$ and $\\lambda > 0$ is a bifurcation parameter. It is known that $\\lambda$ is parameterized by the maximum norm $\\alpha = \\Vert u_\\lambda\\Vert_\\infty$ of the solution $u_\\lambda$ associated with $\\lambda$ and is written as $\\lambda = \\lambda(k,\\alpha$. When we focus on the asymptotic behavior of $\\lambda(k,\\alpha$ as $\\alpha \\to \\infty$, it is natural to expect that $\\lambda(k, \\alpha \\to \\pi^2/4$, and its convergence rate is common to $k$. Contrary to this expectation, we show that $\\lambda(2n_1+1,\\alpha$ tends to $\\pi^2/4$ faster than $\\lambda(2n_2,\\alpha$ as $\\alpha \\to \\infty$, where $n_1\\ge 1,\\ n_2 \\ge 1$ are arbitrary given integers.
Equilibrium-torus bifurcation in nonsmooth systems
DEFF Research Database (Denmark)
Zhusubahyev, Z.T.; Mosekilde, Erik
2008-01-01
Considering a set of two coupled nonautonomous differential equations with discontinuous right-hand sides describing the behavior of a DC/DC power converter, we discuss a border-collision bifurcation that can lead to the birth of a two-dimensional invariant torus from a stable node equilibrium...... point. We obtain the chart of dynamic modes and show that there is a region of parameter space in which the system has a single stable node equilibrium point. Under variation of the parameters, this equilibrium may disappear as it collides with a discontinuity boundary between two smooth regions...... in the phase space. The disappearance of the equilibrium point is accompanied by the soft appearance of an unstable focus period-1 orbit surrounded by a resonant or ergodic torus. Detailed numerical calculations are supported by a theoretical investigation of the normal form map that represents the piecewise...
Clausius entropy for arbitrary bifurcate null surfaces
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2014-01-01
Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation dS=đQ/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations. (paper)
Simulating deep convection with a shallow convection scheme
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C. Hohenegger
2011-10-01
Full Text Available Convective processes profoundly affect the global water and energy balance of our planet but remain a challenge for global climate modeling. Here we develop and investigate the suitability of a unified convection scheme, capable of handling both shallow and deep convection, to simulate cases of tropical oceanic convection, mid-latitude continental convection, and maritime shallow convection. To that aim, we employ large-eddy simulations (LES as a benchmark to test and refine a unified convection scheme implemented in the Single-column Community Atmosphere Model (SCAM. Our approach is motivated by previous cloud-resolving modeling studies, which have documented the gradual transition between shallow and deep convection and its possible importance for the simulated precipitation diurnal cycle.
Analysis of the LES reveals that differences between shallow and deep convection, regarding cloud-base properties as well as entrainment/detrainment rates, can be related to the evaporation of precipitation. Parameterizing such effects and accordingly modifying the University of Washington shallow convection scheme, it is found that the new unified scheme can represent both shallow and deep convection as well as tropical and mid-latitude continental convection. Compared to the default SCAM version, the new scheme especially improves relative humidity, cloud cover and mass flux profiles. The new unified scheme also removes the well-known too early onset and peak of convective precipitation over mid-latitude continental areas.
Magnetic targeting to enhance microbubble delivery in an occluded microarterial bifurcation.
de Saint Victor, M; Carugo, D; Barnsley, L C; Owen, J; Coussios, C-C; Stride, E
2017-09-05
Ultrasound and microbubbles have been shown to accelerate the breakdown of blood clots both in vitro and in vivo. Clinical translation of this technology is still limited, however, in part by inefficient microbubble delivery to the thrombus. This study examines the obstacles to delivery posed by fluid dynamic conditions in occluded vasculature and investigates whether magnetic targeting can improve microbubble delivery. A 2D computational fluid dynamic model of a fully occluded Y-shaped microarterial bifurcation was developed to determine: (i) the fluid dynamic field in the vessel with inlet velocities from 1-100 mm s -1 (corresponding to Reynolds numbers 0.25-25); (ii) the transport dynamics of fibrinolytic drugs; and (iii) the flow behavior of microbubbles with diameters in the clinically-relevant range (0.6-5 µm). In vitro experiments were carried out in a custom-built microfluidic device. The flow field was characterized using tracer particles, and fibrinolytic drug transport was assessed using fluorescence microscopy. Lipid-shelled magnetic microbubbles were fluorescently labelled to determine their spatial distribution within the microvascular model. In both the simulations and experiments, the formation of laminar vortices and an abrupt reduction of fluid velocity were observed in the occluded branch of the bifurcation, severely limiting drug transport towards the occlusion. In the absence of a magnetic field, no microbubbles reached the occlusion, remaining trapped in the first vortex, within 350 µm from the bifurcation center. The number of microbubbles trapped within the vortex decreased as the inlet velocity increased, but was independent of microbubble size. Application of a magnetic field (magnetic flux density of 76 mT, magnetic flux density gradient of 10.90 T m -1 at the centre of the bifurcation) enabled delivery of microbubbles to the occlusion and the number of microbubbles delivered increased with bubble size and with decreasing inlet
Subcritical thermal convection of liquid metals in a rapidly rotating sphere
Cardin, P.; Schaeffer, N.; Guervilly, C.; Kaplan, E.
2017-12-01
Planetary cores consist of liquid metals (low Prandtl number Pr) that convect as the core cools. Here we study nonlinear convection in a rotating (low Ekman number Ek) planetary core using a fully 3D direct (down to Ek=10-7) and a quasi geostrophic (down to Ek=10-10) numerical simulations. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are continuously connected. As the planetary core rotates faster, the continuous transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at Ekforcing decreases well below the linear onset of convection (Ra 0.4Racrit in this study for Ek=10-10 and Pr=0.01). We highlight the importance of the Reynolds stress, which is required for convection to persist below the linear onset. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective subcritical state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for planetary interiors, thermal convection of liquid metals in a sphere onsets and shuts down through a subcritical bifurcation. This scenario may be relevant to explain the lunar and martian dynamo extinctions.
Fractional noise destroys or induces a stochastic bifurcation
Energy Technology Data Exchange (ETDEWEB)
Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China); Wang, Cong, E-mail: wangcong@scut.edu.cn [School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China)
2013-12-15
Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
Directory of Open Access Journals (Sweden)
Chao Su
2015-01-01
Full Text Available Underground reinforced concrete bifurcation pipe is an important part of conveyance structure. During construction, the workload of excavation and concrete pouring can be significantly decreased according to optimized pipe structure, and the engineering quality can be improved. This paper presents an optimization mathematical model of underground reinforced concrete bifurcation pipe structure according to real working status of several common pipe structures from real cases. Then, an optimization design system was developed based on Particle Swarm Optimization algorithm. Furthermore, take the bifurcation pipe of one hydropower station as an example: optimization analysis was conducted, and accuracy and stability of the optimization design system were verified successfully.
Arctic melt ponds and bifurcations in the climate system
Sudakov, I.; Vakulenko, S. A.; Golden, K. M.
2015-05-01
Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo - a key parameter in climate modeling. Here we explore the possibility of a conceptual sea ice climate model passing through a bifurcation point - an irreversible critical threshold as the system warms, by incorporating geometric information about melt pond evolution. This study is based on a bifurcation analysis of the energy balance climate model with ice-albedo feedback as the key mechanism driving the system to bifurcation points.
FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions
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L. Borkowski
2015-01-01
Full Text Available The dynamics of a ring of seven unidirectionally coupled nonlinear Duffing oscillators is studied. We show that the FFT analysis presented in form of a bifurcation graph, that is, frequency distribution versus a control parameter, can provide a valuable and helpful complement to the corresponding typical bifurcation diagram and the course of Lyapunov exponents, especially in context of detailed identification of the observed attractors. As an example, bifurcation analysis of routes to chaos via 2-frequency and 3-frequency quasiperiodicity is demonstrated.
Bifurcation of learning and structure formation in neuronal maps
DEFF Research Database (Denmark)
Marschler, Christian; Faust-Ellsässer, Carmen; Starke, Jens
2014-01-01
to map formation in the laminar nucleus of the barn owl's auditory system. Using equation-free methods, we perform a bifurcation analysis of spatio-temporal structure formation in the associated synaptic-weight matrix. This enables us to analyze learning as a bifurcation process and follow the unstable...... states as well. A simple time translation of the learning window function shifts the bifurcation point of structure formation and goes along with traveling waves in the map, without changing the animal's sound localization performance....
Mixed thermal convection: fundamental issues and analysis of the planar case
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JACQUES PADET
2015-09-01
Full Text Available This paper aims to renew interest on mixed thermal convection research and to emphasize three issues that arise from the present analysis: (i a clear definition of the reference temperature in the Boussinesq approximation; (ii a practical delimitation of the three convective modes, which are the forced convection (FC, mixed convection (MC and natural (or free convection (NC; (iii and, finally, a uniform description of the set FC/MC/NC in the similarity framework. The planar case, for which analytical solutions are available, allows a detailed illustration of the answers here advanced to the above issues.
Convection and stellar oscillations
DEFF Research Database (Denmark)
Aarslev, Magnus Johan
2017-01-01
for asteroseismology, because of the challenges inherent in modelling turbulent convection in 1D stellar models. As a result of oversimplifying the physics near the surface, theoretical calculations systematically overestimate the oscillation frequencies. This has become known as the asteroseismic surface effect. Due...... to lacking better options, this frequency difference is typically corrected for with ad-hoc formulae. The topic of this thesis is the improvement of 1D stellar convection models and the effects this has on asteroseismic properties. The source of improvements is 3D simulations of radiation...... atmospheres to replace the outer layers of stellar models. The additional turbulent pressure and asymmetrical opacity effects in the atmosphere model, compared to convection in stellar evolution models, serve to expand the atmosphere. The enlarged acoustic cavity lowers the pulsation frequencies bringing them...
Convective transport in tokamaks
International Nuclear Information System (INIS)
D'Ippolito, D.A.; Myra, J.R.; Russell, D.A.; Krasheninnikov, S.I.; Pigarov, A.Yu.; Yu, G.Q.; Xu, X.Q.; Nevins, W.M.
2005-01-01
Scrape-off-layer (SOL) convection in fusion experiments appears to be a universal phenomenon that can 'short-circuit' the divertor in some cases. The theory of 'blob' transport provides a simple and robust physical paradigm for studying convective transport. This paper summarizes recent advances in the theory of blob transport and its comparison with 2D and 3D computer simulations. We also discuss the common physical basis relating radial transport of blobs, pellets, and ELMs and a new blob regime that may lead to a connection between blob transport and the density limit. (author)
Arnett, W. David
2009-05-01
We review recent progress using numerical simulations as a testbed for development of a theory of stellar convection, much as envisaged by John von Newmann. Necessary features of the theory, non-locality and fluctuations, are illustrated by computer movies. It is found that the common approximation of convection as a diffusive process presents the wrong physical picture, and improvements are suggested. New observational results discussed at the conference are gratifying in their validation of some of our theoretical ideas, especially the idea that SNIb and SNIc events are related to the explosion of massive star cores which have been stripped by mass loss and binary interactions [1
Parameterizing convective organization
Directory of Open Access Journals (Sweden)
Brian Earle Mapes
2011-06-01
Full Text Available Lateral mixing parameters in buoyancy-driven deep convection schemes are among the most sensitive and important unknowns in atmosphere models. Unfortunately, there is not a true optimum value for plume mixing rate, but rather a dilemma or tradeoff: Excessive dilution of updrafts leads to unstable stratification bias in the mean state, while inadequate dilution allows deep convection to occur too easily, causing poor space and time distributions and variability. In this too-small parameter space, compromises are made based on competing metrics of model performance. We attempt to escape this “entrainment dilemma” by making bulk plume parameters (chiefly entrainment rate depend on a new prognostic variable (“organization,” org meant to reflect the rectified effects of subgrid-scale structure in meteorological fields. We test an org scheme in the Community Atmosphere Model (CAM5 with a new unified shallow-deep convection scheme (UW-ens, a 2-plume version of the University of Washington scheme. Since buoyant ascent involves natural selection, subgrid structure makes convection systematically deeper and stronger than the pure unorganized case: plumes of average (or randomly sampled air rising in the average environment. To reflect this, org is nonnegative, but we leave it dimensionless. A time scale characterizes its behavior (here ∼3 h for a 2o model. Currently its source is rain evaporation, but other sources can be added easily. We also let org be horizontally transported by advection, as a mass-weighted mean over the convecting layer. Linear coefficients link org to a plume ensemble, which it assists via: 1 plume base warmth above the mean temperature 2 plume radius enhancement (reduced mixing, and 3 increased probability of overlap in a multi-plume scheme, where interactions benefit later generations (this part has only been implemented in an offline toy column model. Since rain evaporation is a source for org, it functions as a time
Mathematical models of convection
Andreev, Victor K; Goncharova, Olga N; Pukhnachev, Vladislav V
2012-01-01
Phenomena of convection are abundant in nature as well as in industry. This volume addresses the subject of convection from the point of view of both, theory and application. While the first three chapters provide a refresher on fluid dynamics and heat transfer theory, the rest of the book describes the modern developments in theory. Thus it brings the reader to the ""front"" of the modern research. This monograph provides the theoretical foundation on a topic relevant to metallurgy, ecology, meteorology, geo-and astrophysics, aerospace industry, chemistry, crystal physics, and many other fiel
Convective aggregation in realistic convective-scale simulations
Holloway, Christopher E.
2017-01-01
To investigate the real-world relevance of idealized-model convective self-aggregation, five 15-day cases of real organized convection in the tropics are simulated. These include multiple simulations of each case to test sensitivities of the convective organization and mean states to interactive radiation, interactive surface fluxes, and evaporation of rain. These simulations are compared to self-aggregation seen in the same model configured to run in idealized radiative-convective equilibriu...
CDM Convective Forecast Planning guidance
National Oceanic and Atmospheric Administration, Department of Commerce — The CDM Convective Forecast Planning (CCFP) guidance product provides a foreast of en-route aviation convective hazards. The forecasts are updated every 2 hours and...
CISM Session on Bifurcation and Stability of Dissipative Systems
1993-01-01
The first theme concerns the plastic buckling of structures in the spirit of Hill’s classical approach. Non-bifurcation and stability criteria are introduced and post-bifurcation analysis performed by asymptotic development method in relation with Hutchinson’s work. Some recent results on the generalized standard model are given and their connection to Hill’s general formulation is presented. Instability phenomena of inelastic flow processes such as strain localization and necking are discussed. The second theme concerns stability and bifurcation problems in internally damaged or cracked colids. In brittle fracture or brittle damage, the evolution law of crack lengths or damage parameters is time-independent like in plasticity and leads to a similar mathematical description of the quasi-static evolution. Stability and non-bifurcation criteria in the sense of Hill can be again obtained from the discussion of the rate response.
Bifurcation dynamics of the tempered fractional Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Zeng, Caibin, E-mail: macbzeng@scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China); Chen, YangQuan, E-mail: ychen53@ucmerced.edu [MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)
2016-08-15
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Deformable 4DCT lung registration with vessel bifurcations
International Nuclear Information System (INIS)
Hilsmann, A.; Vik, T.; Kaus, M.; Franks, K.; Bissonette, J.P.; Purdie, T.; Beziak, A.; Aach, T.
2007-01-01
In radiotherapy planning of lung cancer, breathing motion causes uncertainty in the determination of the target volume. Image registration makes it possible to get information about the deformation of the lung and the tumor movement in the respiratory cycle from a few images. A dedicated, automatic, landmark-based technique was developed that finds corresponding vessel bifurcations. Hereby, we developed criteria to characterize pronounced bifurcations for which correspondence finding was more stable and accurate. The bifurcations were extracted from automatically segmented vessel trees in maximum inhale and maximum exhale CT thorax data sets. To find corresponding bifurcations in both data sets we used the shape context approach of Belongie et al. Finally, a volumetric lung deformation was obtained using thin-plate spline interpolation and affine registration. The method is evaluated on 10 4D-CT data sets of patients with lung cancer. (orig.)
Multiple bifurcations and periodic 'bubbling' in a delay population model
International Nuclear Information System (INIS)
Peng Mingshu
2005-01-01
In this paper, the flip bifurcation and periodic doubling bifurcations of a discrete population model without delay influence is firstly studied and the phenomenon of Feigenbaum's cascade of periodic doublings is also observed. Secondly, we explored the Neimark-Sacker bifurcation in the delay population model (two-dimension discrete dynamical systems) and the unique stable closed invariant curve which bifurcates from the nontrivial fixed point. Finally, a computer-assisted study for the delay population model is also delved into. Our computer simulation shows that the introduction of delay effect in a nonlinear difference equation derived from the logistic map leads to much richer dynamic behavior, such as stable node → stable focus → an lower-dimensional closed invariant curve (quasi-periodic solution, limit cycle) or/and stable periodic solutions → chaotic attractor by cascading bubbles (the combination of potential period doubling and reverse period-doubling) and the sudden change between two different attractors, etc
Bifurcation theory for hexagonal agglomeration in economic geography
Ikeda, Kiyohiro
2014-01-01
This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distri...
Periodic solutions and bifurcations of delay-differential equations
International Nuclear Information System (INIS)
He Jihuan
2005-01-01
In this Letter a simple but effective iteration method is proposed to search for limit cycles or bifurcation curves of delay-differential equations. An example is given to illustrate its convenience and effectiveness
Presentation on Tropical Mesoscale convective Systems and ...
Indian Academy of Sciences (India)
IAS Admin
Shallow convection- 70% of the storm heights are below 6 km. ♢ Deep convection ... Decay convection, the convective top is found at a higher altitude than deep .... Stratospheric Fountain – Two step process. Warm tropopause- preferable for.
Defining Electron Bifurcation in the Electron-Transferring Flavoprotein Family.
Garcia Costas, Amaya M; Poudel, Saroj; Miller, Anne-Frances; Schut, Gerrit J; Ledbetter, Rhesa N; Fixen, Kathryn R; Seefeldt, Lance C; Adams, Michael W W; Harwood, Caroline S; Boyd, Eric S; Peters, John W
2017-11-01
Electron bifurcation is the coupling of exergonic and endergonic redox reactions to simultaneously generate (or utilize) low- and high-potential electrons. It is the third recognized form of energy conservation in biology and was recently described for select electron-transferring flavoproteins (Etfs). Etfs are flavin-containing heterodimers best known for donating electrons derived from fatty acid and amino acid oxidation to an electron transfer respiratory chain via Etf-quinone oxidoreductase. Canonical examples contain a flavin adenine dinucleotide (FAD) that is involved in electron transfer, as well as a non-redox-active AMP. However, Etfs demonstrated to bifurcate electrons contain a second FAD in place of the AMP. To expand our understanding of the functional variety and metabolic significance of Etfs and to identify amino acid sequence motifs that potentially enable electron bifurcation, we compiled 1,314 Etf protein sequences from genome sequence databases and subjected them to informatic and structural analyses. Etfs were identified in diverse archaea and bacteria, and they clustered into five distinct well-supported groups, based on their amino acid sequences. Gene neighborhood analyses indicated that these Etf group designations largely correspond to putative differences in functionality. Etfs with the demonstrated ability to bifurcate were found to form one group, suggesting that distinct conserved amino acid sequence motifs enable this capability. Indeed, structural modeling and sequence alignments revealed that identifying residues occur in the NADH- and FAD-binding regions of bifurcating Etfs. Collectively, a new classification scheme for Etf proteins that delineates putative bifurcating versus nonbifurcating members is presented and suggests that Etf-mediated bifurcation is associated with surprisingly diverse enzymes. IMPORTANCE Electron bifurcation has recently been recognized as an electron transfer mechanism used by microorganisms to maximize
Convective overshooting in stars
Andrássy, R.
2015-01-01
Numerous observations provide evidence that the standard picture, in which convective mixing is limited to the unstable layers of a star, is incomplete. The mixing layers in real stars are significantly more extended than what the standard models predict. Some of the observations require changing
Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models
Giona, M.; Brasiello, A.; Crescitelli, S.
2015-11-01
One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.
Bunch lengthening with bifurcation in electron storage rings
Energy Technology Data Exchange (ETDEWEB)
Kim, Eun-San; Hirata, Kohji [National Lab. for High Energy Physics, Tsukuba, Ibaraki (Japan)
1996-08-01
The mapping which shows equilibrium particle distribution in synchrotron phase space for electron storage rings is discussed with respect to some localized constant wake function based on the Gaussian approximation. This mapping shows multi-periodic states as well as double bifurcation in dynamical states of the equilibrium bunch length. When moving around parameter space, the system shows a transition/bifurcation which is not always reversible. These results derived by mapping are confirmed by multiparticle tracking. (author)
Hopf bifurcation of the stochastic model on business cycle
International Nuclear Information System (INIS)
Xu, J; Wang, H; Ge, G
2008-01-01
A stochastic model on business cycle was presented in thas paper. Simplifying the model through the quasi Hamiltonian theory, the Ito diffusion process was obtained. According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired. Solving the stationary FPK equation and analyzing the stationary probability density, the stochastic Hopf bifurcation was explained. The result indicated that the change of parameter awas the key factor to the appearance of the stochastic Hopf bifurcation
Iterative Controller Tuning for Process with Fold Bifurcations
DEFF Research Database (Denmark)
Huusom, Jakob Kjøbsted; Poulsen, Niels Kjølstad; Jørgensen, Sten Bay
2007-01-01
Processes involving fold bifurcation are notoriously difficult to control in the vicinity of the fold where most often optimal productivity is achieved . In cases with limited process insight a model based control synthesis is not possible. This paper uses a data driven approach with an improved...... version of iterative feedback tuning to optimizing a closed loop performance criterion, as a systematic tool for tuning process with fold bifurcations....
Bifurcated states of the error-field-induced magnetic islands
International Nuclear Information System (INIS)
Zheng, L.-J.; Li, B.; Hazeltine, R.D.
2008-01-01
We find that the formation of the magnetic islands due to error fields shows bifurcation when neoclassical effects are included. The bifurcation, which follows from including bootstrap current terms in a description of island growth in the presence of error fields, provides a path to avoid the island-width pole in the classical description. The theory offers possible theoretical explanations for the recent DIII-D and JT-60 experimental observations concerning confinement deterioration with increasing error field
Attractors, bifurcations, & chaos nonlinear phenomena in economics
Puu, Tönu
2003-01-01
The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics ch...
Bifurcated equilibria in centrifugally confined plasma
International Nuclear Information System (INIS)
Shamim, I.; Teodorescu, C.; Guzdar, P. N.; Hassam, A. B.; Clary, R.; Ellis, R.; Lunsford, R.
2008-01-01
A bifurcation theory and associated computational model are developed to account for abrupt transitions observed recently on the Maryland Centrifugal eXperiment (MCX) [R. F. Ellis et al. Phys. Plasmas 8, 2057 (2001)], a supersonically rotating magnetized plasma that relies on centrifugal forces to prevent thermal expansion of plasma along the magnetic field. The observed transitions are from a well-confined, high-rotation state (HR-mode) to a lower-rotation, lesser-confined state (O-mode). A two-dimensional time-dependent magnetohydrodynamics code is used to simulate the dynamical equilibrium states of the MCX configuration. In addition to the expected viscous drag on the core plasma rotation, a momentum loss term is added that models the friction of plasma on the enhanced level of neutrals expected in the vicinity of the insulators at the throats of the magnetic mirror geometry. At small values of the external rotation drive, the plasma is not well-centrifugally confined and hence experiences the drag from near the insulators. Beyond a critical value of the external drive, the system makes an abrupt transition to a well-centrifugally confined state in which the plasma has pulled away from the end insulator plates; more effective centrifugal confinement lowers the plasma mass near the insulators allowing runaway increases in the rotation speed. The well-confined steady state is reached when the external drive is balanced by only the viscosity of the core plasma. A clear hysteresis phenomenon is shown.
Bursting oscillations, bifurcation and synchronization in neuronal systems
Energy Technology Data Exchange (ETDEWEB)
Wang Haixia [School of Science, Nanjing University of Science and Technology, Nanjing 210094 (China); Wang Qingyun, E-mail: drwangqy@gmail.com [Department of Dynamics and Control, Beihang University, Beijing 100191 (China); Lu Qishao [Department of Dynamics and Control, Beihang University, Beijing 100191 (China)
2011-08-15
Highlights: > We investigate bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. > Two types of fast-slow bursters are analyzed in detail. > We show the properties of some crucial bifurcation points. > Synchronization transition and the neural excitability are explored in the coupled bursters. - Abstract: This paper investigates bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. It is shown that for some appropriate parameters, the modified Morris-Lecar neuron can exhibit two types of fast-slow bursters, that is 'circle/fold cycle' bursting and 'subHopf/homoclinic' bursting with class 1 and class 2 neural excitability, which have different neuro-computational properties. By means of the analysis of fast-slow dynamics and phase plane, we explore bifurcation mechanisms associated with the two types of bursters. Furthermore, the properties of some crucial bifurcation points, which can determine the type of the burster, are studied by the stability and bifurcation theory. In addition, we investigate the influence of the coupling strength on synchronization transition and the neural excitability in two electrically coupled bursters with the same bursting type. More interestingly, the multi-time-scale synchronization transition phenomenon is found as the coupling strength varies.
Bifurcation magnetic resonance in films magnetized along hard magnetization axis
Energy Technology Data Exchange (ETDEWEB)
Vasilevskaya, Tatiana M., E-mail: t_vasilevs@mail.ru [Ulyanovsk State University, Leo Tolstoy 42, 432017 Ulyanovsk (Russian Federation); Sementsov, Dmitriy I.; Shutyi, Anatoliy M. [Ulyanovsk State University, Leo Tolstoy 42, 432017 Ulyanovsk (Russian Federation)
2012-09-15
We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range. - Highlights: Black-Right-Pointing-Pointer An additional bifurcation resonance arises in a case of a thin film magnetized along HMA. Black-Right-Pointing-Pointer Bifurcation resonance occurs due to the presence of two closely spaced equilibrium magnetization states. Black-Right-Pointing-Pointer Both regular and chaotic precession modes are realized within bifurcation resonance range. Black-Right-Pointing-Pointer Appearance of dynamic bistability is typical for bifurcation resonance.
Bifurcation magnetic resonance in films magnetized along hard magnetization axis
International Nuclear Information System (INIS)
Vasilevskaya, Tatiana M.; Sementsov, Dmitriy I.; Shutyi, Anatoliy M.
2012-01-01
We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range. - Highlights: ► An additional bifurcation resonance arises in a case of a thin film magnetized along HMA. ► Bifurcation resonance occurs due to the presence of two closely spaced equilibrium magnetization states. ► Both regular and chaotic precession modes are realized within bifurcation resonance range. ► Appearance of dynamic bistability is typical for bifurcation resonance.
Convective Propagation Characteristics Using a Simple Representation of Convective Organization
Neale, R. B.; Mapes, B. E.
2016-12-01
Observed equatorial wave propagation is intimately linked to convective organization and it's coupling to features of the larger-scale flow. In this talk we a use simple 4 level model to accommodate vertical modes of a mass flux convection scheme (shallow, mid-level and deep). Two paradigms of convection are used to represent convective processes. One that has only both random (unorganized) diagnosed fluctuations of convective properties and one with organized fluctuations of convective properties that are amplified by previously existing convection and has an explicit moistening impact on the local convecting environment We show a series of model simulations in single-column, 2D and 3D configurations, where the role of convective organization in wave propagation is shown to be fundamental. For the optimal choice of parameters linking organization to local atmospheric state, a broad array of convective wave propagation emerges. Interestingly the key characteristics of propagating modes are the low-level moistening followed by deep convection followed by mature 'large-scale' heating. This organization structure appears to hold firm across timescales from 5-day wave disturbances to MJO-like wave propagation.
International Nuclear Information System (INIS)
Alejaldre, C.; Alonso, J.; Almoguera, L.
2005-01-01
This paper presents an overview of experimental results and progress made in investigating the role of magnetic configuration on stability and transport in the TJ-II stellarator. Global confinement studies have revealed a positive dependence of energy confinement on the rotational transform and plasma density, together with different parametric dependences for metallic and boronised wall conditions. Spontaneous and biasing-induced improved confinement transitions, with some characteristics that resemble those of previously reported H-mode regimes in other stellarator devices, have been observed. Also, magnetic configuration scan experiments have shown an interplay between magnetic structure (rationals, magnetic shear), transport and electric fields. Although the DC radial electric fields are comparable with those expected from neoclassical calculations, additional mechanisms based on neoclassical/turbulent bifurcations and kinetic effects are needed to explain the impact of magnetic topology on flows and radial electric fields. Local transport studies have demonstrated a dependence of plasma diffusivities and convective velocities on plasma density and heating power in consistency with global confinement properties. Hydrocarbon fuelling experiments in configurations with a low order rational value in the rotational transform located in the proximity of the last close flux surface (n = 4/m = 2) have shown the impurity screening properties related to the expected divertor effect. First experiments in NBI plasmas are reported. (author)
Bhadauria, B. S.; Singh, M. K.; Singh, A.; Singh, B. K.; Kiran, P.
2016-12-01
In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.
Directory of Open Access Journals (Sweden)
Bhadauria B.S.
2016-12-01
Full Text Available In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.
Dynamical behaviour of natural convection in closed loops
International Nuclear Information System (INIS)
Ehrhard, P.
1988-04-01
A one dimensional model is presented together with experiments, which describe the natural convective flow in closed loops heated at the bottom and cooled in the upper semicircle. Starting from a single loop, mechanical and thermal coupling with a second loop is discussed. The experiments and the theoretical model both concurrently demonstrate that the investigated natural convection is clearly influenced by non-linear effects. Beside the variety of stable steady flows there are extensive subcritical ranges of convective flow. In these parameter ranges subcritical instabilities of the steady state flow could occur in the presence of finite amplitude disturbances. However, the supercritical, global unstable range is characterized by chaotic histories of the variables of state. Non-symmetric heating generates an imperfect bifurcation out of the steady solution with zero velocity in the loop. This effect stabilizes the flow in the preferred direction. The flow in the opposite direction only remains stable in a small isolated interval of the heating parameter. Furthermore the calculations with the model equations demonstrate that a stable periodic behaviour of the flow is possible in a small parameter window. However, it has not been possible to verify this particular effect in the experiments conducted to date. (orig./GL) [de
Bejan, Adrian
2013-01-01
Written by an internationally recognized authority on heat transfer and thermodynamics, this second edition of Convection Heat Transfer contains new and updated problems and examples reflecting real-world research and applications, including heat exchanger design. Teaching not only structure but also technique, the book begins with the simplest problem solving method (scale analysis), and moves on to progressively more advanced and exact methods (integral method, self similarity, asymptotic behavior). A solutions manual is available for all problems and exercises.
Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack
Directory of Open Access Journals (Sweden)
Xin Qi
2015-02-01
Full Text Available Bifurcation analysis and stability design for aircraft longitudinal motion are investigated when the nonlinearity in flight dynamics takes place severely at high angle of attack regime. To predict the special nonlinear flight phenomena, bifurcation theory and continuation method are employed to systematically analyze the nonlinear motions. With the refinement of the flight dynamics for F-8 Crusader longitudinal motion, a framework is derived to identify the stationary bifurcation and dynamic bifurcation for high-dimensional system. Case study shows that the F-8 longitudinal motion undergoes saddle node bifurcation, Hopf bifurcation, Zero-Hopf bifurcation and branch point bifurcation under certain conditions. Moreover, the Hopf bifurcation renders series of multiple frequency pitch oscillation phenomena, which deteriorate the flight control stability severely. To relieve the adverse effects of these phenomena, a stabilization control based on gain scheduling and polynomial fitting for F-8 longitudinal motion is presented to enlarge the flight envelope. Simulation results validate the effectiveness of the proposed scheme.
Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate
Ren, Jingli; Yuan, Qigang
2017-08-01
A three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincaré map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincaré map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last.
Concepts of magnetospheric convection
International Nuclear Information System (INIS)
Vasyliunas, V.M.
1975-01-01
Magnetospheric physics, which grew out of attempts to understand the space environment of the Earth, is becoming increasingly applicable to other systems in the Universe. Among the planets, in addition to the Earth, Jupiter, Mercury, Mars and (in a somewhat different way) Venus are now known to have magnetospheres. The magnetospheres of pulsars have been regarded as an essential part of the pulsar phenomenon. Other astrophysical systems, such as supernova remnant shells or magnetic stars and binary star systems, may be describable as magnetospheres. The major concepts of magnetospheric physics thus need to be formulated in a general way not restricted to the geophysical context in which they may have originated. Magnetospheric convection has been one of the most important and fruitful concepts in the study of the Earth's magnetosphere. This paper describes the basic theoretical notions of convection in a manner applicable to magnetospheres generally and discusses the relative importance of convective corotational motions, with particular reference to the comparison of the Earth and Jupiter. (Auth.)
Bifurcation and Fractal of the Coupled Logistic Map
Wang, Xingyuan; Luo, Chao
The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.
Secondary Channel Bifurcation Geometry: A Multi-dimensional Problem
Gaeuman, D.; Stewart, R. L.
2017-12-01
The construction of secondary channels (or side channels) is a popular strategy for increasing aquatic habitat complexity in managed rivers. Such channels, however, frequently experience aggradation that prevents surface water from entering the side channels near their bifurcation points during periods of relatively low discharge. This failure to maintain an uninterrupted surface water connection with the main channel can reduce the habitat value of side channels for fish species that prefer lotic conditions. Various factors have been proposed as potential controls on the fate of side channels, including water surface slope differences between the main and secondary channels, the presence of main channel secondary circulation, transverse bed slopes, and bifurcation angle. A quantitative assessment of more than 50 natural and constructed secondary channels in the Trinity River of northern California indicates that bifurcations can assume a variety of configurations that are formed by different processes and whose longevity is governed by different sets of factors. Moreover, factors such as bifurcation angle and water surface slope vary with discharge level and are continuously distributed in space, such that they must be viewed as a multi-dimensional field rather than a single-valued attribute that can be assigned to a particular bifurcation.
Magneto-elastic dynamics and bifurcation of rotating annular plate*
International Nuclear Information System (INIS)
Hu Yu-Da; Piao Jiang-Min; Li Wen-Qiang
2017-01-01
In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton’s principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincaré maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions, and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos. (paper)
Shells, orbit bifurcations, and symmetry restorations in Fermi systems
Energy Technology Data Exchange (ETDEWEB)
Magner, A. G., E-mail: magner@kinr.kiev.ua; Koliesnik, M. V. [NASU, Institute for Nuclear Research (Ukraine); Arita, K. [Nagoya Institute of Technology, Department of Physics (Japan)
2016-11-15
The periodic-orbit theory based on the improved stationary-phase method within the phase-space path integral approach is presented for the semiclassical description of the nuclear shell structure, concerning themain topics of the fruitful activity ofV.G. Soloviev. We apply this theory to study bifurcations and symmetry breaking phenomena in a radial power-law potential which is close to the realistic Woods–Saxon one up to about the Fermi energy. Using the realistic parametrization of nuclear shapes we explain the origin of the double-humped fission barrier and the asymmetry in the fission isomer shapes by the bifurcations of periodic orbits. The semiclassical origin of the oblate–prolate shape asymmetry and tetrahedral shapes is also suggested within the improved periodic-orbit approach. The enhancement of shell structures at some surface diffuseness and deformation parameters of such shapes are explained by existence of the simple local bifurcations and new non-local bridge-orbit bifurcations in integrable and partially integrable Fermi-systems. We obtained good agreement between the semiclassical and quantum shell-structure components of the level density and energy for several surface diffuseness and deformation parameters of the potentials, including their symmetry breaking and bifurcation values.
Inverse bifurcation analysis: application to simple gene systems
Directory of Open Access Journals (Sweden)
Schuster Peter
2006-07-01
Full Text Available Abstract Background Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties. Results We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability in existing numerical bifurcation software. As applications of the proposed method, we show that the problem of maximizing regions of a given qualitative behavior as well as the reverse engineering of bistable gene switches can be modelled and efficiently solved.
Stochastic Bifurcation Analysis of an Elastically Mounted Flapping Airfoil
Directory of Open Access Journals (Sweden)
Bose Chandan
2018-01-01
Full Text Available The present paper investigates the effects of noisy flow fluctuations on the fluid-structure interaction (FSI behaviour of a span-wise flexible wing modelled as a two degree-of-freedom elastically mounted flapping airfoil. In the sterile flow conditions, the system undergoes a Hopf bifurcation as the free-stream velocity exceeds a critical limit resulting in a stable limit-cycle oscillation (LCO from a fixed point response. On the other hand, the qualitative dynamics changes from a stochastic fixed point to a random LCO through an intermittent state in the presence of irregular flow fluctuations. The probability density function depicts the most probable system state in the phase space. A phenomenological bifurcation (P-bifurcation analysis based on the transition in the topology associated with the structure of the joint probability density function (pdf of the response variables has been carried out. The joint pdf corresponding to the stochastic fixed point possesses a Dirac delta function like structure with a sharp single peak around zero. As the mean flow speed crosses the critical value, the joint pdf bifurcates to a crater-like structure indicating the occurrence of a P-bifurcation. The intermittent state is characterized by the co-existence of the unimodal as well as the crater like structure.
Convective parameters in fuel elements for research nuclear reactors
International Nuclear Information System (INIS)
Lopez Martinez, C.D.
1992-01-01
The study of a prototype for the simulation of fuel elements for research nuclear reactors by natural convection in water is presented in this paper. This project is carry out in the thermofluids laboratory of National Institute of Nuclear Research. The fuel prototype has already been test for natural convection in air, and the first results in water are presented in this work. In chapter I, a general description of Triga Mark III is made, paying special atention to fuel-moderator components. In chapter II and III an approach to convection subject in its global aspects is made, since the intention is to give a general idea of the events occuring around fuel elements in a nuclear reactor. In chapter II, where an emphasis on forced convection is made, some basic concepts for forced convection as well as for natural convection are included. The subject of flow through cylinders is annotated only as a comparative reference with natural convection in vertical cylinders, noting the difference between used correlations and the involved variables. In chapter III a compilation of correlation found in the bibliography about natural convection in vertical cylinders is presented, since its geometry is the more suitable in the analysis of a fuel rod. Finally, in chapter IV performed experiments in the test bench are detailed, and the results are presented in form of tables and graphs, showing the used equations for the calculations and the restrictions used in each case. For the analysis of the prototypes used in the test bench, a constant and uniform flow of heat in the whole length of the fuel rod is considered. At the end of this chapter, the work conclusions and a brief explanation of the results are presented (Author)
A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds
Hagos, Samson; Feng, Zhe; Plant, Robert S.; Houze, Robert A.; Xiao, Heng
2018-02-01
A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii) the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. In addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.
Sediment sorting at a side channel bifurcation
van Denderen, Pepijn; Schielen, Ralph; Hulscher, Suzanne
2017-04-01
Side channels have been constructed to reduce the flood risk and to increase the ecological value of the river. In various Dutch side channels large aggradation in these channels occurred after construction. Measurements show that the grain size of the deposited sediment in the side channel is smaller than the grain size found on the bed of the main channel. This suggest that sorting occurs at the bifurcation of the side channel. The objective is to reproduce with a 2D morphological model the fining of the bed in the side channel and to study the effect of the sediment sorting on morphodynamic development of the side channel. We use a 2D Delft3D model with two sediment fractions. The first fraction corresponds with the grain size that can be found on the bed of the main channel and the second fraction corresponds with the grain size found in the side channel. With the numerical model we compute several side channel configurations in which we vary the length and the width of the side channel, and the curvature of the upstream channel. From these computations we can derive the equilibrium state and the time scale of the morphodynamic development of the side channel. Preliminary results show that even when a simple sediment transport relation is used, like Engelund & Hansen, more fine sediment enters the side channel than coarse sediment. This is as expected, and is probably related to the bed slope effects which are a function of the Shields parameter. It is expected that by adding a sill at the entrance of the side channel the slope effect increases. This might reduce the amount of coarse sediment which enters the side channel even more. It is unclear whether the model used is able to reproduce the effect of such a sill correctly as modelling a sill and reproducing the correct hydrodynamic and morphodynamic behaviour is not straightforward in a 2D model. Acknowledgements: This research is funded by STW, part of the Dutch Organization for Scientific Research under
Localized traveling pulses in natural doubly diffusive convection
Lo Jacono, D.; Bergeon, A.; Knobloch, E.
2017-09-01
Two-dimensional natural doubly diffusive convection in a vertical slot driven by an imposed temperature difference in the horizontal is studied using numerical continuation and direct numerical simulation. Two cases are considered and compared. In the first a concentration difference that balances thermal buoyancy is imposed in the horizontal and stationary localized structures are found to be organized in a standard snakes-and-ladders bifurcation diagram. Disconnected branches of traveling pulses TPn consisting of n ,n =1 ,2 ,⋯ , corotating cells are identified and shown to accumulate on a tertiary branch of traveling waves. With Robin or mixed concentration boundary conditions on one wall all localized states travel and the hitherto stationary localized states may connect up with the traveling pulses. The stability of the TPn states is determined and unstable TPn shown to evolve into spatio-temporal chaos. The calculations are done with no-slip boundary conditions in the horizontal and periodic boundary conditions in the vertical.
NUMERICAL ANALYSIS OF NATURAL CONVECTION IN A PRISMATIC ENCLOSURE
Directory of Open Access Journals (Sweden)
Walid AICH
2011-01-01
Full Text Available Natural convection heat transfer and fluid flow have been examined numerically using the control-volume finite-element method in an isosceles prismatic cavity, submitted to a uniform heat flux from below when inclined sides are maintained isothermal and vertical walls are assumed to be perfect thermal insulators, without symmetry assumptions for the flow structure. The aim of the study is to examine a pitchfork bifurcation occurrence. Governing parameters on heat transfer and flow fields are the Rayleigh number and the aspect ratio of the enclosure. It has been found that the heated wall is not isothermal and the flow structure is sensitive to the aspect ratio. It is also found that heat transfer increases with increasing of Rayleigh number and decreases with increasing aspect ratio. The effects of aspect ratio become significant especially for higher values of Rayleigh number. Eventually the obtained results show that a pitchfork bifurcation occurs at a critical Rayleigh number, above which the symmetric solutions becomes unstable and asymmetric solutions are instead obtained.
EXPERIMENTAL STUDY ON SEDIMENT DISTRIBUTION AT CHANNEL BIFURCATION
Institute of Scientific and Technical Information of China (English)
G.M. Tarekul ISLAM; M.R. KABIR; Ainun NISHAT
2002-01-01
This paper presents the experimental results on the distribution of sediments at channel bifurcation.The experiments have been conducted in a physical model of channel bifurcation. It consists of a straight main channel which bifurcates into two branch channels of different widths. The test rig is a mobile bed with fixed bank. Four different noses have been used to study the phenomenon. For each nose, three upstream discharges viz. 20 l/s, 30 l/s and 40 l/s have been employed. From the measured data, discharges and sediment transport ratios per unit width are calculated in the downstream branches.These data have been set to the general nodal point relation and a set of equations has been developed to describe the distribution of sediments to the downstream branches for different nose angles.
Adaptive Control of Electromagnetic Suspension System by HOPF Bifurcation
Directory of Open Access Journals (Sweden)
Aming Hao
2013-01-01
Full Text Available EMS-type maglev system is essentially nonlinear and unstable. It is complicated to design a stable controller for maglev system which is under large-scale disturbance and parameter variance. Theory analysis expresses that this phenomenon corresponds to a HOPF bifurcation in mathematical model. An adaptive control law which adjusts the PID control parameters is given in this paper according to HOPF bifurcation theory. Through identification of the levitated mass, the controller adjusts the feedback coefficient to make the system far from the HOPF bifurcation point and maintain the stability of the maglev system. Simulation result indicates that adjusting proportion gain parameter using this method can extend the state stability range of maglev system and avoid the self-excited vibration efficiently.
Hopf bifurcation and chaos in macroeconomic models with policy lag
International Nuclear Information System (INIS)
Liao Xiaofeng; Li Chuandong; Zhou Shangbo
2005-01-01
In this paper, we consider the macroeconomic models with policy lag, and study how lags in policy response affect the macroeconomic stability. The local stability of the nonzero equilibrium of this equation is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation. Some general stability criteria involving the policy lag and the system parameter are derived. By choosing the policy lag as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcation. The direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Moreover, we show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system become locally unstable when the policy lag is too long. We also find the chaotic behavior in some range of the policy lag
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
International Nuclear Information System (INIS)
Ottaviani, M.; Tebaldi, C.
1998-12-01
In this work we analyzed the sequence of bifurcated equilibria in two-dimensional reduced magnetohydrodynamics. Diamagnetic effects are studied under the assumption of a constant equilibrium pressure gradient, not altered by the formation of the magnetic island. The formation of an island when the symmetric equilibrium becomes unstable is studied as a function of the tearing mode stability parameter Δ' and of the diamagnetic frequency, by employing fixed-points numerical techniques and an initial value code. At larger values of Δ' a tangent bifurcation takes place, above which no small island solutions exist. This bifurcation persists up to fairly large values of the diamagnetic frequency (of the order of one tenth of the Alfven frequency). The implications of this phenomenology for the intermittent MHD dynamics observed in tokamaks is discussed. (authors)
Bifurcations of propellant burning rate at oscillatory pressure
Energy Technology Data Exchange (ETDEWEB)
Novozhilov, Boris V. [N. N. Semenov Institute of Chemical Physics, Russian Academy of Science, 4 Kosygina St., Moscow 119991 (Russian Federation)
2006-06-15
A new phenomenon, the disparity between pressure and propellant burning rate frequencies, has revealed in numerical studies of propellant burning rate response to oscillatory pressure. As is clear from the linear approximation, under small pressure amplitudes, h, pressure and propellant burning rate oscillations occur with equal period T (T-solution). In the paper, however, it is shown that at a certain critical value of the parameter h the system in hand undergoes a bifurcation so that the T-solution converts to oscillations with period 2T (2T-solution). When the bifurcation parameter h increases, the subsequent behavior of the system becomes complicated. It is obtained a sequence of period doubling to 4T-solution and 8T-solution. Beyond a certain value of the bifurcation parameter h an apparently fully chaotic solution is found. These effects undoubtedly should be taken into account in studies of oscillatory processes in combustion chambers. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Stochastic stability and bifurcation in a macroeconomic model
International Nuclear Information System (INIS)
Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei
2007-01-01
On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis
Dynamical systems V bifurcation theory and catastrophe theory
1994-01-01
Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of w...
Bifurcation analysis of a delayed mathematical model for tumor growth
International Nuclear Information System (INIS)
Khajanchi, Subhas
2015-01-01
In this study, we present a modified mathematical model of tumor growth by introducing discrete time delay in interaction terms. The model describes the interaction between tumor cells, healthy tissue cells (host cells) and immune effector cells. The goal of this study is to obtain a better compatibility with reality for which we introduced the discrete time delay in the interaction between tumor cells and host cells. We investigate the local stability of the non-negative equilibria and the existence of Hopf-bifurcation by considering the discrete time delay as a bifurcation parameter. We estimate the length of delay to preserve the stability of bifurcating periodic solutions, which gives an idea about the mode of action for controlling oscillations in the tumor growth. Numerical simulations of the model confirm the analytical findings
Bifurcations in the optimal elastic foundation for a buckling column
International Nuclear Information System (INIS)
Rayneau-Kirkhope, Daniel; Farr, Robert; Ding, K.; Mao, Yong
2010-01-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcations in the optimal elastic foundation for a buckling column
Energy Technology Data Exchange (ETDEWEB)
Rayneau-Kirkhope, Daniel, E-mail: ppxdr@nottingham.ac.u [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom); Farr, Robert [Unilever R and D, Olivier van Noortlaan 120, AT3133, Vlaardingen (Netherlands); London Institute for Mathematical Sciences, 22 South Audley Street, Mayfair, London (United Kingdom); Ding, K. [Department of Physics, Fudan University, Shanghai, 200433 (China); Mao, Yong [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)
2010-12-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcation-free design method of pulse energy converter controllers
International Nuclear Information System (INIS)
Kolokolov, Yury; Ustinov, Pavel; Essounbouli, Najib; Hamzaoui, Abdelaziz
2009-01-01
In this paper, a design method of pulse energy converter (PEC) controllers is proposed. This method develops a classical frequency domain design, based on the small signal modeling, by means of an addition of a nonlinear dynamics analysis stage. The main idea of the proposed method consists in fact that the PEC controller, designed with an application of the small signal modeling, is tuned after with taking into the consideration an essentially nonlinear nature of the PEC that makes it possible to avoid bifurcation phenomena in the PEC dynamics at the design stage (bifurcation-free design). Also application of the proposed method allows an improvement of the designed controller performance. The application of this bifurcation-free design method is demonstrated on an example of the controller design of direct current-direct current (DC-DC) buck converter with an input electromagnetic interference filter.
Bidispersive-inclined convection
Mulone, Giuseppe; Straughan, Brian
2016-01-01
A model is presented for thermal convection in an inclined layer of porous material when the medium has a bidispersive structure. Thus, there are the usual macropores which are full of a fluid, but there are also a system of micropores full of the same fluid. The model we employ is a modification of the one proposed by Nield & Kuznetsov (2006 Int. J. Heat Mass Transf. 49, 3068–3074. (doi:10.1016/j.ijheatmasstransfer.2006.02.008)), although we consider a single temperature field only. PMID:27616934
An Approach to Robust Control of the Hopf Bifurcation
Directory of Open Access Journals (Sweden)
Giacomo Innocenti
2011-01-01
Full Text Available The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.
Three dimensional nilpotent singularity and Sil'nikov bifurcation
International Nuclear Information System (INIS)
Li Xindan; Liu Haifei
2007-01-01
In this paper, by using the normal form, blow-up theory and the technique of global bifurcations, we study the singularity at the origin with threefold zero eigenvalue for nonsymmetric vector fields with nilpotent linear part and 4-jet C ∼ -equivalent toy-bar -bar x+z-bar -bar y+ax 3 y-bar -bar z,with a 0, and analytically prove the existence of Sil'nikov bifurcation, and then of the strange attractor for certain subfamilies of the nonsymmetric versal unfoldings of this singularity under some conditions
Global bifurcations in a piecewise-smooth Cournot duopoly game
International Nuclear Information System (INIS)
Tramontana, Fabio; Gardini, Laura; Puu, Toenu
2010-01-01
The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu . The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the Neimark-Sacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties differ significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist.
Communication: Mode bifurcation of droplet motion under stationary laser irradiation
Energy Technology Data Exchange (ETDEWEB)
Takabatake, Fumi [Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502 (Japan); Department of Bioengineering and Robotics, Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579 (Japan); Yoshikawa, Kenichi [Faculty of Life and Medical Sciences, Doshisha University, Kyotanabe, Kyoto 610-0394 (Japan); Ichikawa, Masatoshi, E-mail: ichi@scphys.kyoto-u.ac.jp [Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502 (Japan)
2014-08-07
The self-propelled motion of a mm-sized oil droplet floating on water, induced by a local temperature gradient generated by CW laser irradiation is reported. The circular droplet exhibits two types of regular periodic motion, reciprocal and circular, around the laser spot under suitable laser power. With an increase in laser power, a mode bifurcation from rectilinear reciprocal motion to circular motion is caused. The essential aspects of this mode bifurcation are discussed in terms of spontaneous symmetry-breaking under temperature-induced interfacial instability, and are theoretically reproduced with simple coupled differential equations.
Transportation and concentration inequalities for bifurcating Markov chains
DEFF Research Database (Denmark)
Penda, S. Valère Bitseki; Escobar-Bach, Mikael; Guillin, Arnaud
2017-01-01
We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful...... concentration inequalities.We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive...
Bifurcated transition of radial transport in the HIEI tandem mirror
International Nuclear Information System (INIS)
Sakai, O.; Yasaka, Y.
1995-01-01
Transition to a high radial confinement mode in a mirror plasma is triggered by limiter biasing. Sheared plasma rotation is induced in the high confinement phase which is characterized by reduction of edge turbulence and a confinement enhancement factor of 2-4. Edge plasma parameters related to radial confinement show a hysteresis phenomenon as a function of bias voltage or bias current, leading to the fact that transition from low to high confinement mode occurs between the bifurcated states. A transition model based on azimuthal momentum balance is employed to clarify physics of the observed bifurcation. copyright 1995 American Institute of Physics
Bifurcation analysis of nephron pressure and flow regulation
DEFF Research Database (Denmark)
Barfred, Mikael; Mosekilde, Erik; Holstein-Rathlou, N.-H.
1996-01-01
One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between...... the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period...
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Lóczi, Lajos
2015-01-07
© 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.
Transport phenomena II essentials
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Transport Phenomena II covers forced convention, temperature distribution, free convection, diffusitivity and the mechanism of mass transfer, convective mass transfer, concentration
REA, The Editors of
1988-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Heat Transfer II reviews correlations for forced convection, free convection, heat exchangers, radiation heat transfer, and boiling and condensation.
Complex dynamics of a Holling type II prey-predator system with state feedback control
International Nuclear Information System (INIS)
Jiang Guirong; Lu Qishao; Qian Linning
2007-01-01
The complex dynamics of a Holling type II prey-predator system with impulsive state feedback control is studied in both theoretical and numerical ways. The sufficient conditions for the existence and stability of semi-trivial and positive periodic solutions are obtained by using the Poincare map and the analogue of the Poincare criterion. The qualitative analysis shows that the positive periodic solution bifurcates from the semi-trivial solution through a fold bifurcation. The bifurcation diagrams, Lyapunov exponents, and phase portraits are illustrated by an example, in which the chaotic solutions appear via a cascade of period-doubling bifurcations. The superiority of the state feedback control strategy is also discussed
Hamiltonian Description of Convective-cell Generation
International Nuclear Information System (INIS)
Krommes, J.A.; Kolesnikov, R.A.
2004-01-01
The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted
Hopf bifurcation analysis of Chen circuit with direct time delay feedback
International Nuclear Information System (INIS)
Hai-Peng, Ren; Wen-Chao, Li; Ding, Liu
2010-01-01
Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding of the dynamics of such circuits described by delay differential equations, Hopf bifurcation in the circuit is analysed using the Hopf bifurcation theory and the central manifold theorem in this paper. Bifurcation points and bifurcation directions are derived in detail, which prove to be consistent with the previous bifurcation diagram. Numerical simulations and experimental results are given to verify the theoretical analysis. Hopf bifurcation analysis can explain and predict the periodical orbit (oscillation) in Chen circuit with direct time delay feedback. Bifurcation boundaries are derived using the Hopf bifurcation analysis, which will be helpful for determining the parameters in the stabilisation of the originally chaotic circuit
Kan-On, Yukio
2007-04-01
This paper is concerned with the bifurcation structure of positive stationary solutions for a generalized Lotka-Volterra competition model with diffusion. To establish the structure, the bifurcation theory and the interval arithmetic are employed.
An experimental study of mixed convection
International Nuclear Information System (INIS)
Saez, Manuel
1998-01-01
The aim of our study is to establish a reliable data base for improving thermal-hydraulic codes, in the field of turbulent flows with buoyancy forces. The flow considered is mixed convection in the Reynolds and Richardson number range: Re=10"3 to 6*10"4 and Ri=10"-"4 to 1. Experiments are carried out in an upward turbulent flow between vertical parallel plates at different wall temperatures. Part 1 gives a detailed data base of turbulent mixed flow of free and forced convection. Part II presents the installation and the calibration system intended for probes calibration. Part III describes the measurement technique (constant-temperature probe and cold-wire probe) and the method for measuring the position of the hot-wire anemometer from the wall surface. The measurement accuracy is within 0.001 mm in the present system. Part IV relates the development of a method for near wall measurements. This correction procedure for hot-wire anemometer close to wall has been derived on the basis of a two-dimensional numerical study. The method permits to obtain a quantitative correction of the wall influence on hot-wires and takes into account the velocity profile and the effects the wall material has on the heat loss. Part V presents the experimental data obtained in the channel in forced and mixed convection. Results obtained in the forced convection regime serve as a verification of the measurement technique close to the wall and give the conditions at the entrance of the test section. The effects of the buoyancy force on the mean velocity and temperature profiles are confirmed. The buoyancy strongly affects the flow structure and deforms the distribution of mean velocity. The velocity profiles are asymmetric. The second section of part V gives an approach of analytical wall functions with buoyancy forces, on the basis of the experimental data obtained in the test section. (author) [fr
Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay
International Nuclear Information System (INIS)
Liu Xiaoming; Liao Xiaofeng
2009-01-01
In this paper, we consider the delayed differential equations modeling three-neuron equations with only a time delay. Using the time delay as a bifurcation parameter, necessary and sufficient conditions for Hopf bifurcation to occur are derived. Numerical results indicate that for this model, Hopf bifurcation is likely to occur at suitable delay parameter values.
Local bifurcation analysis in nuclear reactor dynamics by Sotomayor’s theorem
International Nuclear Information System (INIS)
Pirayesh, Behnam; Pazirandeh, Ali; Akbari, Monireh
2016-01-01
Highlights: • When the feedback reactivity is considered as a nonlinear function some complex behaviors may emerge in the system such as local bifurcation phenomenon. • The qualitative behaviors of a typical nuclear reactor near its equilibrium points have been studied analytically. • Comprehensive analytical bifurcation analyses presented in this paper are transcritical bifurcation, saddle- node bifurcation and pitchfork bifurcation. - Abstract: In this paper, a qualitative approach has been used to explore nuclear reactor behaviors with nonlinear feedback. First, a system of four dimensional ordinary differential equations governing the dynamics of a typical nuclear reactor is introduced. These four state variables are the relative power of the reactor, the relative concentration of delayed neutron precursors, the fuel temperature and the coolant temperature. Then, the qualitative behaviors of the dynamical system near its equilibria have been studied analytically by using local bifurcation theory and Sotomayor’s theorem. The results indicated that despite the uncertainty of the reactivity, we can analyze the qualitative behavior changes of the reactor from the bifurcation point of view. Notably, local bifurcations that were considered in this paper include transcritical bifurcation, saddle-node bifurcation and pitchfork bifurcation. The theoretical analysis showed that these three types of local bifurcations may occur in the four dimensional dynamical system. In addition, to confirm the analytical results the numerical simulations are given.
Bifurcation of limit cycles for cubic reversible systems
Directory of Open Access Journals (Sweden)
Yi Shao
2014-04-01
Full Text Available This article is concerned with the bifurcation of limit cycles of a class of cubic reversible system having a center at the origin. We prove that this system has at least four limit cycles produced by the period annulus around the center under cubic perturbations
Chaos and bifurcations in periodic windows observed in plasmas
International Nuclear Information System (INIS)
Qin, J.; Wang, L.; Yuan, D.P.; Gao, P.; Zhang, B.Z.
1989-01-01
We report the experimental observations of deterministic chaos in a steady-state plasma which is not driven by any extra periodic forces. Two routes to chaos have been found, period-doubling and intermittent chaos. The fine structures in chaos such as periodic windows and bifurcations in windows have also been observed
Coronary bifurcation lesions treated with simple or complex stenting
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels R; de Belder, Adam J
2016-01-01
AIMS: Randomized trials of coronary bifurcation stenting have shown better outcomes from a simple (provisional) strategy rather than a complex (planned two-stent) strategy in terms of short-term efficacy and safety. Here, we report the 5-year all-cause mortality based on pooled patient-level data...
The Boundary-Hopf-Fold Bifurcation in Filippov Systems
Efstathiou, Konstantinos; Liu, Xia; Broer, Henk W.
2015-01-01
This paper studies the codimension-3 boundary-Hopf-fold (BHF) bifurcation of planar Filippov systems. Filippov systems consist of at least one discontinuity boundary locally separating the phase space to disjoint components with different dynamics. Such systems find applications in several fields,
Stability and Hopf bifurcation analysis of a new system
International Nuclear Information System (INIS)
Huang Kuifei; Yang Qigui
2009-01-01
In this paper, a new chaotic system is introduced. The system contains special cases as the modified Lorenz system and conjugate Chen system. Some subtle characteristics of stability and Hopf bifurcation of the new chaotic system are thoroughly investigated by rigorous mathematical analysis and symbolic computations. Meanwhile, some numerical simulations for justifying the theoretical analysis are also presented.
Pitchfork bifurcation and vibrational resonance in a fractional-order ...
Indian Academy of Sciences (India)
The fractional-order damping mainly determines the pattern of the vibrational resonance. There is a bifurcation point of the fractional order which, in the case of double-well potential, transforms vibrational resonance pattern from a single resonance to a double resonance, while in the case of single-well potential, transforms ...
Nonintegrability of the unfolding of the fold-Hopf bifurcation
Yagasaki, Kazuyuki
2018-02-01
We consider the unfolding of the codimension-two fold-Hopf bifurcation and prove its meromorphic nonintegrability in the meaning of Bogoyavlenskij for almost all parameter values. Our proof is based on a generalized version of the Morales-Ramis-Simó theory for non-Hamiltonian systems and related variational equations up to second order are used.
Bifurcations and complete chaos for the diamagnetic Kepler problem
Hansen, Kai T.
1995-03-01
We describe the structure of bifurcations in the unbounded classical diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the nonwandering set is described by a complete trinary symbolic dynamics for scaled energies larger than ɛc=0.328 782. . ..
Bifurcations and Complete Chaos for the Diamagnetic Kepler Problem
Hansen, Kai T.
1995-01-01
We describe the structure of bifurcations in the unbounded classical Diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the non-wandering set is described by a complete trinary symbolic dynamics for scaled energies larger then $\\epsilon_c=0.328782\\ldots$.
Experimental Investigation of Bifurcations in a Thermoacoustic Engine
Directory of Open Access Journals (Sweden)
Vishnu R. Unni
2015-06-01
Full Text Available In this study, variation in the characteristics of the pressure oscillations in a thermoacoustic engine is explored as the input heat flux is varied. A bifurcation diagram is plotted to study the variation in the qualitative behavior of the acoustic oscillations as the input heat flux changes. At a critical input heat flux (60 Watt, the engine begins to produce acoustic oscillations in its fundamental longitudinal mode. As the input heat flux is increased, incommensurate frequencies appear in the power spectrum. The simultaneous presence of incommensurate frequencies results in quasiperiodic oscillations. On further increase of heat flux, the fundamental mode disappears and second mode oscillations are observed. These bifurcations in the characteristics of the pressure oscillations are the result of nonlinear interaction between multiple modes present in the thermoacoustic engine. Hysteresis in the bifurcation diagram suggests that the bifurcation is subcritical. Further, the qualitative analysis of different dynamic regimes is performed using nonlinear time series analysis. The physical reason for the observed nonlinear behavior is discussed. Suggestions to avert the variations in qualitative behavior of the pressure oscillations in thermoacoustic engines are also provided.
Stability of Bifurcating Stationary Solutions of the Artificial Compressible System
Teramoto, Yuka
2018-02-01
The artificial compressible system gives a compressible approximation of the incompressible Navier-Stokes system. The latter system is obtained from the former one in the zero limit of the artificial Mach number ɛ which is a singular limit. The sets of stationary solutions of both systems coincide with each other. It is known that if a stationary solution of the incompressible system is asymptotically stable and the velocity field of the stationary solution satisfies an energy-type stability criterion, then it is also stable as a solution of the artificial compressible one for sufficiently small ɛ . In general, the range of ɛ shrinks when the spectrum of the linearized operator for the incompressible system approaches to the imaginary axis. This can happen when a stationary bifurcation occurs. It is proved that when a stationary bifurcation from a simple eigenvalue occurs, the range of ɛ can be taken uniformly near the bifurcation point to conclude the stability of the bifurcating solution as a solution of the artificial compressible system.
Long term results of kissing stents in the aortic bifurcation
Hinnen, J.W.; Konickx, M.A.; Meerwaldt, Robbert; Kolkert, J.L.P.; van der Palen, Jacobus Adrianus Maria; Huisman, A.B.
2015-01-01
BACKGROUND: To evaluate the long-term outcome after aortoiliac kissing stent placement and to analyze variables, which potentially influence the outcome of endovascular reconstruction of the aortic bifurcation. METHODS: All patients treated with aortoiliac kissing stents at our institution between
Femoral bifurcation with ipsilateral tibia hemimelia: Early outcome of ...
African Journals Online (AJOL)
Hereby, we present a case report of a 2-year-old boy who first presented in our orthopedic clinic as a 12-day-old neonate, with a grossly deformed right lower limb from a combination of complete tibia hemimelia and ipsilateral femoral bifurcation. Excision of femoral exostosis, knee disarticulation and prosthetic fitting gives ...
Hopf bifurcation formula for first order differential-delay equations
Rand, Richard; Verdugo, Anael
2007-09-01
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The derivation is accomplished using Lindstedt's perturbation method.
Direction and stability of bifurcating solutions for a Signorini problem
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Kučera, Milan; Recke, L.
2015-01-01
Roč. 113, January (2015), s. 357-371 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : Signorini problem * variational inequality * bifurcation direction Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X14003228
Smooth bifurcation for a Signorini problem on a rectangle
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Kučera, Milan; Recke, L.
2012-01-01
Roč. 137, č. 2 (2012), s. 131-138 ISSN 0862-7959 R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : Signorini problem * smooth bifurcation * variational inequality Subject RIV: BA - General Mathematics http://dml.cz/dmlcz/142859
Bifurcation analysis and the travelling wave solutions of the Klein
Indian Academy of Sciences (India)
In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by ...
Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback
Directory of Open Access Journals (Sweden)
Shao-Fang Wen
2018-01-01
Full Text Available The heteroclinic bifurcation and chaos of a Duffing oscillator with forcing excitation under both delayed displacement feedback and delayed velocity feedback are studied by Melnikov method. The Melnikov function is analytically established to detect the necessary conditions for generating chaos. Through the analysis of the analytical necessary conditions, we find that the influences of the delayed displacement feedback and delayed velocity feedback are separable. Then the influences of the displacement and velocity feedback parameters on heteroclinic bifurcation and threshold value of chaotic motion are investigated individually. In order to verify the correctness of the analytical conditions, the Duffing oscillator is also investigated by numerical iterative method. The bifurcation curves and the largest Lyapunov exponents are provided and compared. From the analysis of the numerical simulation results, it could be found that two types of period-doubling bifurcations occur in the Duffing oscillator, so that there are two paths leading to the chaos in this oscillator. The typical dynamical responses, including time histories, phase portraits, and Poincare maps, are all carried out to verify the conclusions. The results reveal some new phenomena, which is useful to design or control this kind of system.
Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
Directory of Open Access Journals (Sweden)
Wei Tan
2015-01-01
Full Text Available The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K-βxy/N-(μ+mx], y→y+δ[βxy/N-(μ+dy]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
Epidemic model with vaccinated age that exhibits backward bifurcation
International Nuclear Information System (INIS)
Yang Junyuan; Zhang Fengqin; Li Xuezhi
2009-01-01
Vaccination of susceptibilities is included in a transmission model for a disease that confers immunity. In this paper, interplay of vaccination strategy together with vaccine efficacy and the vaccinated age is studied. In particular, vaccine efficacy can lead to a backward bifurcation. At the same time, we also discuss an abstract formulation of the problem, and establish the well-posedness of the model.
Bifurcation methods of dynamical systems for handling nonlinear ...
Indian Academy of Sciences (India)
physics pp. 863–868. Bifurcation methods of dynamical systems for handling nonlinear wave equations. DAHE FENG and JIBIN LI. Center for Nonlinear Science Studies, School of Science, Kunming University of Science and Technology .... (b) It can be shown from (15) and (18) that the balance between the weak nonlinear.
Bifurcation analysis of wind-driven flows with MOM4
Bernsen, E.; Dijkstra, H.A.; Wubs, F.W.
2009-01-01
In this paper, the methodology of bifurcation analysis is applied to the explicit time-stepping ocean model MOM4 using a Jacobian–Free Newton–Krylov (JFNK) approach. We in detail present the implementation of the JFNK method in MOM4 but restrict the preconditioning technique to the case for which
Chemical reaction systems with a homoclinic bifurcation: an inverse problem
Czech Academy of Sciences Publication Activity Database
Plesa, T.; Vejchodský, Tomáš; Erban, R.
2016-01-01
Roč. 54, č. 10 (2016), s. 1884-1915 ISSN 0259-9791 EU Projects: European Commission(XE) 328008 - STOCHDETBIOMODEL Institutional support: RVO:67985840 Keywords : nonnegative dynamical systems * bifurcations * oscillations Subject RIV: BA - General Mathematics Impact factor: 1.308, year: 2016 http://link.springer.com/article/10.1007%2Fs10910-016-0656-1
Bifurcation Analysis of Spiral Growth Processes in Plants
DEFF Research Database (Denmark)
Andersen, C.A.; Ernstsen, C.N.; Mosekilde, Erik
1999-01-01
In order to examine the significance of different assumptions about the range of the inhibitory forces, we have performed a series of bifurcation analyses of a simple model that can explain the formation of helical structures in phyllotaxis. Computer simulations are used to illustrate the role...
Smooth bifurcation for variational inequalities based on Lagrange multipliers
Czech Academy of Sciences Publication Activity Database
Eisner, Jan; Kučera, Milan; Recke, L.
2006-01-01
Roč. 19, č. 9 (2006), s. 981-1000 ISSN 0893-4983 R&D Projects: GA AV ČR(CZ) IAA100190506 Institutional research plan: CEZ:AV0Z10190503 Keywords : abstract variational inequality * bifurcation * Lagrange multipliers Subject RIV: BA - General Mathematics
Experimental bifurcation analysis of an impact oscillator – Determining stability
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Elmegård, Michael
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior...
Regularization of the Boundary-Saddle-Node Bifurcation
Directory of Open Access Journals (Sweden)
Xia Liu
2018-01-01
Full Text Available In this paper we treat a particular class of planar Filippov systems which consist of two smooth systems that are separated by a discontinuity boundary. In such systems one vector field undergoes a saddle-node bifurcation while the other vector field is transversal to the boundary. The boundary-saddle-node (BSN bifurcation occurs at a critical value when the saddle-node point is located on the discontinuity boundary. We derive a local topological normal form for the BSN bifurcation and study its local dynamics by applying the classical Filippov’s convex method and a novel regularization approach. In fact, by the regularization approach a given Filippov system is approximated by a piecewise-smooth continuous system. Moreover, the regularization process produces a singular perturbation problem where the original discontinuous set becomes a center manifold. Thus, the regularization enables us to make use of the established theories for continuous systems and slow-fast systems to study the local behavior around the BSN bifurcation.
Topography of Aortic Bifurcation in a Black Kenyan Population ...
African Journals Online (AJOL)
After removal of abdominal viscera, peritoneum, fibrofatty connective tissue, inferior vena cava was removed to expose the termination of abdominal aorta. Vertebral level, angle and asymmetry of bifurcation were recorded. Data were analysed by SPSS version 17.0 for windows and are presented in tables and bar charts.
International Nuclear Information System (INIS)
Rao, Y.F.; Fukuda, K.; Hasegawa, S.
1986-01-01
Steady and transient analytical investigation with the Galerkin method has been performed on natural convection in a horizontal porous annulus heated from the inner surface. Three families of convergent solutions, appearing one after another with increasing RaDa numbers, were obtained corresponding to different initial conditions. Despite the fact that the flow structures of two branching solutions are quite different, there exists a critical RaDa number at which their overall heat transfer rates have the same value. The bifurcation point was determined numerically, which coincided very well with that from experimental observation. The solutions in which higher wavenumber modes are dominant agree better with experimental data of overall heat transfer
Numerical bifurcation analysis of conformal formulations of the Einstein constraints
International Nuclear Information System (INIS)
Holst, M.; Kungurtsev, V.
2011-01-01
The Einstein constraint equations have been the subject of study for more than 50 years. The introduction of the conformal method in the 1970s as a parametrization of initial data for the Einstein equations led to increased interest in the development of a complete solution theory for the constraints, with the theory for constant mean curvature (CMC) spatial slices and closed manifolds completely developed by 1995. The first general non-CMC existence result was establish by Holst et al. in 2008, with extensions to rough data by Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC theory remains mostly open; moreover, recent work of Maxwell on specific symmetry models sheds light on fundamental nonuniqueness problems with the conformal method as a parametrization in non-CMC settings. In parallel with these mathematical developments, computational physicists have uncovered surprising behavior in numerical solutions to the extended conformal thin sandwich formulation of the Einstein constraints. In particular, numerical evidence suggests the existence of multiple solutions with a quadratic fold, and a recent analysis of a simplified model supports this conclusion. In this article, we examine this apparent bifurcation phenomena in a methodical way, using modern techniques in bifurcation theory and in numerical homotopy methods. We first review the evidence for the presence of bifurcation in the Hamiltonian constraint in the time-symmetric case. We give a brief introduction to the mathematical framework for analyzing bifurcation phenomena, and then develop the main ideas behind the construction of numerical homotopy, or path-following, methods in the analysis of bifurcation phenomena. We then apply the continuation software package AUTO to this problem, and verify the presence of the fold with homotopy-based numerical methods. We discuss these results and their physical significance, which lead to some interesting remaining questions to
Nield, Donald A
2013-01-01
Convection in Porous Media, 4th Edition, provides a user-friendly introduction to the subject, covering a wide range of topics, such as fibrous insulation, geological strata, and catalytic reactors. The presentation is self-contained, requiring only routine mathematics and the basic elements of fluid mechanics and heat transfer. The book will be of use not only to researchers and practicing engineers as a review and reference, but also to graduate students and others entering the field. The new edition features approximately 1,750 new references and covers current research in nanofluids, cellular porous materials, strong heterogeneity, pulsating flow, and more. Recognized as the standard reference in the field Includes a comprehensive, 250-page reference list Cited over 2300 times to date in its various editions Serves as an introduction for those entering the field and as a comprehensive reference for experienced researchers Features new sections on nanofluids, carbon dioxide sequestration, and applications...
Bohan, Richard J.; Vandegrift, Guy
2003-02-01
Warm air aloft is stable. This explains the lack of strong winds in a warm front and how nighttime radiative cooling can lead to motionless air that can trap smog. The stability of stratospheric air can be attributed to the fact that it is heated from above as ultraviolet radiation strikes the ozone layer. On the other hand, fluid heated from below is unstable and can lead to Bernard convection cells. This explains the generally turbulent nature of the troposphere, which receives a significant fraction of its heat directly from the Earth's warmer surface. The instability of cold fluid aloft explains the violent nature of a cold front, as well as the motion of Earth's magma, which is driven by radioactive heating deep within the Earth's mantle. This paper describes how both effects can be demonstrated using four standard beakers, ice, and a bit of food coloring.
Nield, Donald A
1992-01-01
This book provides a user-friendly introduction to the topic of convection in porous media The authors as- sume that the reader is familiar with the basic elements of fluid mechanics and heat transfer, but otherwise the book is self-contained The book will be useful both as a review (for reference) and as a tutorial work, suitable as a textbook in a graduate course or seminar The book brings into perspective the voluminous research that has been performed during the last two decades The field has recently exploded because of worldwide concern with issues such as energy self-sufficiency and pollution of the environment Areas of application include the insulation of buildings and equipment, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering, and the storage of heat-generating materials such as grain and coal Geophysical applications range from the flow of groundwater around hot intrusions to the stability of snow against avalanches
Heat Flux Sensors for Infrared Thermography in Convective Heat Transfer
Carlomagno, Giovanni Maria; de Luca, Luigi; Cardone, Gennaro; Astarita, Tommaso
2014-01-01
This paper reviews the most dependable heat flux sensors, which can be used with InfraRed (IR) thermography to measure convective heat transfer coefficient distributions, and some of their applications performed by the authors' research group at the University of Naples Federico II. After recalling the basic principles that make IR thermography work, the various heat flux sensors to be used with it are presented and discussed, describing their capability to investigate complex thermo-fluid-dynamic flows. Several applications to streams, which range from natural convection to hypersonic flows, are also described. PMID:25386758
Heat Flux Sensors for Infrared Thermography in Convective Heat Transfer
Directory of Open Access Journals (Sweden)
Giovanni Maria Carlomagno
2014-11-01
Full Text Available This paper reviews the most dependable heat flux sensors, which can be used with InfraRed (IR thermography to measure convective heat transfer coefficient distributions, and some of their applications performed by the authors’ research group at the University of Naples Federico II. After recalling the basic principles that make IR thermography work, the various heat flux sensors to be used with it are presented and discussed, describing their capability to investigate complex thermo-fluid-dynamic flows. Several applications to streams, which range from natural convection to hypersonic flows, are also described.
Stellar convection and dynamo theory
Energy Technology Data Exchange (ETDEWEB)
Jennings, R L
1989-10-01
In considering the large scale stellar convection problem the outer layers of a star are modelled as two co-rotating plane layers coupled at a fluid/fluid interface. Heating from below causes only the upper fluid to convect, although this convection can penetrate into the lower fluid. Stability analysis is then used to find the most unstable mode of convection. With parameters appropriate to the Sun the most unstable mode is steady convection in thin cells (aspect ratio {approx equal} 0.2) filling the convection zone. There is negligible vertical motion in the lower fluid, but considerable thermal penetration, and a large jump in helicity at the interface, which has implications for dynamo theory. An {alpha}{omega} dynamo is investigated in isolation from the convection problem. Complexity is included by allowing both latitudinal and time dependence in the magnetic fields. The nonlinear dynamics of the resulting partial differential equations are analysed in considerable detail. On varying the main control parameter D (the dynamo number), many transitions of behaviour are found involving many forms of time dependence, but not chaos. Further, solutions which break equatorial symmetry are common and provide a theoretical explanation of solar observations which have this symmetry. Overall the behaviour was more complicated than expected. In particular, there were multiple stable solutions at fixed D, meaning that similar stars can have very different magnetic patterns, depending upon their history. (author).
The convection patterns in microemulsions
International Nuclear Information System (INIS)
Korneta, W.; Lopez Quintela, M.A.; Fernandez Novoa, A.
1991-07-01
The Rayleigh-Benard convection in the microemulsion consisting of water (7.5%), cyclohexan (oil-61.7%) and diethylenglycolmonobutylether (surfactant-30.8%) is studied from the onset of convection to the phase separation. The five classes of convection patterns are observed and recorded on the video: localized travelling waves, travelling waves, travelling waves and localized steady rolls, steady rolls and steady polygons. The Fourier transforms and histograms of these patterns are presented. The origin of any pattern is discussed. The intermittent behaviour close to the phase separation was observed. Possible applications of the obtained results are suggested. (author). 6 refs, 4 figs
Simanovskii, Ilya B.; Viviani, Antonio; Dubois, Frank
2018-06-01
An influence of a spatial temperature modulation of the interfacial heat release/consumption on nonlinear convective flows in the 47v2 silicone oil - water system, is studied. Rigid heat-insulated lateral walls, corresponding to the case of closed cavities, have been considered. Transitions between the flows with different spatial structures, have been investigated. It is shown that the spatial modulation can change the sequence of bifurcations and lead to the appearance of specific steady and oscillatory flows in the system.
Khechiba, Khaled; Mamou, Mahmoud; Hachemi, Madjid; Delenda, Nassim; Rebhi, Redha
2017-06-01
The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau-Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.
Beer bottle whistling: a stochastic Hopf bifurcation
Boujo, Edouard; Bourquard, Claire; Xiong, Yuan; Noiray, Nicolas
2017-11-01
Blowing in a bottle to produce sound is a popular and yet intriguing entertainment. We reproduce experimentally the common observation that the bottle ``whistles'', i.e. produces a distinct tone, for large enough blowing velocity and over a finite interval of blowing angle. For a given set of parameters, the whistling frequency stays constant over time while the acoustic pressure amplitude fluctuates. Transverse oscillations of the shear layer in the bottle's neck are clearly identified with time-resolved particle image velocimetry (PIV) and proper orthogonal decomposition (POD). To account for these observations, we develop an analytical model of linear acoustic oscillator (the air in the bottle) subject to nonlinear stochastic forcing (the turbulent jet impacting the bottle's neck). We derive a stochastic differential equation and, from the associated Fokker-Planck equation and the measured acoustic pressure signals, we identify the model's parameters with an adjoint optimization technique. Results are further validated experimentally, and allow us to explain (i) the occurrence of whistling in terms of linear instability, and (ii) the amplitude of the limit cycle as a competition between linear growth rate, noise intensity, and nonlinear saturation. E. B. and N. N. acknowledge support by Repower and the ETH Zurich Foundation.
Kučinskas, A.; Klevas, J.; Ludwig, H.-G.; Bonifacio, P.; Steffen, M.; Caffau, E.
2018-05-01
Aims: We studied the influence of convection on the spectral energy distributions (SEDs), photometric magnitudes, and colour indices of different types of stars across the H-R diagram. Methods: The 3D hydrodynamical CO5BOLD, averaged ⟨3D⟩, and 1D hydrostatic LHD model atmospheres were used to compute SEDs of stars on the main sequence (MS), main sequence turn-off (TO), subgiant branch (SGB), and red giant branch (RGB), in each case at two different effective temperatures and two metallicities, [M/H] = 0.0 and - 2.0. Using the obtained SEDs, we calculated photometric magnitudes and colour indices in the broad-band Johnson-Cousins UBVRI and 2MASS JHKs, and the medium-band Strömgren uvby photometric systems. Results: The 3D-1D differences in photometric magnitudes and colour indices are small in both photometric systems and typically do not exceed ± 0.03 mag. Only in the case of the coolest giants located on the upper RGB are the differences in the U and u bands able reach ≈-0.2 mag at [M/H] = 0.0 and ≈-0.1 mag at [M/H] = -2.0. Generally, the 3D-1D differences are largest in the blue-UV part of the spectrum and decrease towards longer wavelengths. They are also sensitive to the effective temperature and are significantly smaller in hotter stars. Metallicity also plays a role and leads to slightly larger 3D-1D differences at [M/H] = 0.0. All these patterns are caused by a complex interplay between the radiation field, opacities, and horizontal temperature fluctuations that occur due to convective motions in stellar atmospheres. Although small, the 3D-1D differences in the magnitudes and colour indices are nevertheless comparable to or larger than typical photometric uncertainties and may therefore cause non-negligible systematic differences in the estimated effective temperatures.
Convection in the Labrador Sea
National Research Council Canada - National Science Library
Davis, R
1997-01-01
The long-term goal of this grant was to describe the process of deep oceanic convection well enough to provide critical tests of, and guidance to, models used to predict subsurface ocean conditions...
Dunn, James C.; Hardee, Harry C.; Striker, Richard P.
1985-01-01
A convective heat flow probe device is provided which measures heat flow and fluid flow magnitude in the formation surrounding a borehole. The probe comprises an elongate housing adapted to be lowered down into the borehole; a plurality of heaters extending along the probe for heating the formation surrounding the borehole; a plurality of temperature sensors arranged around the periphery of the probe for measuring the temperature of the surrounding formation after heating thereof by the heater elements. The temperature sensors and heater elements are mounted in a plurality of separate heater pads which are supported by the housing and which are adapted to be radially expanded into firm engagement with the walls of the borehole. The heat supplied by the heater elements and the temperatures measured by the temperature sensors are monitored and used in providing the desired measurements. The outer peripheral surfaces of the heater pads are configured as segments of a cylinder and form a full cylinder when taken together. A plurality of temperature sensors are located on each pad so as to extend along the length and across the width thereof, with a heating element being located in each pad beneath the temperature sensors. An expansion mechanism driven by a clamping motor provides expansion and retraction of the heater pads and expandable packer-type seals are provided along the probe above and below the heater pads.
Efficient algorithm for bifurcation problems of variational inequalities
International Nuclear Information System (INIS)
Mittelmann, H.D.
1983-01-01
For a class of variational inequalities on a Hilbert space H bifurcating solutions exist and may be characterized as critical points of a functional with respect to the intersection of the level surfaces of another functional and a closed convex subset K of H. In a recent paper [13] we have used a gradient-projection type algorithm to obtain the solutions for discretizations of the variational inequalities. A related but Newton-based method is given here. Global and asymptotically quadratic convergence is proved. Numerical results show that it may be used very efficiently in following the bifurcating branches and that is compares favorably with several other algorithms. The method is also attractive for a class of nonlinear eigenvalue problems (K = H) for which it reduces to a generalized Rayleigh-quotient interaction. So some results are included for the path following in turning-point problems
Bifurcation and chaos of an axially accelerating viscoelastic beam
International Nuclear Information System (INIS)
Yang Xiaodong; Chen Liqun
2005-01-01
This paper investigates bifurcation and chaos of an axially accelerating viscoelastic beam. The Kelvin-Voigt model is adopted to constitute the material of the beam. Lagrangian strain is used to account for the beam's geometric nonlinearity. The nonlinear partial-differential equation governing transverse motion of the beam is derived from the Newton second law. The Galerkin method is applied to truncate the governing equation into a set of ordinary differential equations. By use of the Poincare map, the dynamical behavior is identified based on the numerical solutions of the ordinary differential equations. The bifurcation diagrams are presented in the case that the mean axial speed, the amplitude of speed fluctuation and the dynamic viscoelasticity is respectively varied while other parameters are fixed. The Lyapunov exponent is calculated to identify chaos. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the transverse vibrations of the axially accelerating viscoelastic beam
Hybrid intravenous digital subtraction angiography of the carotid bifurcation
International Nuclear Information System (INIS)
Burbank, F.H.; Enzmann, D.; Keyes, G.S.; Brody, W.R.
1984-01-01
A hybrid digital subtraction angiography technique and noise-reduction algorithm were used to evaluate the carotid bifurcation. Temporal, hybrid, and reduced-noise hybrid images were obtained in right and left anterior oblique projections, and both single- and multiple-frame images were created with each method. The resulting images were graded on a scale of 1 to 5 by three experienced neuroradiologists. Temporal images were preferred over hybrid images. The percentage of nondiagnostic examinations, as agreed upon by two readers, was higher for temporal alone than temporal + hybrid. In addition, also by agreement between two readers, temporal + hybrid images significantly increased the number of bifurcations seen in two views (87%) compared to temporal subtraction alone
Local bifurcations in differential equations with state-dependent delay.
Sieber, Jan
2017-11-01
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.
A bifurcation analysis for the Lugiato-Lefever equation
Godey, Cyril
2017-05-01
The Lugiato-Lefever equation is a cubic nonlinear Schrödinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a four-dimensional reversible dynamical system in which the evolutionary variable is the space variable. Relying upon tools from bifurcation theory and normal forms theory, we discuss the codimension 1 bifurcations. We prove the existence of various types of steady solutions, including spatially localized, periodic, or quasi-periodic solutions. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Local bifurcations in differential equations with state-dependent delay
Sieber, Jan
2017-11-01
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.
Synchronization of diffusively coupled oscillators near the homoclinic bifurcation
International Nuclear Information System (INIS)
Postnov, D.; Han, Seung Kee; Kook, Hyungtae
1998-09-01
It has been known that a diffusive coupling between two limit cycle oscillations typically leads to the inphase synchronization and also that it is the only stable state in the weak coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which often occurs especially for the neuronal oscillators. In this paper we propose a simple physical model using the modified van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe changes in the synchronization behaviors between the distinctive regimes as well. The dephasing mechanism is analyzed both qualitatively and quantitatively in the weak coupling limit. A general form of coupling is introduced and the synchronization behaviors over a wide range of the coupling parameters are explored to construct the phase diagram using the bifurcation analysis. (author)
Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation
Abdelkefi, Abdessattar
2013-06-18
In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.
Bifurcations and Crises in a Shape Memory Oscillator
Directory of Open Access Journals (Sweden)
Luciano G. Machado
2004-01-01
Full Text Available The remarkable properties of shape memory alloys have been motivating the interest in applications in different areas varying from biomedical to aerospace hardware. The dynamical response of systems composed by shape memory actuators presents nonlinear characteristics and a very rich behavior, showing periodic, quasi-periodic and chaotic responses. This contribution analyses some aspects related to bifurcation phenomenon in a shape memory oscillator where the restitution force is described by a polynomial constitutive model. The term bifurcation is used to describe qualitative changes that occur in the orbit structure of a system, as a consequence of parameter changes, being related to chaos. Numerical simulations show that the response of the shape memory oscillator presents period doubling cascades, direct and reverse, and crises.
Limit cycles bifurcating from a perturbed quartic center
Energy Technology Data Exchange (ETDEWEB)
Coll, Bartomeu, E-mail: dmitcv0@ps.uib.ca [Dept. de Matematiques i Informatica, Universitat de les Illes Balears, Facultat de ciencies, 07071 Palma de Mallorca (Spain); Llibre, Jaume, E-mail: jllibre@mat.uab.ca [Dept. de Matematiques, Universitat Autonoma de Barcelona, Edifici Cc 08193 Bellaterra, Barcelona, Catalonia (Spain); Prohens, Rafel, E-mail: dmirps3@ps.uib.ca [Dept. de Matematiques i Informatica, Universitat de les Illes Balears, Facultat de ciencies, 07071 Palma de Mallorca (Spain)
2011-04-15
Highlights: We study polynomial perturbations of a quartic center. We get simultaneous upper and lower bounds for the bifurcating limit cycles. A higher lower bound for the maximum number of limit cycles is obtained. We obtain more limit cycles than the number obtained in the cubic case. - Abstract: We consider the quartic center x{sup .}=-yf(x,y),y{sup .}=xf(x,y), with f(x, y) = (x + a) (y + b) (x + c) and abc {ne} 0. Here we study the maximum number {sigma} of limit cycles which can bifurcate from the periodic orbits of this quartic center when we perturb it inside the class of polynomial vector fields of degree n, using the averaging theory of first order. We prove that 4[(n - 1)/2] + 4 {<=} {sigma} {<=} 5[(n - 1)/2] + 14, where [{eta}] denotes the integer part function of {eta}.
Fold points and singularity induced bifurcation in inviscid transonic flow
International Nuclear Information System (INIS)
Marszalek, Wieslaw
2012-01-01
Transonic inviscid flow equation of elliptic–hyperbolic type when written in terms of the velocity components and similarity variable results in a second order nonlinear ODE having several features typical of differential–algebraic equations rather than ODEs. These features include the fold singularities (e.g. folded nodes and saddles, forward and backward impasse points), singularity induced bifurcation behavior and singularity crossing phenomenon. We investigate the above properties and conclude that the quasilinear DAEs of transonic flow have interesting properties that do not occur in other known quasilinear DAEs, for example, in MHD. Several numerical examples are included. -- Highlights: ► A novel analysis of inviscid transonic flow and its similarity solutions. ► Singularity induced bifurcation, singular points of transonic flow. ► Projection method, index of transonic flow DAEs, linearization via matrix pencil.
Bifurcation theory applied to buckling states of a cylindrical shell
Chaskalovic, J.; Naili, S.
1995-01-01
Veins, bronchii, and many other vessels in the human body are flexible enough to be capable of collapse if submitted to suitable applied external and internal loads. One way to describe this phenomenon is to consider an inextensible elastic and infinite tube, with a circular cross section in the reference configuration, subjected to a uniform external pressure. In this paper, we establish that the nonlinear equilibrium equation for this model has nontrivial solutions which appear for critical values of the pressure. To this end, the tools we use are the Liapunov-Schmidt decomposition and the bifurcation theorem for simple multiplicity. We conclude with the bifurcation diagram, showing the dependence between the cross-sectional area and the pressure.
Fully developed turbulence via Feigenbaum's period-doubling bifurcations
International Nuclear Information System (INIS)
Duong-van, M.
1987-08-01
Since its publication in 1978, Feigenbaum's predictions of the onset of turbulence via period-doubling bifurcations have been thoroughly borne out experimentally. In this paper, Feigenbaum's theory is extended into the regime in which we expect to see fully developed turbulence. We develop a method of averaging that imposes correlations in the fluctuating system generated by this map. With this averaging method, the field variable is obtained by coarse-graining, while microscopic fluctuations are preserved in all averaging scales. Fully developed turbulence will be shown to be a result of microscopic fluctuations with proper averaging. Furthermore, this model preserves Feigenbaum's results on the physics of bifurcations at the onset of turbulence while yielding additional physics both at the onset of turbulence and in the fully developed turbulence regime
Convection-enhanced water evaporation
B. M. Weon; J. H. Je; C. Poulard
2011-01-01
Water vapor is lighter than air; this can enhance water evaporation by triggering vapor convection but there is little evidence. We directly visualize evaporation of nanoliter (2 to 700 nL) water droplets resting on silicon wafer in calm air using a high-resolution dual X-ray imaging method. Temporal evolutions of contact radius and contact angle reveal that evaporation rate linearly changes with surface area, indicating convective (instead of diffusive) evaporation in nanoliter water droplet...
Structural bifurcation of microwave helium jet discharge at atmospheric pressure
International Nuclear Information System (INIS)
Takamura, Shuichi; Kitoh, Masakazu; Soga, Tadasuke
2008-01-01
Structural bifurcation of microwave-sustained jet discharge at atmospheric gas pressure was found to produce a stable helium plasma jet, which may open the possibility of a new type of high-flux test plasma beam for plasma-wall interactions in fusion devices. The fundamental discharge properties are presented including hysteresis characteristics, imaging of discharge emissive structure, and stable ignition parameter area. (author)
Bifurcation analysis of magnetization dynamics driven by spin transfer
International Nuclear Information System (INIS)
Bertotti, G.; Magni, A.; Bonin, R.; Mayergoyz, I.D.; Serpico, C.
2005-01-01
Nonlinear magnetization dynamics under spin-polarized currents is discussed by the methods of the theory of nonlinear dynamical systems. The fixed points of the dynamics are calculated. It is shown that there may exist 2, 4, or 6 fixed points depending on the values of the external field and of the spin-polarized current. The stability of the fixed points is analyzed and the conditions for the occurrence of saddle-node and Hopf bifurcations are determined
Bifurcation analysis of magnetization dynamics driven by spin transfer
Energy Technology Data Exchange (ETDEWEB)
Bertotti, G. [IEN Galileo Ferraris, Strada delle Cacce 91, 10135 Turin (Italy); Magni, A. [IEN Galileo Ferraris, Strada delle Cacce 91, 10135 Turin (Italy); Bonin, R. [Dipartimento di Fisica, Politecnico di Torino, Corso degli Abbruzzi, 10129 Turin (Italy)]. E-mail: bonin@ien.it; Mayergoyz, I.D. [Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742 (United States); Serpico, C. [Department of Electrical Engineering, University of Napoli Federico II, via Claudio 21, 80125 Naples (Italy)
2005-04-15
Nonlinear magnetization dynamics under spin-polarized currents is discussed by the methods of the theory of nonlinear dynamical systems. The fixed points of the dynamics are calculated. It is shown that there may exist 2, 4, or 6 fixed points depending on the values of the external field and of the spin-polarized current. The stability of the fixed points is analyzed and the conditions for the occurrence of saddle-node and Hopf bifurcations are determined.
An alternative bifurcation analysis of the Rose-Hindmarsh model
International Nuclear Information System (INIS)
Nikolov, Svetoslav
2005-01-01
The paper presents an alternative study of the bifurcation behavior of the Rose-Hindmarsh model using Lyapunov-Andronov's theory. This is done on the basis of the obtained analytical formula expressing the first Lyapunov's value (this is not Lyapunov exponent) at the boundary of stability. From the obtained results the following new conclusions are made: Transition to chaos and the occurrence of chaotic oscillations in the Rose-Hindmarsh system take place under hard stability loss
Stability and bifurcation of an SIS epidemic model with treatment
International Nuclear Information System (INIS)
Li Xuezhi; Li Wensheng; Ghosh, Mini
2009-01-01
An SIS epidemic model with a limited resource for treatment is introduced and analyzed. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.
Bifurcation in Z2-symmetry quadratic polynomial systems with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Zheng Baodong
2009-01-01
Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.
Experimental Investigation of Bifurcations in a Thermoacoustic Engine
Vishnu R. Unni; Yogesh M. S. Prasaad; N. T. Ravi; S. Md Iqbal; Bala Pesala; R. I. Sujith
2015-01-01
In this study, variation in the characteristics of the pressure oscillations in a thermoacoustic engine is explored as the input heat flux is varied. A bifurcation diagram is plotted to study the variation in the qualitative behavior of the acoustic oscillations as the input heat flux changes. At a critical input heat flux (60 Watt), the engine begins to produce acoustic oscillations in its fundamental longitudinal mode. As the input heat flux is increased, incommensurate frequencies appear i...
Streamline topology: Patterns in fluid flows and their bifurcations
DEFF Research Database (Denmark)
Brøns, Morten
2007-01-01
Using dynamical systems theory, we consider structures such as vortices and separation in the streamline patterns of fluid flows. Bifurcation of patterns under variation of external parameters is studied using simplifying normal form transformations. Flows away from boundaries, flows close to fix...... walls, and axisymmetric flows are analyzed in detail. We show how to apply the ideas from the theory to analyze numerical simulations of the vortex breakdown in a closed cylindrical container....
Application of the bifurcation method to the modified Boussinesq equation
Directory of Open Access Journals (Sweden)
Shaoyong Li
2014-08-01
Firstly, we give a property of the solutions of the equation, that is, if $1+u(x, t$ is a solution, so is $1-u(x, t$. Secondly, by using the bifurcation method of dynamical systems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.
Spiral blood flow in aorta-renal bifurcation models.
Javadzadegan, Ashkan; Simmons, Anne; Barber, Tracie
2016-01-01
The presence of a spiral arterial blood flow pattern in humans has been widely accepted. It is believed that this spiral component of the blood flow alters arterial haemodynamics in both positive and negative ways. The purpose of this study was to determine the effect of spiral flow on haemodynamic changes in aorta-renal bifurcations. In this regard, a computational fluid dynamics analysis of pulsatile blood flow was performed in two idealised models of aorta-renal bifurcations with and without flow diverter. The results show that the spirality effect causes a substantial variation in blood velocity distribution, while causing only slight changes in fluid shear stress patterns. The dominant observed effect of spiral flow is on turbulent kinetic energy and flow recirculation zones. As spiral flow intensity increases, the rate of turbulent kinetic energy production decreases, reducing the region of potential damage to red blood cells and endothelial cells. Furthermore, the recirculation zones which form on the cranial sides of the aorta and renal artery shrink in size in the presence of spirality effect; this may lower the rate of atherosclerosis development and progression in the aorta-renal bifurcation. These results indicate that the spiral nature of blood flow has atheroprotective effects in renal arteries and should be taken into consideration in analyses of the aorta and renal arteries.
Bifurcation and category learning in network models of oscillating cortex
Baird, Bill
1990-06-01
A genetic model of oscillating cortex, which assumes “minimal” coupling justified by known anatomy, is shown to function as an associative memory, using previously developed theory. The network has explicit excitatory neurons with local inhibitory interneuron feedback that forms a set of nonlinear oscillators coupled only by long-range excitatory connections. Using a local Hebb-like learning rule for primary and higher-order synapses at the ends of the long-range connections, the system learns to store the kinds of oscillation amplitude patterns observed in olfactory and visual cortex. In olfaction, these patterns “emerge” during respiration by a pattern forming phase transition which we characterize in the model as a multiple Hopf bifurcation. We argue that these bifurcations play an important role in the operation of real digital computers and neural networks, and we use bifurcation theory to derive learning rules which analytically guarantee CAM storage of continuous periodic sequences-capacity: N/2 Fourier components for an N-node network-no “spurious” attractors.
Endodontic-periodontic bifurcation lesions: a novel treatment option.
Lin, Shaul; Tillinger, Gabriel; Zuckerman, Offer
2008-05-01
The purpose of this preliminary clinical report is to suggest a novel treatment modality for periodontal bifurcation lesions of endodontic origin. The study consisted of 11 consecutive patients who presented with periodontal bifurcation lesions of endodontic origin (endo-perio lesions). All patients were followed-up for at least 12 months. Treatment included calcium hydroxide with iodine-potassium iodide placed in the root canals for 90 days followed by canal sealing with gutta-percha and cement during a second stage. Dentin bonding was used to seal the furcation floor to prevent the ingress of bacteria and their by-products to the furcation root area through the accessory canals. A radiographic examination showed complete healing of the periradicular lesion in all patients. Probing periodontal pocket depths decreased to 2 to 4 mm (mean 3.5 mm), and resolution of the furcation involvement was observed in post-operative clinical evaluations. The suggested treatment of endo-perio lesions may result in complete healing. Further studies are warranted. This treatment method improves both the disinfection of the bifurcation area and the healing process in endodontically treated teeth considered to be hopeless.
Ternary choices in repeated games and border collision bifurcations
International Nuclear Information System (INIS)
Dal Forno, Arianna; Gardini, Laura; Merlone, Ugo
2012-01-01
Highlights: ► We extend a model of binary choices with externalities to include more alternatives. ► Introducing one more option affects the complexity of the dynamics. ► We find bifurcation structures which where impossible to observe in binary choices. ► A ternary choice cannot simply be considered as a binary choice plus one. - Abstract: Several recent contributions formalize and analyze binary choices games with externalities as those described by Schelling. Nevertheless, in the real world choices are not always binary, and players have often to decide among more than two alternatives. These kinds of interactions are examined in game theory where, starting from the well known rock-paper-scissor game, several other kinds of strategic interactions involving more than two choices are examined. In this paper we investigate how the dynamics evolve introducing one more option in binary choice games with externalities. The dynamics we obtain are always in a stable regime, that is, the structurally stable dynamics are only attracting cycles, but of any possible positive integer as period. We show that, depending on the structure of the game, the dynamics can be quite different from those existing when considering binary choices. The bifurcation structure, due to border collisions, is explained, showing the existence of so-called big-bang bifurcation points.
Observation of bifurcation phenomena in an electron beam plasma system
International Nuclear Information System (INIS)
Hayashi, N.; Tanaka, M.; Shinohara, S.; Kawai, Y.
1995-01-01
When an electron beam is injected into a plasma, unstable waves are excited spontaneously near the electron plasma frequency f pe by the electron beam plasma instability. The experiment on subharmonics in an electron beam plasma system was performed with a glow discharge tube. The bifurcation of unstable waves with the electron plasma frequency f pe and 1/2 f pe was observed using a double-plasma device. Furthermore, the period doubling route to chaos around the ion plasma frequency in an electron beam plasma system was reported. However, the physical mechanism of bifurcation phenomena in an electron beam plasma system has not been clarified so far. We have studied nonlinear behaviors of the electron beam plasma instability. It was found that there are some cases: the fundamental unstable waves and subharmonics of 2 period are excited by the electron beam plasma instability, the fundamental unstable waves and subharmonics of 3 period are excited. In this paper, we measured the energy distribution functions of electrons and the dispersion relation of test waves in order to examine the physical mechanism of bifurcation phenomena in an electron beam plasma system
Reverse bifurcation and fractal of the compound logistic map
Wang, Xingyuan; Liang, Qingyong
2008-07-01
The nature of the fixed points of the compound logistic map is researched and the boundary equation of the first bifurcation of the map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, the paper reveal the general features of the compound logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the map may emerge out of double-periodic bifurcation and (2) the chaotic crisis phenomena and the reverse bifurcation are found. At the same time, we analyze the orbit of critical point of the compound logistic map and put forward the definition of Mandelbrot-Julia set of compound logistic map. We generalize the Welstead and Cromer's periodic scanning technology and using this technology construct a series of Mandelbrot-Julia sets of compound logistic map. We investigate the symmetry of Mandelbrot-Julia set and study the topological inflexibility of distributing of period region in the Mandelbrot set, and finds that Mandelbrot set contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot set qualitatively.
Bifurcation in autonomous and nonautonomous differential equations with discontinuities
Akhmet, Marat
2017-01-01
This book is devoted to bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types. That is, those with jumps present either in the right-hand-side or in trajectories or in the arguments of solutions of equations. The results obtained in this book can be applied to various fields such as neural networks, brain dynamics, mechanical systems, weather phenomena, population dynamics, etc. Without any doubt, bifurcation theory should be further developed to different types of differential equations. In this sense, the present book will be a leading one in this field. The reader will benefit from the recent results of the theory and will learn in the very concrete way how to apply this theory to differential equations with various types of discontinuity. Moreover, the reader will learn new ways to analyze nonautonomous bifurcation scenarios in these equations. The book will be of a big interest both for beginners and experts in the field. For the former group o...
Hopf Bifurcation Control of Subsynchronous Resonance Utilizing UPFC
Directory of Open Access Journals (Sweden)
Μ. Μ. Alomari
2017-06-01
Full Text Available The use of a unified power flow controller (UPFC to control the bifurcations of a subsynchronous resonance (SSR in a multi-machine power system is introduced in this study. UPFC is one of the flexible AC transmission systems (FACTS where a voltage source converter (VSC is used based on gate-turn-off (GTO thyristor valve technology. Furthermore, UPFC can be used as a stabilizer by means of a power system stabilizer (PSS. The considered system is a modified version of the second system of the IEEE second benchmark model of subsynchronous resonance where the UPFC is added to its transmission line. The dynamic effects of the machine components on SSR are considered. Time domain simulations based on the complete nonlinear dynamical mathematical model are used for numerical simulations. The results in case of including UPFC are compared to the case where the transmission line is conventionally compensated (without UPFC where two Hopf bifurcations are predicted with unstable operating point at wide range of compensation levels. For UPFC systems, it is worth to mention that the operating point of the system never loses stability at all realistic compensation degrees and therefore all power system bifurcations have been eliminated.
Nonlinear stability, bifurcation and resonance in granular plane Couette flow
Shukla, Priyanka; Alam, Meheboob
2010-11-01
A weakly nonlinear stability theory is developed to understand the effect of nonlinearities on various linear instability modes as well as to unveil the underlying bifurcation scenario in a two-dimensional granular plane Couette flow. The relevant order parameter equation, the Landau-Stuart equation, for the most unstable two-dimensional disturbance has been derived using the amplitude expansion method of our previous work on the shear-banding instability.ootnotetextShukla and Alam, Phys. Rev. Lett. 103, 068001 (2009). Shukla and Alam, J. Fluid Mech. (2010, accepted). Two types of bifurcations, Hopf and pitchfork, that result from travelling and stationary linear instabilities, respectively, are analysed using the first Landau coefficient. It is shown that the subcritical instability can appear in the linearly stable regime. The present bifurcation theory shows that the flow is subcritically unstable to disturbances of long wave-lengths (kx˜0) in the dilute limit, and both the supercritical and subcritical states are possible at moderate densities for the dominant stationary and traveling instabilities for which kx=O(1). We show that the granular plane Couette flow is prone to a plethora of resonances.ootnotetextShukla and Alam, J. Fluid Mech. (submitted, 2010)
Bifurcation-based approach reveals synergism and optimal combinatorial perturbation.
Liu, Yanwei; Li, Shanshan; Liu, Zengrong; Wang, Ruiqi
2016-06-01
Cells accomplish the process of fate decisions and form terminal lineages through a series of binary choices in which cells switch stable states from one branch to another as the interacting strengths of regulatory factors continuously vary. Various combinatorial effects may occur because almost all regulatory processes are managed in a combinatorial fashion. Combinatorial regulation is crucial for cell fate decisions because it may effectively integrate many different signaling pathways to meet the higher regulation demand during cell development. However, whether the contribution of combinatorial regulation to the state transition is better than that of a single one and if so, what the optimal combination strategy is, seem to be significant issue from the point of view of both biology and mathematics. Using the approaches of combinatorial perturbations and bifurcation analysis, we provide a general framework for the quantitative analysis of synergism in molecular networks. Different from the known methods, the bifurcation-based approach depends only on stable state responses to stimuli because the state transition induced by combinatorial perturbations occurs between stable states. More importantly, an optimal combinatorial perturbation strategy can be determined by investigating the relationship between the bifurcation curve of a synergistic perturbation pair and the level set of a specific objective function. The approach is applied to two models, i.e., a theoretical multistable decision model and a biologically realistic CREB model, to show its validity, although the approach holds for a general class of biological systems.
Bifurcating Particle Swarms in Smooth-Walled Fractures
Pyrak-Nolte, L. J.; Sun, H.
2010-12-01
Particle swarms can occur naturally or from industrial processes where small liquid drops containing thousands to millions of micron-size to colloidal-size particles are released over time from seepage or leaks into fractured rock. The behavior of these particle swarms as they fall under gravity are affected by particle interactions as well as interactions with the walls of the fractures. In this paper, we present experimental results on the effect of fractures on the cohesiveness of the swarm and the formation of bifurcation structures as they fall under gravity and interact with the fracture walls. A transparent cubic sample (100 mm x 100 mm x 100 mm) containing a synthetic fracture with uniform aperture distributions was optically imaged to quantify the effect of confinement within fractures on particle swarm formation, swarm velocity, and swarm geometry. A fracture with a uniform aperture distribution was fabricated from two polished rectangular prisms of acrylic. A series of experiments were performed to determine how swarm movement and geometry are affected as the walls of the fracture are brought closer together from 50 mm to 1 mm. During the experiments, the fracture was fully saturated with water. We created the swarms using two different particle sizes in dilute suspension (~ 1.0% by mass). The particles were 3 micron diameter fluorescent polymer beads and 25 micron diameter soda-lime glass beads. Experiments were performed using swarms that ranged in size from 5 µl to 60 µl. The swarm behavior was imaged using an optical fluorescent imaging system composed of a CCD camera illuminated by a 100 mW diode-pumped doubled YAG laser. As a swarm falls in an open-tank of water, it forms a torroidal shape that is stable as long as no ambient or background currents exist in the water tank. When a swarm is released into a fracture with an aperture less than 5 mm, the swarm forms the torroidal shape but it is distorted because of the presence of the walls. The
Modelling, singular perturbation and bifurcation analyses of bitrophic food chains.
Kooi, B W; Poggiale, J C
2018-04-20
Two predator-prey model formulations are studied: for the classical Rosenzweig-MacArthur (RM) model and the Mass Balance (MB) chemostat model. When the growth and loss rate of the predator is much smaller than that of the prey these models are slow-fast systems leading mathematically to singular perturbation problem. In contradiction to the RM-model, the resource for the prey are modelled explicitly in the MB-model but this comes with additional parameters. These parameter values are chosen such that the two models become easy to compare. In both models a transcritical bifurcation, a threshold above which invasion of predator into prey-only system occurs, and the Hopf bifurcation where the interior equilibrium becomes unstable leading to a stable limit cycle. The fast-slow limit cycles are called relaxation oscillations which for increasing differences in time scales leads to the well known degenerated trajectories being concatenations of slow parts of the trajectory and fast parts of the trajectory. In the fast-slow version of the RM-model a canard explosion of the stable limit cycles occurs in the oscillatory region of the parameter space. To our knowledge this type of dynamics has not been observed for the RM-model and not even for more complex ecosystem models. When a bifurcation parameter crosses the Hopf bifurcation point the amplitude of the emerging stable limit cycles increases. However, depending of the perturbation parameter the shape of this limit cycle changes abruptly from one consisting of two concatenated slow and fast episodes with small amplitude of the limit cycle, to a shape with large amplitude of which the shape is similar to the relaxation oscillation, the well known degenerated phase trajectories consisting of four episodes (concatenation of two slow and two fast). The canard explosion point is accurately predicted by using an extended asymptotic expansion technique in the perturbation and bifurcation parameter simultaneously where the small
Codimension-two bifurcation analysis on firing activities in Chay neuron model
International Nuclear Information System (INIS)
Duan Lixia; Lu Qishao
2006-01-01
Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing
Codimension-Two Bifurcation Analysis in DC Microgrids Under Droop Control
Lenz, Eduardo; Pagano, Daniel J.; Tahim, André P. N.
This paper addresses local and global bifurcations that may appear in electrical power systems, such as DC microgrids, which recently has attracted interest from the electrical engineering society. Most sources in these networks are voltage-type and operate in parallel. In such configuration, the basic technique for stabilizing the bus voltage is the so-called droop control. The main contribution of this work is a codimension-two bifurcation analysis of a small DC microgrid considering the droop control gain and the power processed by the load as bifurcation parameters. The codimension-two bifurcation set leads to practical rules for achieving a robust droop control design. Moreover, the bifurcation analysis also offers a better understanding of the dynamics involved in the problem and how to avoid possible instabilities. Simulation results are presented in order to illustrate the bifurcation analysis.
Global Hopf Bifurcation for a Predator-Prey System with Three Delays
Jiang, Zhichao; Wang, Lin
2017-06-01
In this paper, a delayed predator-prey model is considered. The existence and stability of the positive equilibrium are investigated by choosing the delay τ = τ1 + τ2 as a bifurcation parameter. We see that Hopf bifurcation can occur as τ crosses some critical values. The direction of the Hopf bifurcations and the stability of the bifurcation periodic solutions are also determined by using the center manifold and normal form theory. Furthermore, based on the global Hopf bifurcation theorem for general function differential equations, which was established by J. Wu using fixed point theorem and degree theory methods, the existence of global Hopf bifurcation is investigated. Finally, numerical simulations to support the analytical conclusions are carried out.
Codimension-two bifurcation analysis on firing activities in Chay neuron model
Energy Technology Data Exchange (ETDEWEB)
Duan Lixia [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China); Lu Qishao [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China)]. E-mail: qishaolu@hotmail.com
2006-12-15
Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.
Mantle Convection on Modern Supercomputers
Weismüller, J.; Gmeiner, B.; Huber, M.; John, L.; Mohr, M.; Rüde, U.; Wohlmuth, B.; Bunge, H. P.
2015-12-01
Mantle convection is the cause for plate tectonics, the formation of mountains and oceans, and the main driving mechanism behind earthquakes. The convection process is modeled by a system of partial differential equations describing the conservation of mass, momentum and energy. Characteristic to mantle flow is the vast disparity of length scales from global to microscopic, turning mantle convection simulations into a challenging application for high-performance computing. As system size and technical complexity of the simulations continue to increase, design and implementation of simulation models for next generation large-scale architectures is handled successfully only in an interdisciplinary context. A new priority program - named SPPEXA - by the German Research Foundation (DFG) addresses this issue, and brings together computer scientists, mathematicians and application scientists around grand challenges in HPC. Here we report from the TERRA-NEO project, which is part of the high visibility SPPEXA program, and a joint effort of four research groups. TERRA-NEO develops algorithms for future HPC infrastructures, focusing on high computational efficiency and resilience in next generation mantle convection models. We present software that can resolve the Earth's mantle with up to 1012 grid points and scales efficiently to massively parallel hardware with more than 50,000 processors. We use our simulations to explore the dynamic regime of mantle convection and assess the impact of small scale processes on global mantle flow.
Sliding bifurcations and chaos induced by dry friction in a braking system
International Nuclear Information System (INIS)
Yang, F.H.; Zhang, W.; Wang, J.
2009-01-01
In this paper, non-smooth bifurcations and chaotic dynamics are investigated for a braking system. A three-degree-of-freedom model is considered to capture the complicated nonlinear characteristics, in particular, non-smooth bifurcations in the braking system. The stick-slip transition is analyzed for the braking system. From the results of numerical simulation, it is observed that there also exist the grazing-sliding bifurcation and stick-slip chaos in the braking system.
Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2013-01-01
Full Text Available A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.
Bifurcation Analysis of the QI 3-D Four-Wing Chaotic System
International Nuclear Information System (INIS)
Sun, Y.; Qi, G.; Wang, Z.; Wyk, B.J. van
2010-01-01
This paper analyzes the pitchfork and Hopf bifurcations of a new 3-D four-wing quadratic autonomous system proposed by Qi et al. The center manifold technique is used to reduce the dimensions of this system. The pitchfork and Hopf bifurcations of the system are theoretically analyzed. The influence of system parameters on other bifurcations are also investigated. The theoretical analysis and simulations demonstrate the rich dynamics of the system. (authors)
Period-doubling bifurcation and chaos control in a discrete-time mosquito model
Directory of Open Access Journals (Sweden)
Qamar Din
2017-12-01
Full Text Available This article deals with the study of some qualitative properties of a discrete-time mosquito Model. It is shown that there exists period-doubling bifurcation for wide range of bifurcation parameter for the unique positive steady-state of given system. In order to control the bifurcation we introduced a feedback strategy. For further confirmation of complexity and chaotic behavior largest Lyapunov exponents are plotted.
Stability and bifurcation of a discrete BAM neural network model with delays
International Nuclear Information System (INIS)
Zheng Baodong; Zhang Yang; Zhang Chunrui
2008-01-01
A map modelling a discrete bidirectional associative memory neural network with delays is investigated. Its dynamics is studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Numerical simulation is performed to verify the analytical results
International Nuclear Information System (INIS)
Karaoglu, Esra; Merdan, Huseyin
2014-01-01
Highlights: • A ratio-dependent predator–prey system involving two discrete maturation time delays is studied. • Hopf bifurcations are analyzed by choosing delay parameters as bifurcation parameters. • When a delay parameter passes through a critical value, Hopf bifurcations occur. • The direction of bifurcation, the period and the stability of periodic solution are also obtained. - Abstract: In this paper we give a detailed Hopf bifurcation analysis of a ratio-dependent predator–prey system involving two different discrete delays. By analyzing the characteristic equation associated with the model, its linear stability is investigated. Choosing delay terms as bifurcation parameters the existence of Hopf bifurcations is demonstrated. Stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. Furthermore, some of the bifurcation properties including direction, stability and period are given. Finally, theoretical results are supported by some numerical simulations
Convective behaviour in severe accidents
International Nuclear Information System (INIS)
Clement, C.F.
1988-01-01
The nature and magnitude of the hazard from radioactivity posed by a possible nuclear accident depend strongly on convective behaviour within and immediately adjacent to the plant in question. This behaviour depends upon the nature of the vapour-gas-aerosol mixture concerned, and can show unusual properties such as 'upside-down' convection in which hot mixtures fall and cold mixtures rise. Predictions and criteria as to the types of behaviour which could possibly occur are summarised. Possible applications to present reactors are considered, and ways in which presently expected convection could be drastically modified are described. In some circumstances these could be used to suppress the radioactive source term or to switch its effect between distant dilute contamination and severe local contamination. (author). 8 refs, 2 figs, 2 tabs
Peters, Karsten; Jakob, Christian; Möbis, Benjamin
2015-04-01
An adequate representation of convective processes in numerical models of the atmospheric circulation (general circulation models, GCMs) remains one of the grand challenges in atmospheric science. In particular, the models struggle with correctly representing the spatial distribution and high variability of tropical convection. It is thought that this model deficiency partly results from formulating current convection parameterisation schemes in a purely deterministic manner. Here, we use observations of tropical convection to inform the design of a novel convection parameterisation with stochastic elements. The novel scheme is built around the Stochastic MultiCloud Model (SMCM, Khouider et al 2010). We present the progress made in utilising SMCM-based estimates of updraft area fractions at cloud base as part of the deep convection scheme of a GCM. The updraft area fractions are used to yield one part of the cloud base mass-flux used in the closure assumption of convective mass-flux schemes. The closure thus receives a stochastic component, potentially improving modeled convective variability and coherence. For initial investigations, we apply the above methodology to the operational convective parameterisation of the ECHAM6 GCM. We perform 5-year AMIP simulations, i.e. with prescribed observed SSTs. We find that with the SMCM, convection is weaker and more coherent and continuous from timestep to timestep compared to the standard model. Total global precipitation is reduced in the SMCM run, but this reduces i) the overall error compared to observed global precipitation (GPCP) and ii) middle tropical tropospheric temperature biases compared to ERA-Interim. Hovmoeller diagrams indicate a slightly higher degree of convective organisation compared to the base case and Wheeler-Kiladis frequency wavenumber diagrams indicate slightly more spectral power in the MJO range.
Analysis of stability and Hopf bifurcation for a viral infectious model with delay
International Nuclear Information System (INIS)
Sun Chengjun; Cao Zhijie; Lin Yiping
2007-01-01
In this paper, a four-dimensional viral infectious model with delay is considered. The stability of the two equilibria and the existence of Hopf bifurcation are investigated. It is found that there are stability switches and Hopf bifurcations occur when the delay τ passes through a sequence of critical values. Using the normal form theory and center manifold argument [Hassard B, Kazarino D, Wan Y. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981], the explicit formulaes which determine the stability, the direction and the period of bifurcating periodic solutions are derived. Numerical simulations are carried out to illustrate the validity of the main results
Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion
Parra-Rivas, P.; Gomila, D.; Gelens, L.; Knobloch, E.
2018-04-01
The origin, stability, and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation are studied. This mean field model describes the nonlinear dynamics of light circulating in fiber cavities and microresonators. In the case of anomalous group velocity dispersion and low values of the intracavity phase detuning these bright states are organized in a homoclinic snaking bifurcation structure. We describe how this bifurcation structure is destroyed when the detuning is increased across a critical value, and determine how a bifurcation structure known as foliated snaking emerges.
Hopf bifurcation in a delayed reaction-diffusion-advection population model
Chen, Shanshan; Lou, Yuan; Wei, Junjie
2018-04-01
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.
A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory
International Nuclear Information System (INIS)
Li, Xiantao
2014-01-01
Crack initiation under dynamic loading conditions is studied under the framework of dynamic bifurcation theory. An atomistic model for BCC iron is considered to explicitly take into account the detailed molecular interactions. To understand the strain-rate dependence of the crack initiation process, we first obtain the bifurcation diagram from a computational procedure using continuation methods. The stability transition associated with a crack initiation, as well as the connection to the bifurcation diagram, is studied by comparing direct numerical results to the dynamic bifurcation theory [R. Haberman, SIAM J. Appl. Math. 37, 69–106 (1979)].
Numerical Hopf bifurcation of Runge-Kutta methods for a class of delay differential equations
International Nuclear Information System (INIS)
Wang Qiubao; Li Dongsong; Liu, M.Z.
2009-01-01
In this paper, we consider the discretization of parameter-dependent delay differential equation of the form y ' (t)=f(y(t),y(t-1),τ),τ≥0,y element of R d . It is shown that if the delay differential equation undergoes a Hopf bifurcation at τ=τ * , then the discrete scheme undergoes a Hopf bifurcation at τ(h)=τ * +O(h p ) for sufficiently small step size h, where p≥1 is the order of the Runge-Kutta method applied. The direction of numerical Hopf bifurcation and stability of bifurcating invariant curve are the same as that of delay differential equation.
Stability and bifurcation analysis in a kind of business cycle model with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Wei Junjie
2004-01-01
A kind of business cycle model with delay is considered. Firstly, the linear stability of the model is studied and bifurcation set is drawn in the appropriate parameter plane. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived, using the normal form method and center manifold theorem. Finally, a group conditions to guarantee the global existence of periodic solutions is given, and numerical simulations are performed to illustrate the analytical results found
Stability, bifurcation and a new chaos in the logistic differential equation with delay
International Nuclear Information System (INIS)
Jiang Minghui; Shen Yi; Jian Jigui; Liao Xiaoxin
2006-01-01
This Letter is concerned with bifurcation and chaos in the logistic delay differential equation with a parameter r. The linear stability of the logistic equation is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, the formula for determining the direction of Hopf bifurcation and the stability of bifurcation periodic solution in the first bifurcation values is obtained. By theoretical analysis and numerical simulation, we found a new chaos in the logistic delay differential equation
Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection.
Cao, Hui; Zhou, Yicang; Ma, Zhien
2013-01-01
A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.
Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms
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Tao Zhao
2017-01-01
Full Text Available A delayed SEIQRS worm propagation model with different infection rates for the exposed computers and the infectious computers is investigated in this paper. The results are given in terms of the local stability and Hopf bifurcation. Sufficient conditions for the local stability and the existence of Hopf bifurcation are obtained by using eigenvalue method and choosing the delay as the bifurcation parameter. In particular, the direction and the stability of the Hopf bifurcation are investigated by means of the normal form theory and center manifold theorem. Finally, a numerical example is also presented to support the obtained theoretical results.
Bifurcation of the Kuroshio Extension at the Shatsky Rise
Hurlburt, Harley E.; Metzger, E. Joseph
1998-04-01
A 1/16° six-layer Pacific Ocean model north of 20°S is used to investigate the bifurcation of the Kuroshio Extension at the main Shatsky Rise and the pathway of the northern branch from the bifurcation to the subarctic front. Upper ocean-topographic coupling via a mixed barotropic-baroclinic instability is essential to this bifurcation and to the formation and mean pathway of the northern branch as are several aspects of the Shatsky Rise complex of topography and the latitude of the Kuroshio Extension in relation to the topography. The flow instabilities transfer energy to the abyssal layer where it is constrained by geostrophic contours of the bottom topography. The topographically constrained abyssal currents in turn steer upper ocean currents, which do not directly impinge on the bottom topography. This includes steering of mean pathways. Obtaining sufficient coupling requires very fine resolution of mesoscale variability and sufficient eastward penetration of the Kuroshio as an unstable inertial jet. Resolution of 1/8° for each variable was not sufficient in this case. The latitudinal extent of the main Shatsky Rise (31°N-36°N) and the shape of the downward slope on the north side are crucial to the bifurcation at the main Shatsky Rise, with both branches passing north of the peak. The well-defined, relatively steep and straight eastern edge of the Shatsky Rise topographic complex (30°N-42°N) and the southwestward abyssal flow along it play a critical role in forming the rest of the Kuroshio northern branch which flows in the opposite direction. A deep pass between the main Shatsky Rise and the rest of the ridge to the northeast helps to link the northern fork of the bifurcation at the main rise to the rest of the northern branch. Two 1/16° "identical twin" interannual simulations forced by daily winds 1981-1995 show that the variability in this region is mostly nondeterministic on all timescales that could be examined (up to 7 years in these 15-year
Topology Optimization for Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
2011-01-01
This report deals with the topology optimization of convection problems.That is, the aim of the project is to develop, implement and examine topology optimization of purely thermal and coupled thermomechanical problems,when the design-dependent eects of convection are taken into consideration.......This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...
Experimental methods in natural convection
International Nuclear Information System (INIS)
Koster, J.N.
1982-11-01
Some common experimental techniques to determine local velocities and to visualize temperature fields in natural convection research are discussed. First the physics and practice of anemometers are discussed with emphasis put on optical anemometers. In the second and third case the physics and practice of the most developed interferometers are discussed; namely differential interferometry for visualization of temperature gradient fields and holographic interferometry for visualization of temperature fields. At the Institut fuer Reaktorbauelemente these three measuring techniques are applied for convection and pipe flow studies. (orig.) [de
Dynamic stability and bifurcation analysis in fractional thermodynamics
Béda, Péter B.
2018-02-01
In mechanics, viscoelasticity was the first field of applications in studying geomaterials. Further possibilities arise in spatial non-locality. Non-local materials were already studied in the 1960s by several authors as a part of continuum mechanics and are still in focus of interest because of the rising importance of materials with internal micro- and nano-structure. When material instability gained more interest, non-local behavior appeared in a different aspect. The problem was concerned to numerical analysis, because then instability zones exhibited singular properties for local constitutive equations. In dynamic stability analysis, mathematical aspects of non-locality were studied by using the theory of dynamic systems. There the basic set of equations describing the behavior of continua was transformed to an abstract dynamic system consisting of differential operators acting on the perturbation field variables. Such functions should satisfy homogeneous boundary conditions and act as indicators of stability of a selected state of the body under consideration. Dynamic systems approach results in conditions for cases, when the differential operators have critical eigenvalues of zero real parts (dynamic stability or instability conditions). When the critical eigenvalues have non-trivial eigenspace, the way of loss of stability is classified as a typical (or generic) bifurcation. Our experiences show that material non-locality and the generic nature of bifurcation at instability are connected, and the basic functions of the non-trivial eigenspace can be used to determine internal length quantities of non-local mechanics. Fractional calculus is already successfully used in thermo-elasticity. In the paper, non-locality is introduced via fractional strain into the constitutive relations of various conventional types. Then, by defining dynamic systems, stability and bifurcation are studied for states of thermo-mechanical solids. Stability conditions and genericity
Technique and results of femoral bifurcation endarterectomy by eversion.
Dufranc, Julie; Palcau, Laura; Heyndrickx, Maxime; Gouicem, Djelloul; Coffin, Olivier; Felisaz, Aurélien; Berger, Ludovic
2015-03-01
This study evaluated, in a contemporary prospective series, the safety and efficacy of femoral endarterectomy using the eversion technique and compared our results with results obtained in the literature for the standard endarterectomy with patch closure. Between 2010 and 2012, 121 patients (76% male; mean age, 68.7 years; diabetes, 28%; renal insufficiency, 20%) underwent 147 consecutive femoral bifurcation endarterectomies using the eversion technique, associating or not inflow or outflow concomitant revascularization. The indications were claudication in 89 procedures (60%) and critical limb ischemia in 58 (40%). Primary, primary assisted, and secondary patency of the femoral bifurcation, clinical improvement, limb salvage, and survival were assessed using Kaplan-Meier life-table analysis. Factors associated with those primary end-points were evaluated with univariate analysis. The technical success of eversion was of 93.2%. The 30-day mortality was 0%, and the complication rate was 8.2%; of which, half were local and benign. Median follow-up was 16 months (range, 1.6-31.2 months). Primary, primary assisted, and secondary patencies were, respectively, 93.2%, 97.2%, and 98.6% at 2 years. Primary, primary assisted, and secondary maintenance of clinical improvement were, respectively, 79.9%, 94.6%, and 98.6% at 2 years. The predictive factors for clinical degradation were clinical stage (Rutherford category 5 or 6, P = .024), platelet aggregation inhibitor treatment other than clopidogrel (P = .005), malnutrition (P = .025), and bad tibial runoff (P = .0016). A reintervention was necessary in 18.3% of limbs at 2 years: 2% involving femoral bifurcation, 6.1% inflow improvement, and 9.5% outflow improvement. The risk factors of reintervention were platelet aggregation inhibitor (other than clopidogrel, P = .049) and cancer (P = .011). Limb preservation at 2 years was 100% in the claudicant population. Limb salvage was 88.6% in the critical limb ischemia population
One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Mosekilde, Erik
1996-01-01
The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform...... dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed....
Stochastic Calculus: Application to Dynamic Bifurcations and Threshold Crossings
Jansons, Kalvis M.; Lythe, G. D.
1998-01-01
For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function of the noise level ∈ and the rate of change of the parameter μ. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density, and last crossing time of zero are compared with results from numerical generation of paths.
Bifurcation and stability analysis of a nonlinear milling process
Weremczuk, Andrzej; Rusinek, Rafal; Warminski, Jerzy
2018-01-01
Numerical investigations of milling operations dynamics are presented in this paper. A two degree of freedom nonlinear model is used to study workpiece-tool vibrations. The analyzed model takes into account both flexibility of the tool and the workpiece. The dynamics of the milling process is described by the discontinuous ordinary differential equation with time delay, which can cause process instability. First, stability lobes diagrams are created on the basis of the parameters determined in impact test of an end mill and workpiece. Next, the bifurcations diagrams are performed for different values of rotational speeds.
Square-lattice random Potts model: criticality and pitchfork bifurcation
International Nuclear Information System (INIS)
Costa, U.M.S.; Tsallis, C.
1983-01-01
Within a real space renormalization group framework based on self-dual clusters, the criticality of the quenched bond-mixed q-state Potts ferromagnet on square lattice is discussed. On qualitative grounds it is exhibited that the crossover from the pure fixed point to the random one occurs, while q increases, through a pitchfork bifurcation; the relationship with Harris criterion is analyzed. On quantitative grounds high precision numerical values are presented for the critical temperatures corresponding to various concentrations of the coupling constants J 1 and J 2 , and various ratios J 1 /J 2 . The pure, random and crossover critical exponents are discussed as well. (Author) [pt
Bifurcation analysis of dengue transmission model in Baguio City, Philippines
Libatique, Criselda P.; Pajimola, Aprimelle Kris J.; Addawe, Joel M.
2017-11-01
In this study, we formulate a deterministic model for the transmission dynamics of dengue fever in Baguio City, Philippines. We analyzed the existence of the equilibria of the dengue model. We computed and obtained conditions for the existence of the equilibrium states. Stability analysis for the system is carried out for disease free equilibrium. We showed that the system becomes stable under certain conditions of the parameters. A particular parameter is taken and with the use of the Theory of Centre Manifold, the proposed model demonstrates a bifurcation phenomenon. We performed numerical simulation to verify the analytical results.
Energy Technology Data Exchange (ETDEWEB)
Simanovskii, Ilya B, E-mail: cesima@tx.technion.ac.il [Department of Mathematics, Technion—Israel Institute of Technology, 32000 Haifa (Israel)
2016-12-15
The influence of an interfacial heat release on nonlinear convective regimes, developed under the action of an imposed temperature gradient in the 47v2 silicone oil–water system, has been studied. Two types of boundary conditions—periodic boundary conditions and rigid heat-insulated lateral walls—have been considered. Transitions between the flows with different spatial structures have been investigated. It is shown that the presence of an interfacial heat release can change the sequence of bifurcations and can lead to the appearance of new oscillatory regimes. The period-three phase trajectory has been found. (paper)
Kozitskiy, Sergey
2018-05-01
Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection has been performed by using the previously derived system of complex Ginzburg-Landau type amplitude equations, valid in a neighborhood of Hopf bifurcation points. Simulation has shown that the state of spatiotemporal chaos develops in the system. It has the form of nonstationary structures that depend on the parameters of the system. The shape of structures does not depend on the initial conditions, and a limited number of spectral components participate in their formation.
Segregation and convection in dendritic alloys
Poirier, D. R.
1990-01-01
Microsegregation in dentritic alloys is discussed, including solidification with and without thermal gradient, the convection of interdendritic liquid. The conservation of momentum, energy, and solute is considered. Directional solidification and thermosolutal convection are discussed.
Boiling Suppression in Convective Flow
International Nuclear Information System (INIS)
Aounallah, Y.
2004-01-01
The development of convective boiling heat transfer correlations and analytical models has almost exclusively been based on measurements of the total heat flux, and therefore on the overall two-phase heat transfer coefficient, when the well-known heat transfer correlations have often assumed additive mechanisms, one for each mode of heat transfer, convection and boiling. While the global performance of such correlations can readily be assessed, the predictive capability of the individual components of the correlation has usually remained elusive. This becomes important when, for example, developing mechanistic models for subcooled void formation based on the partitioning of the wall heat flux into a boiling and a convective component, or when extending a correlation beyond its original range of applications where the preponderance of the heat transfer mechanisms involved can be significantly different. A new examination of existing experimental heat transfer data obtained under fixed hydrodynamic conditions, whereby the local flow conditions are decoupled from the local heat flux, has allowed the unequivocal isolation of the boiling contribution over a broad range of thermodynamic qualities (0 to 0.8) for water at 7 MPa. Boiling suppression, as the quality increases, has consequently been quantified, thus providing valuable new insights on the functionality and contribution of boiling in convective flows. (author)
Bifurcations in two-image photometric stereo for orthogonal illuminations
Kozera, R.; Prokopenya, A.; Noakes, L.; Śluzek, A.
2017-07-01
This paper discusses the ambiguous shape recovery in two-image photometric stereo for a Lambertian surface. The current uniqueness analysis refers to linearly independent light-source directions p = (0, 0, -1) and q arbitrary. For this case necessary and sufficient condition determining ambiguous reconstruction is governed by a second-order linear partial differential equation with constant coefficients. In contrast, a general position of both non-colinear illumination directions p and q leads to a highly non-linear PDE which raises a number of technical difficulties. As recently shown, the latter can also be handled for another family of orthogonal illuminations parallel to the OXZ-plane. For the special case of p = (0, 0, -1) a potential ambiguity stems also from the possible bifurcations of sub-local solutions glued together along a curve defined by an algebraic equation in terms of the data. This paper discusses the occurrence of similar bifurcations for such configurations of orthogonal light-source directions. The discussion to follow is supplemented with examples based on continuous reflectance map model and generated synthetic images.
Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System
Directory of Open Access Journals (Sweden)
Wen-Qing Zhang
2013-01-01
Full Text Available Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.
Modal bifurcation in a high-Tc superconducting levitation system
International Nuclear Information System (INIS)
Taguchi, D; Fujiwara, S; Sugiura, T
2011-01-01
This paper deals with modal bifurcation of a multi-degree-of-freedom high-T c superconducting levitation system. As modeling of large-scale high-T c superconducting levitation applications, where plural superconducting bulks are often used, it can be helpful to consider a system constituting of multiple oscillators magnetically coupled with each other. This paper investigates nonlinear dynamics of two permanent magnets levitated above high-T c superconducting bulks and placed between two fixed permanent magnets without contact. First, the nonlinear equations of motion of the levitated magnets were derived. Then the method of averaging was applied to them. It can be found from the obtained solutions that this nonlinear two degree-of-freedom system can have two asymmetric modes, in addition to a symmetric mode and an antisymmetric mode both of which also exist in the linearized system. One of the backbone curves in the frequency response shows a modal bifurcation where the two stable asymmetric modes mentioned above appear with destabilization of the antisymmetric mode, thus leading to modal localization. These analytical predictions have been confirmed in our numerical analysis and experiments of free vibration and forced vibration. These results, never predicted by linear analysis, can be important for application of high-T c superconducting levitation systems.
Local viscosity distribution in bifurcating microfluidic blood flows
Kaliviotis, E.; Sherwood, J. M.; Balabani, S.
2018-03-01
The red blood cell (RBC) aggregation phenomenon is majorly responsible for the non-Newtonian nature of blood, influencing the blood flow characteristics in the microvasculature. Of considerable interest is the behaviour of the fluid at the bifurcating regions. In vitro experiments, using microchannels, have shown that RBC aggregation, at certain flow conditions, affects the bluntness and skewness of the velocity profile, the local RBC concentration, and the cell-depleted layer at the channel walls. In addition, the developed RBC aggregates appear unevenly distributed in the outlets of these channels depending on their spatial distribution in the feeding branch, and on the flow conditions in the outlet branches. In the present work, constitutive equations of blood viscosity, from earlier work of the authors, are applied to flows in a T-type bifurcating microchannel to examine the local viscosity characteristics. Viscosity maps are derived for various flow distributions in the outlet branches of the channel, and the location of maximum viscosity magnitude is obtained. The viscosity does not appear significantly elevated in the branches of lower flow rate as would be expected on the basis of the low shear therein, and the maximum magnitude appears in the vicinity of the junction, and towards the side of the outlet branch with the higher flow rate. The study demonstrates that in the branches of lower flow rate, the local viscosity is also low, helping us to explain why the effects of physiological red blood cell aggregation have no adverse effects in terms of in vivo vascular resistance.
Prediction of fibre architecture and adaptation in diseased carotid bifurcations.
LENUS (Irish Health Repository)
Creane, Arthur
2011-12-01
Many studies have used patient-specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. In complex geometries, few studies have incorporated the anisotropic material response of arterial tissue. This paper presents a fibre remodelling algorithm to predict the fibre architecture, and thus anisotropic material response in four patient-specific models of the carotid bifurcation. The change in fibre architecture during disease progression and its affect on the stress environment in the plaque were predicted. The mean fibre directions were assumed to lie at an angle between the two positive principal strain directions. The angle and the degree of dispersion were assumed to depend on the ratio of principal strain values. Results were compared with experimental observations and other numerical studies. In non-branching regions of each model, the typical double helix arterial fibre pattern was predicted while at the bifurcation and in regions of plaque burden, more complex fibre architectures were found. The predicted change in fibre architecture in the arterial tissue during plaque progression was found to alter the stress environment in the plaque. This suggests that the specimen-specific anisotropic response of the tissue should be taken into account to accurately predict stresses in the plaque. Since determination of the fibre architecture in vivo is a difficult task, the system presented here provides a useful method of estimating the fibre architecture in complex arterial geometries.
Partitioning of red blood cell aggregates in bifurcating microscale flows
Kaliviotis, E.; Sherwood, J. M.; Balabani, S.
2017-03-01
Microvascular flows are often considered to be free of red blood cell aggregates, however, recent studies have demonstrated that aggregates are present throughout the microvasculature, affecting cell distribution and blood perfusion. This work reports on the spatial distribution of red blood cell aggregates in a T-shaped bifurcation on the scale of a large microvessel. Non-aggregating and aggregating human red blood cell suspensions were studied for a range of flow splits in the daughter branches of the bifurcation. Aggregate sizes were determined using image processing. The mean aggregate size was marginally increased in the daughter branches for a range of flow rates, mainly due to the lower shear conditions and the close cell and aggregate proximity therein. A counterintuitive decrease in the mean aggregate size was apparent in the lower flow rate branches. This was attributed to the existence of regions depleted by aggregates of certain sizes in the parent branch, and to the change in the exact flow split location in the T-junction with flow ratio. The findings of the present investigation may have significant implications for microvascular flows and may help explain why the effects of physiological RBC aggregation are not deleterious in terms of in vivo vascular resistance.
Bifurcation to Enhanced Performance H-mode on NSTX
Battaglia, D. J.; Chang, C. S.; Gerhardt, S. P.; Kaye, S. M.; Maingi, R.; Smith, D. R.
2015-11-01
The bifurcation from H-mode (H98 Performance (EP)H-mode (H98 = 1.2 - 2.0) on NSTX is found to occur when the ion thermal (χi) and momentum transport become decoupled from particle transport, such that the ion temperature (Ti) and rotation pedestals increase independent of the density pedestal. The onset of the EPH-mode transition is found to correlate with decreased pedestal collisionality (ν*ped) and an increased broadening of the density fluctuation (dn/n) spectrum in the pedestal as measured with beam emission spectroscopy. The spectrum broadening at decreased ν*ped is consistent with GEM simulations that indicate the toroidal mode number of the most unstable instability increases as ν*ped decreases. The lowest ν*ped, and thus largest spectrum broadening, is achieved with low pedestal density via lithium wall conditioning and when Zeff in the pedestal is significantly reduced via large edge rotation shear from external 3D fields or a large ELM. Kinetic neoclassical transport calculations (XGC0) confirm that Zeff is reduced when edge rotation braking leads to a more negative Er that shifts the impurity density profiles inward relative to the main ion density. These calculations also describe the role kinetic neoclassical and anomalous transport effects play in the decoupling of energy, momentum and particle transport at the bifurcation to EPH-mode. This work was sponsored by the U.S. Department of Energy.
Hydrodynamic bifurcation in electro-osmotically driven periodic flows
Morozov, Alexander; Marenduzzo, Davide; Larson, Ronald G.
2018-06-01
In this paper, we report an inertial instability that occurs in electro-osmotically driven channel flows. We assume that the charge motion under the influence of an externally applied electric field is confined to a small vicinity of the channel walls that, effectively, drives a bulk flow through a prescribed slip velocity at the boundaries. Here, we study spatially periodic wall velocity modulations in a two-dimensional straight channel numerically. At low slip velocities, the bulk flow consists of a set of vortices along each wall that are left-right symmetric, while at sufficiently high slip velocities, this flow loses its stability through a supercritical bifurcation. Surprisingly, the flow state that bifurcates from a left-right symmetric base flow has a rather strong mean component along the channel, which is similar to pressure-driven velocity profiles. The instability sets in at rather small Reynolds numbers of about 20-30, and we discuss its potential applications in microfluidic devices.
DEFF Research Database (Denmark)
Maeng, M.; Holm, N. R.; Erglis, A.
2013-01-01
Objectives This study sought to report the 5-year follow-up results of the Nordic Bifurcation Study. Background Randomized clinical trials with short-term follow-up have indicated that coronary bifurcation lesions may be optimally treated using the optional side branch stenting strategy. Methods...... complex strategy of planned stenting of both the main vessel and the side branch. (C) 2013 by the American College of Cardiology Foundation...
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
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Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
International Nuclear Information System (INIS)
Kwok, Philip Chong-hei; Ng, Wai Fu; Lam, Christine Suk-yee; Tsui, Polly Po; Faruqi, Asma
2003-01-01
Purpose: The relationship of the portalvein bifurcation to the liver capsule in Asians, which is an important landmark for transjugular intrahepatic portosystemic shunt, has not previously been described. Methods: The anatomy of the portal vein bifurcation was studied in 70 adult Chinese cadavers; it was characterized as intrahepatic or extrahepatic. The length of the exposed portion of the right and left portal veins was measured when the bifurcation was extrahepatic. Results: The portal vein bifurcation was intrahepatic in 37 cadavers (53%) and extrahepatic in 33 cadavers (47%). The mean length of the right and left extrahepatic portal veins was 0.96 cm and 0.85 cm respectively.Both were less than or equal to 2 cm in 94% of the cadavers with extrahepatic bifurcation. There was no correlation between the presence of cirrhosis and the location of the portal vein bifurcation(p 1.0). There was no statistically significant difference in liver mass in cadavers with either extrahepatic or intrahepatic bifurcation (p =0.40). Conclusions: These findings suggest that fortransjugular intrahepatic portosystemic shunt placement, a portal vein puncture 2 cm from the bifurcation will be safe in most cases
Hopf bifurcation of a free boundary problem modeling tumor growth with two time delays
International Nuclear Information System (INIS)
Xu Shihe
2009-01-01
In this paper, a free boundary problem modeling tumor growth with two discrete delays is studied. The delays respectively represents the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis. We show the influence of time delays on the Hopf bifurcation when one of delays as a bifurcation parameter.
Bifurcation approach to the predator-prey population models (Version of the computer book)
International Nuclear Information System (INIS)
Bazykin, A.D.; Zudin, S.L.
1993-09-01
Hierarchically organized family of predator-prey systems is studied. The classification is founded on two interacting principles: the biological and mathematical ones. The different combinations of biological factors included correspond to different bifurcations (up to codimension 3). As theoretical so computing methods are used for analysis, especially concerning non-local bifurcations. (author). 6 refs, figs
Bifurcation direction and exchange of stability for variational inequalities on nonconvex sets
Czech Academy of Sciences Publication Activity Database
Eisner, Jan; Kučera, Milan; Recke, L.
2007-01-01
Roč. 67, č. 5 (2007), s. 1082-1101 ISSN 0362-546X R&D Projects: GA AV ČR IAA100190506 Institutional research plan: CEZ:AV0Z10190503 Keywords : multiparameter variational inequality * direction of bifurcation * stability of bifurcating solutions Subject RIV: BA - General Mathematics Impact factor: 1.097, year: 2007
Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays
International Nuclear Information System (INIS)
Song Yongli; Han Maoan; Peng Yahong
2004-01-01
We consider a Lotka-Volterra competition system with two delays. We first investigate the stability of the positive equilibrium and the existence of Hopf bifurcations, and then using the normal form theory and center manifold argument, derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions
Hopf bifurcation in a dynamic IS-LM model with time delay
International Nuclear Information System (INIS)
Neamtu, Mihaela; Opris, Dumitru; Chilarescu, Constantin
2007-01-01
The paper investigates the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. We show when the system is stable with respect to the delay. Some numerical examples are given to confirm the theoretical results
The period adding and incrementing bifurcations: from rotation theory to applications
DEFF Research Database (Denmark)
Granados, Albert; Alseda, Lluis; Krupa, Maciej
2017-01-01
This survey article is concerned with the study of bifurcations of piecewise-smooth maps. We review the literature in circle maps and quasi-contractions and provide paths through this literature to prove sufficient conditions for the occurrence of two types of bifurcation scenarios involving rich...
International Nuclear Information System (INIS)
Gellert, M; Beltrame, P; Egbers, C
2005-01-01
Spherical Rayleigh-Benard convection under the influence of an artificial central force field produced by the so-called dielectrophoretic effect is studied as a simplified model of the flow in the outer earth core. The fluid motion there is most probably driving the earth's dynamo and the energy source for the earth's magnetic field. Studying convective flows in earth-like geometry could lead to a deeper understanding of the basics of these processes. This research is a preparatory study for the experiments on the International Space Station (ISS). A bifurcation-theoretical approach shows the existence of heteroclinic cycles between spherical modes (l, l + 1) for the non-rotating system. This behavior depends strong on the radius ratio of the spheres and will be hard to detect in the experiment. For slow rotations interactions of the azimuthal modes (m, m + 1) found in numerical simulations for supercritical states are supposed to be experimentally observable
Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model
Erban, Radek; Chapman, S. Jonathan; Kevrekidis, Ioannis G.; Vejchodský , Tomá š
2009-01-01
A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example
Thermal convection in a co-rotating cylindrical annulus
Kang, Changwoo; Meyer, Antoine; Mutabazi, Innocent
2017-11-01
We investigate thermal convection in a fluid of thermal expansion coefficient α, kinematic viscosity ν, thermal diffusivity κ in a cylindrical annulus of inner radius a and outer radius bwith a solid body rotation of angular frequency Ω and an inward heating with a temperature difference ΔT. The control parameters are η = a/b, Pr = ν / κ and the Rayleigh number Ra = αΔ T gd3 / νκ where the centrifugal gravity gc =Ω2 (a +b)/2. We adopt the generalized Boussinesq approximation. Linear stability analysis shows that for infinite annulus, the threshold Rac decreases with η and tends to the value Rac = 1708 when η -> 1 and that critical modes are columnar vortices. Direct numerical simulations using periodic boundary conditions in the axial direction, show that the columnar vortices appear via a supercritical bifurcation. Higher modes of columnar vortices have been determined using the frequency spectra and the Nusselt number for Pr =1 and η = 0.5 : drifting vortices, vacillation modes and chaotic modes have been identified from Ra =1700 to Ra =107 The contribution of the centrifugal buoyancy to the variation of the kinetic energy in the flow is analysed. This work was supported by the project BIOENGINE (CPER-FEDER, Normandie) and CNES.
Bifurcation and chaos in a Tessiet type food chain chemostat with pulsed input and washout
International Nuclear Information System (INIS)
Wang Fengyan; Hao Chunping; Chen Lansun
2007-01-01
In this paper, we introduce and study a model of a Tessiet type food chain chemostat with pulsed input and washout. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period doubling and period halving
Experimental observation of bifurcation nature of radial electric field in CHS heliotron/torsatron
International Nuclear Information System (INIS)
Fujisawa, Akihide; Iguchi, Harukazu; Yoshimura, Yasuo; Minami, Takashi; Tanaka, Kenji; Okamura, Shoichi; Matsuoka, Keisuke; Fujiwara, Masami
1999-01-01
Several interesting phenomena, such as the formation of a particular potential profile with a protuberance around the core and oscillatory stationary states termed electric pulsation, have been discovered using a heavy ion beam probe in the electron cyclotron heated plasmas of the CHS. This paper presents experimental observations which indicate that bifurcation of the radial electric field is responsible for such phenomena; existence of an ECH power threshold to obtain the profile with a protuberance, and its striking sensitivity to density. In particular, Flip-flop behavior of the potential near the power threshold clearly demonstrates bifurcation characteristics. Bifurcation of radial electric field in neoclassical theory is presented, and its qualitative expectation is discussed in the bifurcation phenomena. The neoclassical transition time scale between two bifurcative sates is compared with the experimental observations during the electric pulsation. It is confirmed that the neoclassical transition time is not contradictory with the experimental one. (author)
Bifurcation diagram features of a dc-dc converter under current-mode control
International Nuclear Information System (INIS)
Ruzbehani, Mohsen; Zhou Luowei; Wang Mingyu
2006-01-01
A common tool for analysis of the systems dynamics when the system has chaotic behaviour is the bifurcation diagram. In this paper, the bifurcation diagram of an ideal model of a dc-dc converter under current-mode control is analysed. Algebraic relations that give the critical points locations and describe the pattern of the bifurcation diagram are derived. It is shown that these simple algebraic and geometrical relations are responsible for the complex pattern of the bifurcation diagrams in such circuits. More explanation about the previously observed properties and introduction of some new ones are exposited. In addition, a new three-dimensional bifurcation diagram that can give better imagination of the parameters role is introduced
Li, Li; Xu, Jian
Time delay is inevitable in unidirectionally coupled drive-free vibratory gyroscope system. The effect of time delay on the gyroscope system is studied in this paper. To this end, amplitude death and Hopf bifurcation induced by small time delay are first investigated by analyzing the related characteristic equation. Then, the direction of Hopf bifurcations and stability of Hopf-bifurcating periodic oscillations are determined by calculating the normal form on the center manifold. Next, spatiotemporal patterns of these Hopf-bifurcating periodic oscillations are analyzed by using the symmetric bifurcation theory of delay differential equations. Finally, it is found that numerical simulations agree with the associated analytic results. These phenomena could be induced although time delay is very small. Therefore, it is shown that time delay is an important factor which influences the sensitivity and accuracy of the gyroscope system and cannot be neglected during the design and manufacture.
International Nuclear Information System (INIS)
Xue Yunjing; Gao Peiyi; Lin Yan
2007-01-01
Objective: To investigate flow patterns at carotid bifurcation in vivo by combining computational fluid dynamics (CFD)and MR angiography imaging. Methods: Seven subjects underwent contrast-enhanced MR angiography of carotid artery in Siemens 3.0 T MR. Flow patterns of the carotid artery bifurcation were calculated and visualized by combining MR vascular imaging post-processing and CFD. Results: The flow patterns of the carotid bifurcations in 7 subjects were varied with different phases of a cardiac cycle. The turbulent flow and back flow occurred at bifurcation and proximal of internal carotid artery (ICA) and external carotid artery (ECA), their occurrence and conformation were varied with different phase of a cardiac cycle. The turbulent flow and back flow faded out quickly when the blood flow to the distal of ICA and ECA. Conclusion: CFD combined with MR angiography can be utilized to visualize the cyclical change of flow patterns of carotid bifurcation with different phases of a cardiac cycle. (authors)
Bifurcation structures of a cobweb model with memory and competing technologies
Agliari, Anna; Naimzada, Ahmad; Pecora, Nicolò
2018-05-01
In this paper we study a simple model based on the cobweb demand-supply framework with costly innovators and free imitators. The evolutionary selection between technologies depends on a performance measure which is related to the degree of memory. The resulting dynamics is described by a two-dimensional map. The map has a fixed point which may lose stability either via supercritical Neimark-Sacker bifurcation or flip bifurcation and several multistability situations exist. We describe some sequences of global bifurcations involving attracting and repelling closed invariant curves. These bifurcations, characterized by the creation of homoclinic connections or homoclinic tangles, are described through several numerical simulations. Particular bifurcation phenomena are also observed when the parameters are selected inside a periodicity region.
Analysis of stability and Hopf bifurcation for a delayed logistic equation
International Nuclear Information System (INIS)
Sun Chengjun; Han Maoan; Lin Yiping
2007-01-01
The dynamics of a logistic equation with discrete delay are investigated, together with the local and global stability of the equilibria. In particular, the conditions under which a sequence of Hopf bifurcations occur at the positive equilibrium are obtained. Explicit algorithm for determining the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are derived by using the theory of normal form and center manifold [Hassard B, Kazarino D, Wan Y. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981.]. Global existence of periodic solutions is also established by using a global Hopf bifurcation result of Wu [Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc 350:1998;4799-38.
A transilient matrix for moist convection
Energy Technology Data Exchange (ETDEWEB)
Romps, D.; Kuang, Z.
2011-08-15
A method is introduced for diagnosing a transilient matrix for moist convection. This transilient matrix quantifies the nonlocal transport of air by convective eddies: for every height z, it gives the distribution of starting heights z{prime} for the eddies that arrive at z. In a cloud-resolving simulation of deep convection, the transilient matrix shows that two-thirds of the subcloud air convecting into the free troposphere originates from within 100 m of the surface. This finding clarifies which initial height to use when calculating convective available potential energy from soundings of the tropical troposphere.
Liu, Xia; Zhang, Tonghua; Meng, Xinzhu; Zhang, Tongqian
2018-04-01
In this paper, we propose a predator-prey model with herd behavior and prey-taxis. Then, we analyze the stability and bifurcation of the positive equilibrium of the model subject to the homogeneous Neumann boundary condition. By using an abstract bifurcation theory and taking prey-tactic sensitivity coefficient as the bifurcation parameter, we obtain a branch of stable nonconstant solutions bifurcating from the positive equilibrium. Our results show that prey-taxis can yield the occurrence of spatial patterns.
Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow
International Nuclear Information System (INIS)
Smith, L. D.; Rudman, M.; Lester, D. R.; Metcalfe, G.
2016-01-01
Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversal in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.
Convective aggregation in realistic convective-scale simulations
Holloway, Christopher E.
2017-06-01
To investigate the real-world relevance of idealized-model convective self-aggregation, five 15 day cases of real organized convection in the tropics are simulated. These include multiple simulations of each case to test sensitivities of the convective organization and mean states to interactive radiation, interactive surface fluxes, and evaporation of rain. These simulations are compared to self-aggregation seen in the same model configured to run in idealized radiative-convective equilibrium. Analysis of the budget of the spatial variance of column-integrated frozen moist static energy shows that control runs have significant positive contributions to organization from radiation and negative contributions from surface fluxes and transport, similar to idealized runs once they become aggregated. Despite identical lateral boundary conditions for all experiments in each case, systematic differences in mean column water vapor (CWV), CWV distribution shape, and CWV autocorrelation length scale are found between the different sensitivity runs, particularly for those without interactive radiation, showing that there are at least some similarities in sensitivities to these feedbacks in both idealized and realistic simulations (although the organization of precipitation shows less sensitivity to interactive radiation). The magnitudes and signs of these systematic differences are consistent with a rough equilibrium between (1) equalization due to advection from the lateral boundaries and (2) disaggregation due to the absence of interactive radiation, implying disaggregation rates comparable to those in idealized runs with aggregated initial conditions and noninteractive radiation. This points to a plausible similarity in the way that radiation feedbacks maintain aggregated convection in both idealized simulations and the real world.Plain Language SummaryUnderstanding the processes that lead to the organization of tropical rainstorms is an important challenge for weather
CRUCIB: an axisymmetric convection code
International Nuclear Information System (INIS)
Bertram, L.A.
1975-03-01
The CRUCIB code was written in support of an experimental program aimed at measurement of thermal diffusivities of refractory liquids. Precise values of diffusivity are necessary to realistic analysis of reactor safety problems, nuclear waste disposal procedures, and fundamental metal forming processes. The code calculates the axisymmetric transient convective motions produced in a right circular cylindrical crucible, which is surface heated by an annular heat pulse. Emphasis of this report is placed on the input-output options of the CRUCIB code, which are tailored to assess the importance of the convective heat transfer in determining the surface temperature distribution. Use is limited to Prandtl numbers less than unity; larger values can be accommodated by replacement of a single block of the code, if desired. (U.S.)
Non-Boussinesq Dissolution-Driven Convection in Porous Media
Amooie, M. A.; Soltanian, M. R.; Moortgat, J.
2017-12-01
Geological carbon dioxide (CO2) sequestration in deep saline aquifers has been increasingly recognized as a feasible technology to stabilize the atmospheric carbon concentrations and subsequently mitigate the global warming. Solubility trapping is one of the most effective storage mechanisms, which is associated initially with diffusion-driven slow dissolution of gaseous CO2 into the aqueous phase, followed by density-driven convective mixing of CO2 throughout the aquifer. The convection includes both diffusion and fast advective transport of the dissolved CO2. We study the fluid dynamics of CO2 convection in the underlying single aqueous-phase region. Two modeling approaches are employed to define the system: (i) a constant-concentration condition for CO2 in aqueous phase at the top boundary, and (ii) a sufficiently low, constant injection-rate for CO2 from top boundary. The latter allows for thermodynamically consistent evolution of the CO2 composition and the aqueous phase density against the rate at which the dissolved CO2 convects. Here we accurately model the full nonlinear phase behavior of brine-CO2 mixture in a confined domain altered by dissolution and compressibility, while relaxing the common Boussinesq approximation. We discover new flow regimes and present quantitative scaling relations for global characters of spreading, mixing, and dissolution flux in two- and three-dimensional media for the both model types. We then revisit the universal Sherwood-Rayleigh scaling that is under debate for porous media convective flows. Our findings confirm the sublinear scaling for the constant-concentration case, while reconciling the classical linear scaling for the constant-injection model problem. The results provide a detailed perspective into how the available modeling strategies affect the prediction ability for the total amount of CO2 dissolved in the long term within saline aquifers of different permeabilities.
Fluid convection, constraint and causation
Bishop, Robert C.
2012-01-01
Complexity—nonlinear dynamics for my purposes in this essay—is rich with metaphysical and epistemological implications but is receiving sustained philosophical analysis only recently. I will explore some of the subtleties of causation and constraint in Rayleigh–Bénard convection as an example of a complex phenomenon, and extract some lessons for further philosophical reflection on top-down constraint and causation particularly with respect to causal foundationalism. PMID:23386955
Bifurcation in asymmetric plasma divided by a magnetic filter
International Nuclear Information System (INIS)
Ohi, K.; Naitou, H.; Tauchi, Y.; Fukumasa, O.
2001-05-01
A magnetic filter (MF) reflecting electrons from both sides can separate a low-temperature and low-density subplasma from a high-temperature and high-density main plasma. The one-dimensional numerical simulation by the particle-in-cell code revealed that, depending on the asymmetry, the plasma divided by the MF behaves dynamically or statically [K. Ohi et al., Physics of Plasmas 8, 23 (2001)]. The transition between the two bifurcated states is discontinuous. In the dynamic state, the autonomous potential oscillation in the subplasma is synchronized with the passage of the shock wave structure generated by the modulated ion beam from the main plasma. The stationary phase of the dynamic state appears after the amplitude of the potential oscillation in the subplasma grows exponentially from the thermal noise. In the static state, the system is stable to the growth of the potential oscillation in the subplasma. (author)
Active control of continuous air jet with bifurcated synthetic jets
Directory of Open Access Journals (Sweden)
Dančová Petra
2017-01-01
Full Text Available The synthetic jets (SJs have many significant applications and the number of applications is increasing all the time. In this research the main focus is on the primary flow control which can be used effectively for the heat transfer increasing. This paper deals with the experimental research of the effect of two SJs worked in the bifurcated mode used for control of an axisymmetric air jet. First, the control synthetic jets were measured alone. After an adjustment, the primary axisymmetric jet was added in to the system. For comparison, the primary flow without synthetic jets control was also measured. All experiments were performed using PIV method whereby the synchronization between synthetic jets and PIV system was necessary to do.
Passive band-gap reconfiguration born from bifurcation asymmetry.
Bernard, Brian P; Mann, Brian P
2013-11-01
Current periodic structures are constrained to have fixed energy transmission behavior unless active control or component replacement is used to alter their wave propagation characteristics. The introduction of nonlinearity to generate multiple stable equilibria is an alternative strategy for realizing distinct energy propagation behaviors. We investigate the creation of a reconfigurable band-gap system by implementing passive switching between multiple stable states of equilibrium, to alter the level of energy attenuation in response to environmental stimuli. The ability to avoid potentially catastrophic loads is demonstrated by tailoring the bandpass and band-gap regions to coalesce for two stable equilibria and varying an external load parameter to trigger a bifurcation. The proposed phenomenon could be utilized in remote or autonomous applications where component modifications and active control are impractical.
10th International Workshop on Bifurcation and Degradation in Geomaterials
Zhao, Jidong
2015-01-01
This book contains contributions to the 10th International Workshop on Bifurcation and Degradation in Geomaterials held in Hong Kong, May 28-30, 2014. This event marks the silver Jubilee anniversary of an international conference series dedicated to the research on localization, instability, degradation and failure of geomaterials since 1988 when its first workshop was organized in Germany. This volume of book collects the latest progresses and state-of-the-art research from top researchers around the world, and covers topics including multiscale modeling, experimental characterization and theoretical analysis of various instability and degradation phenomena in geomaterials as well as their relevance to contemporary issues in engineering practice. This book can be used as a useful reference for research students, academics and practicing engineers who are interested in the instability and degradation problems in geomechanics and geotechnical engineering.
Stents in Renal Artery Bifurcation Stenosis: A Case Report
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Polytimi Leonardou
2011-01-01
Full Text Available A 39-year-old patient presented with poorly controlled hypertension, and she was referred to renal angiogram and potential renal angioplasty. Renal angiogram showed a bifurcation lesion of the right renal artery. A guide wire was used to cross the upper branch, while the lower branch was protected by another same-type guide wire through the same introducer. Two thin monorail balloons were used to dilate the two branches; however, despite balloon dilatation, the stenosis of the vessels persisted. The “kissing balloon” technique was then attempted by simultaneously inflating both branches using the same balloons, but more than a 70% residual stenosis persisted in each branch. Two stents were finally placed in a “kissing” way through the main renal artery. The imaging and clinical results were good, without any procedure-related complications. Three years clinical followup was also good, without any reason for further interventional approach.
Stents in Renal Artery Bifurcation Stenosis: A Case Report
Leonardou, Polytimi; Pappas, Paris
2011-01-01
A 39-year-old patient presented with poorly controlled hypertension, and she was referred to renal angiogram and potential renal angioplasty. Renal angiogram showed a bifurcation lesion of the right renal artery. A guide wire was used to cross the upper branch, while the lower branch was protected by another same-type guide wire through the same introducer. Two thin monorail balloons were used to dilate the two branches; however, despite balloon dilatation, the stenosis of the vessels persisted. The “kissing balloon” technique was then attempted by simultaneously inflating both branches using the same balloons, but more than a 70% residual stenosis persisted in each branch. Two stents were finally placed in a “kissing” way through the main renal artery. The imaging and clinical results were good, without any procedure-related complications. Three years clinical followup was also good, without any reason for further interventional approach. PMID:21789043
Experimental Bifurcation Analysis Using Control-Based Continuation
DEFF Research Database (Denmark)
Bureau, Emil; Starke, Jens
The focus of this thesis is developing and implementing techniques for performing experimental bifurcation analysis on nonlinear mechanical systems. The research centers around the newly developed control-based continuation method, which allows to systematically track branches of stable...... the resulting behavior, we propose and test three different methods for assessing stability of equilibrium states during experimental continuation. We show that it is possible to determine the stability without allowing unbounded divergence, and that it is under certain circumstances possible to quantify...... and unstable equilibria under variation of parameters. As a test case we demonstrate that it is possible to track the complete frequency response, including the unstable branches, for a harmonically forced impact oscillator with hardening spring nonlinearity, controlled by electromagnetic actuators. The method...
Analysis of Spatiotemporal Dynamic and Bifurcation in a Wetland Ecosystem
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Yi Wang
2015-01-01
Full Text Available A wetland ecosystem is studied theoretically and numerically to reveal the rules of dynamics which can be quite accurate to better describe the observed spatial regularity of tussock vegetation. Mathematical theoretical works mainly investigate the stability of constant steady states, the existence of nonconstant steady states, and bifurcation, which can deduce a standard parameter control relation and in return can provide a theoretical basis for the numerical simulation. Numerical analysis indicates that the theoretical works are correct and the wetland ecosystem can show rich dynamical behaviors not only regular spatial patterns. Our results further deepen and expand the study of dynamics in the wetland ecosystem. In addition, it is successful to display tussock formation in the wetland ecosystem may have important consequences for aquatic community structure, especially for species interactions and biodiversity. All these results are expected to be useful in the study of the dynamic complexity of wetland ecosystems.
Stability of River Bifurcations from Bedload to Suspended Load Dominated Conditions
de Haas, T.; Kleinhans, M. G.
2010-12-01
Bifurcations (also called diffluences) are as common as confluences in braided and anabranched rivers, and more common than confluences on alluvial fans and deltas where the network is essentially distributary. River bifurcations control the partitioning of both water and sediment through these systems with consequences for immediate river and coastal management and long-term evolution. Their stability is poorly understood and seems to differ between braided rivers, meandering river plains and deltas. In particular, it is the question to what extent the division of flow is asymmetrical in stable condition, where highly asymmetrical refers to channel closure and avulsion. Recent work showed that bifurcations in gravel bed braided rivers become more symmetrical with increasing sediment mobility, whereas bifurcations in a lowland sand delta become more asymmetrical with increasing sediment mobility. This difference is not understood and our objective is to resolve this issue. We use a one-dimensional network model with Y-shaped bifurcations to explore the parameter space from low to high sediment mobility. The model solves gradually varied flow, bedload transport and morphological change in a straightforward manner. Sediment is divided at the bifurcation including the transverse slope effect and the spiral flow effect caused by bends at the bifurcation. Width is evolved whilst conserving mass of eroded or built banks with the bed balance. The bifurcations are perturbed from perfect symmetry either by a subtle gradient advantage for one branch or a gentle bend at the bifurcation. Sediment transport was calculated with and without a critical threshold for sediment motion. Sediment mobility, determined in the upstream channel, was varied in three different ways to isolate the causal factor: by increasing discharge, increasing channel gradient and decreasing particle size. In reality the sediment mobility is mostly determined by particle size: gravel bed rivers are near
Cryogenic helium gas convection research
International Nuclear Information System (INIS)
Donnelly, R.J.
1994-10-01
This is a report prepared by a group interested in doing research in thermal convection using the large scale refrigeration facilities available at the SSC Laboratories (SSCL). The group preparing this report consists of Michael McAshan at SSCL, Robert Behringer at Duke University, Katepalli Sreenivasan at Yale University, Xiao-Zhong Wu at Northern Illinois University and Russell Donnelly at the University of Oregon, who served as Editor for this report. This study reports the research and development opportunities in such a project, the technical requirements and feasibility of its construction and operation, and the costs associated with the needed facilities and support activities. The facility will be a unique national resource for studies of high-Reynolds-number and high-Rayleigh-number and high Rayleigh number turbulence phenomena, and is one of the six items determined as suitable for potential funding through a screening of Expressions of Interest. The proposed facility is possible only because of the advanced cryogenic technology available at the SSCL. Typical scientific issues to be addressed in the facility will be discussed. It devolved during our study, that while the main experiment is still considered to be the thermal convection experiment discussed in our original Expression of Interest, there are now a very substantial set of other, important and fundamental experiments which can be done with the large cryostat proposed for the convection experiment. We believe the facility could provide several decades of front-line research in turbulence, and shall describe why this is so
Thermosolutal convection during dendritic solidification
Heinrich, J. C.; Nandapurkar, P.; Poirier, D. R.; Felicelli, S.
1989-01-01
This paper presents a mathematical model for directional solidification of a binary alloy including a dendritic region underlying an all-liquid region. It is assumed initially that there exists a nonconvecting state with planar isotherms and isoconcentrates solidifying at a constant velocity. The stability of this system has been analyzed and nonlinear calculations are performed that show the effect of convection in the solidification process when the system is unstable. Results of calculations for various cases defined by the initial temperature gradient at the dendrite tips and varying strength of the gravitational field are presented for systems involving lead-tin alloys. The results show that the systems are stable for a gravitational constant of 0.0001 g(0) and that convection can be suppressed by appropriate choice of the container's size for higher values of the gravitational constant. It is also concluded that for the lead-tin systems considered, convection in the mushy zone is not significant below the upper 20 percent of the dendritic zone, if al all.
Shell structure and orbit bifurcations in finite fermion systems
Magner, A. G.; Yatsyshyn, I. S.; Arita, K.; Brack, M.
2011-10-01
We first give an overview of the shell-correction method which was developed by V.M. Strutinsky as a practicable and efficient approximation to the general self-consistent theory of finite fermion systems suggested by A.B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M.C. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the "periodic orbit theory". We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called "superdeformed" energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).
O(2) Hopf bifurcation of viscous shock waves in a channel
Pogan, Alin; Yao, Jinghua; Zumbrun, Kevin
2015-07-01
Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O(2) transverse Hopf bifurcation, or "cellular instability", of viscous shock waves in a channel, for a class of quasilinear hyperbolic-parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Fréchet differentiability of the time- T solution operator by appropriate hyperbolic-parabolic energy estimates, and (ii) handle O(2) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyperbolic-parabolic form) the requisite framework for treatment by spatial dynamics on the space of time-periodic functions, the two standard treatments for this problem. The latter issue is resolved by Lyapunov-Schmidt reduction of the time- T map, yielding a four-dimensional problem with O(2) plus approximate S1 symmetry, which we treat "by hand" using direct Implicit Function Theorem arguments. The former is treated by balancing information obtained in Lagrangian coordinates with that from associated constraints. Interestingly, this argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to the infinite-dimensional family of Lagrangian symmetries corresponding to invariance under arbitrary volume-preserving diffeomorphisms.
Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback
Directory of Open Access Journals (Sweden)
Lei Li
2016-10-01
Full Text Available The parametric excitation system consisting of a flexible beam and shuttle mass widely exists in microelectromechanical systems (MEMS, which can exhibit rich nonlinear dynamic behaviors. This article aims to theoretically investigate the nonlinear jumping phenomena and bifurcation conditions of a class of electrostatically-driven MEMS actuators with a time-delay feedback controller. Considering the comb structure consisting of a flexible beam and shuttle mass, the partial differential governing equation is obtained with both the linear and cubic nonlinear parametric excitation. Then, the method of multiple scales is introduced to obtain a slow flow that is analyzed for stability and bifurcation. Results show that time-delay feedback can improve resonance frequency and stability of the system. What is more, through a detailed mathematical analysis, the discriminant of Hopf bifurcation is theoretically derived, and appropriate time-delay feedback force can make the branch from the Hopf bifurcation point stable under any driving voltage value. Meanwhile, through global bifurcation analysis and saddle node bifurcation analysis, theoretical expressions about the system parameter space and maximum amplitude of monostable vibration are deduced. It is found that the disappearance of the global bifurcation point means the emergence of monostable vibration. Finally, detailed numerical results confirm the analytical prediction.
A bench top experimental model of bubble transport in multiple arteriole bifurcations
International Nuclear Information System (INIS)
Eshpuniyani, Brijesh; Fowlkes, J. Brian; Bull, Joseph L.
2005-01-01
Motivated by a novel gas embolotherapy technique, a bench top vascular bifurcation model is used to investigate the splitting of long bubbles in a series of liquid-filled bifurcations. The developmental gas embolotherapy technique aims to treat cancer by infarcting tumors with gas emboli that are formed by selective acoustic vaporization of ∼6 μm, intravascular, perfluorcarbon droplets. The resulting gas bubbles are large enough to extend through several vessel bifurcations. The current bench top experiments examine the effects of gravity and flow on bubble transport through multiple bifurcations. The effect of gravity is varied by changing the roll angle of the bifurcating network about its parent tube. Splitting at each bifurcation is nearly even when the roll angle is zero. It is demonstrated that bubbles can either stick at one of the second bifurcations or in the second generation daughter tubes, even though the flow rate in the parent tube is constant. The findings of this work indicate that both gravity and flow are important in determining the bubble transport, and suggest that a treatment strategy that includes multiple doses may be effective in delivering emboli to vessels not occluded by the initial dose
Ishikawa, Takuji; Fujiwara, Hiroki; Matsuki, Noriaki; Yoshimoto, Takefumi; Imai, Yohsuke; Ueno, Hironori; Yamaguchi, Takami
2011-02-01
Bifurcations and confluences are very common geometries in biomedical microdevices. Blood flow at microchannel bifurcations has different characteristics from that at confluences because of the multiphase properties of blood. Using a confocal micro-PIV system, we investigated the behaviour of red blood cells (RBCs) and cancer cells in microchannels with geometrically symmetric bifurcations and confluences. The behaviour of RBCs and cancer cells was strongly asymmetric at bifurcations and confluences whilst the trajectories of tracer particles in pure water were almost symmetric. The cell-free layer disappeared on the inner wall of the bifurcation but increased in size on the inner wall of the confluence. Cancer cells frequently adhered to the inner wall of the bifurcation but rarely to other locations. Because the wall surface coating and the wall shear stress were almost symmetric for the bifurcation and the confluence, the result indicates that not only chemical mediation and wall shear stress but also microscale haemodynamics play important roles in the adhesion of cancer cells to the microchannel walls. These results provide the fundamental basis for a better understanding of blood flow and cell adhesion in biomedical microdevices.
Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay
International Nuclear Information System (INIS)
Ding Yuting; Jiang Weihua; Wang Hongbin
2012-01-01
Highlights: ► We derive the unfolding of a financial system with Hopf-pitchfork bifurcation. ► We show the coexistence of a pair of stable small amplitudes periodic solutions. ► At the same time, also there is a pair of stable large amplitudes periodic solutions. ► Chaos can appear by period-doubling bifurcation far away from Hopf-pitchfork value. ► The study will be useful for interpreting economics phenomena in theory. - Abstract: In this paper, we identify the critical point for a Hopf-pitchfork bifurcation in a nonlinear financial system with delay, and derive the normal form up to third order with their unfolding in original system parameters near the bifurcation point by normal form method and center manifold theory. Furthermore, we analyze its local dynamical behaviors, and show the coexistence of a pair of stable periodic solutions. We also show that there coexist a pair of stable small-amplitude periodic solutions and a pair of stable large-amplitude periodic solutions for different initial values. Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding parameter values are far away from the critical point of the Hopf-pitchfork bifurcation.
Analysis of the flow at a T-bifurcation for a ternary unit
International Nuclear Information System (INIS)
Campero, P; Beck, J; Jung, A
2014-01-01
The motivation of this research is to understand the flow behavior through a 90° T- type bifurcation, which connects a Francis turbine and the storage pump of a ternary unit, under different operating conditions (namely turbine, pump and hydraulic short-circuit operation). As a first step a CFD optimization process to define the hydraulic geometry of the bifurcation was performed. The CFD results show the complexity of the flow through the bifurcation, especially under hydraulic short-circuit operation. Therefore, it was decided to perform experimental investigations in addition to the CFD analysis, in order to get a better understanding of the flow. The aim of these studies was to investigate the flow development upstream and downstream the bifurcation, the estimation of the bifurcation loss coefficients and also to provide comprehensive data of the flow behavior for the whole operating range of the machine. In order to evaluate the development of the velocity field Stereo Particle Image Velocimetry (S-PIV) measurements at different sections upstream and downstream of the bifurcation on the main penstock and Laser Doppler Anemometrie (LDA) measurements at bifurcation inlet were performed. This paper presents the CFD results obtained for the final design for different operating conditions, the model test procedures and the model test results with special attention to: 1) The bifurcation head loss coefficients, and their extrapolation to prototype conditions, 2) S-PIV and LDA measurements. Additionally, criteria to define the minimal uniformity conditions for the velocity profiles entering the turbine are evaluated. Finally, based on the gathered flow information a better understanding to define the preferred location of a bifurcation is gained and can be applied to future projects
Thermal convection around a heat source embedded in a box containing a saturated porous medium
Energy Technology Data Exchange (ETDEWEB)
Himasekhar, K.; Bau, H.H. (Univ. of Pennsylvania, Philadelphia (USA))
1988-08-01
A study of the thermal convection around a uniform flux cylinder embedded in a box containing a saturated porous medium is carried out experimentally and theoretically. The experimental work includes heat transfer and temperature field measurements. It is observed that for low Rayleigh numbers, the flow is two dimensional and time independent. Once a critical Rayleigh number is exceeded, the flow undergoes a Hopf bifurcation and becomes three dimensional and time dependent. The theoretical study involves the numerical solution of the two-dimensional Darcy-Oberbeck-Boussinesq equations. The complicated geometry is conveniently handled by mapping the physical domain onto a rectangle via the use of boundary-fitted coordinates. The numerical code can easily be extended to handle diverse geometric configurations. For low Rayleigh numbers, the theoretical results agree favorably with the experimental observations. However, the appearance of three-dimensional flow phenomena limits the range of utility of the numerical code.
Numerical investigation of Rayleigh–Bénard convection in a cylinder of unit aspect ratio
Energy Technology Data Exchange (ETDEWEB)
Wang, Bo-Fu; Jiang, Jin [School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072 (China); Zhou, Lin [Institute of Structural Mechanics, Chinese Academy of Engineering Physics, Mianyang, 621900 (China); Sun, De-Jun, E-mail: jinjiang@whu.edu.cn [Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027 (China)
2016-02-15
Thermal convection in a vertical cylindrical cavity with a heated bottom, cooled top and insulated sidewall is investigated numerically. The radius to height ratio (Γ = height/radius) is fixed to unity and the Prandtl number is varied from 0.04 to 1. Rayleigh numbers up to 16 000 are considered in this study. Ten different kinds of flow regime have been identified, including both steady and unsteady patterns. The transition from steady to oscillatory flow occurs at a much lower Rayleigh number for small Prandtl number flow than for large Prandtl number flow. A bifurcation analysis shows the coexistence of two flow patterns in a certain parameter regime. The effect of flow structure on heat transfer is studied for a Prandtl number of unity. (paper)
Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2014-01-01
Full Text Available By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results.
Stability and Hopf bifurcation for a delayed SLBRS computer virus model.
Zhang, Zizhen; Yang, Huizhong
2014-01-01
By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results.
Analysis of the magnetohydrodynamic equations and study of the nonlinear solution bifurcations
International Nuclear Information System (INIS)
Morros Tosas, J.
1989-01-01
The nonlinear problems related to the plasma magnetohydrodynamic instabilities are studied. A bifurcation theory is applied and a general magnetohydrodynamic equation is proposed. Scalar functions, a steady magnetic field and a new equation for the velocity field are taken into account. A method allowing the obtention of suitable reduced equations for the instabilities study is described. Toroidal and cylindrical configuration plasmas are studied. In the cylindrical configuration case, analytical calculations are performed and two steady bifurcated solutions are found. In the toroidal configuration case, a suitable reduced equation system is obtained; a qualitative approach of a steady solution bifurcation on a toroidal Kink type geometry is carried out [fr
Stability and Hopf bifurcation analysis of a prey-predator system with two delays
International Nuclear Information System (INIS)
Li Kai; Wei Junjie
2009-01-01
In this paper, we have considered a prey-predator model with Beddington-DeAngelis functional response and selective harvesting of predator species. Two delays appear in this model to describe the time that juveniles take to mature. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form method and the center manifold theory. Numerical simulation results are given to support the theoretical predictions.
Clip reconstruction of a large right MCA bifurcation aneurysm. Case report
Directory of Open Access Journals (Sweden)
Giovani A.
2014-06-01
Full Text Available We report a case of complex large middle cerebral artery (MCA bifurcation aneurysm that ruptured during dissection from the very adherent MCA branches but was successfully clipped and the MCA bifurcation reconstructed using 4 Yasargill clips. Through a right pterional craniotomy the sylvian fissure was largely opened as to allow enough workspace for clipping the aneurysm and placing a temporary clip on M1. The pacient recovered very well after surgery and was discharged after 1 week with no neurological deficit. Complex MCA bifurcation aneurysms can be safely reconstructed using regular clips, without the need of using fenestrated clips or complex by-pass procedures.
Stability and Hopf bifurcation in a simplified BAM neural network with two time delays.
Cao, Jinde; Xiao, Min
2007-03-01
Various local periodic solutions may represent different classes of storage patterns or memory patterns, and arise from the different equilibrium points of neural networks (NNs) by applying Hopf bifurcation technique. In this paper, a bidirectional associative memory NN with four neurons and multiple delays is considered. By applying the normal form theory and the center manifold theorem, analysis of its linear stability and Hopf bifurcation is performed. An algorithm is worked out for determining the direction and stability of the bifurcated periodic solutions. Numerical simulation results supporting the theoretical analysis are also given.
Directory of Open Access Journals (Sweden)
Yan-Ke Du
2013-09-01
Full Text Available We study a class of discrete-time bidirectional ring neural network model with delay. We discuss the asymptotic stability of the origin and the existence of Neimark-Sacker bifurcations, by analyzing the corresponding characteristic equation. Employing M-matrix theory and the Lyapunov functional method, global asymptotic stability of the origin is derived. Applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the main results.
Bifurcation analysis of the logistic map via two periodic impulsive forces
International Nuclear Information System (INIS)
Jiang Hai-Bo; Li Tao; Zeng Xiao-Liang; Zhang Li-Ping
2014-01-01
The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincaré map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map. (general)
Lassen, Jens Flensted; Burzotta, Francesco; Banning, Adrian P; Lefèvre, Thierry; Darremont, Olivier; Hildick-Smith, David; Chieffo, Alaide; Pan, Manuel; Holm, Niels Ramsing; Louvard, Yves; Stankovic, Goran
2018-01-20
The European Bifurcation Club (EBC) was initiated in 2004 to support a continuous overview of the field of coronary artery bifurcation interventions and aims to facilitate a scientific discussion and an exchange of ideas on the management of bifurcation disease. The EBC hosts an annual, two-day compact meeting, dedicated to bifurcations, which brings together physicians, pathologists, engineers, biologists, physicists, mathematicians, epidemiologists and statisticians for detailed discussions. Every meeting is finalised with a consensus statement that reflects the unique opportunity of combining the opinion of interventional cardiologists with the opinion of a large variety of other scientists on bifurcation management. A series of consensus sessions dedicated to specific topics, to strengthen the consensus debates and focus the discussions, was introduced at this year's meeting. The sessions comprise an intensive overview of the present literature, a pro and con debate and a voting system, to guide the consensus-building process. The present document represents the summary of the up-to-date EBC consensus and recommendations from the 12th annual EBC meeting in 2016 in Rotterdam.
Convective overshoot at the solar tachocline
Brown, Benjamin; Oishi, Jeffrey S.; Anders, Evan H.; Lecoanet, Daniel; Burns, Keaton; Vasil, Geoffrey M.
2017-08-01
At the base of the solar convection zone lies the solar tachocline. This internal interface is where motions from the unstable convection zone above overshoot and penetrate downward into the stiffly stable radiative zone below, driving gravity waves, mixing, and possibly pumping and storing magnetic fields. Here we study the dynamics of convective overshoot across very stiff interfaces with some properties similar to the internal boundary layer within the Sun. We use the Dedalus pseudospectral framework and study fully compressible dynamics at moderate to high Peclet number and low Mach number, probing a regime where turbulent transport is important, and where the compressible dynamics are similar to those of convective motions in the deep solar interior. We find that the depth of convective overshoot is well described by a simple buoyancy equilibration model, and we consider implications for dynamics at the solar tachocline and for the storage of magnetic fields there by overshooting convection.
The convection electric field in auroral substorms
DEFF Research Database (Denmark)
Gjerløv, Jesper Wittendorff; Hoffman, R.A.
2001-01-01
Dynamics Explorer 2 (DE 2) electric field and ion drift data are used in a statistical study of the ionospheric convection electric field in bulge-type auroral substorms. Thirty-one individual DE 2 substorm crossings were carefully selected and organized by the use of global auroral images obtained...... this database enabled us to compile a model of the ionospheric convection electric field. The characteristics of the premidnight convection reversal show a pronounced local time dependency. Far west of the surge it is a fairly well defined point reversal or convection shear. Approaching the surge and within...... the surge it is a region of weak electric fields increasing in width toward midnight that separates regions of equatorward and poleward electric fields. Therefore we adopt the term Harang region rather than the Harang discontinuity for the premidnight convection reversal. A relatively narrow convection...
The pattern of convection in the Sun
International Nuclear Information System (INIS)
Weiss, N.O.
1976-01-01
The structure of solar magnetic fields is dominated by the effects of convection, which should be incorporated in any model of the solar cycle. Although mixing length theory is adequate for calculating the structure of main sequence stars, a better description of convection is needed for any detailed dynamo model. Recent work on nonlinear convection at low Prandt numbers is reviewed. There has been some progress towards a theory of compressible convection, though there is still no firm theoretical evidence for cells with scales less than the depth of the convecting layer. However, it remains likely that the pattern of solar convection is dominated by granules, supergranules and giant cells. The effects of rotation on these cells are briefly considered. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Favre, E.
1997-09-26
coupled buoyancy and thermo-capillary convection lead to a convective motion of the interface liquid/gas which drastically changes the heat and mass transfer across the liquid layer. Two experiments were considered, depending on the fluid: oil or mercury. The liquid is set in a cooled cylindrical vessel, and heated by a heat flux across the center of the free surface. The basic flow, in the case of oil, is a torus. When the heat parameter increases, a stationary flow appears as petals or rays when the aspect ratio. The lateral confinement selects the azimuthal wavelength. In the case of petals-like flow, a sub-critical Hopf bifurcation is underlined. The turbulence is found to be `weak`, even for the largest values of the Marangoni number (Ma = 1.3 10{sup 5}). In the case of mercury, the thermo-capillary effect is reduced to zero to impurities at the surface which have special trajectories we describe and compare to a simpler experiment. Only the buoyancy forces induce a unstationary, weakly turbulent flow as soon as the heating power exceeds 4W (Ra = 4.5 10{sup 3}, calculated with h = 1 mm). The past part concerns the analysis of the effect on the flow of the boundary conditions, the geometry, the Prandtl number and the buoyancy force with the help of the literature. Results concerning heat transfer, in particular the exponent of the law Nusselt number vs. heating power, were compared with available data. (author) 115 refs.
International Nuclear Information System (INIS)
Liu, Yongbao; Wang, Qiang; Xu, Huidong
2017-01-01
The smooth bifurcation and non-smooth grazing bifurcation of periodic solution of three-degree-of-freedom vibro-impact systems with clearance are studied in this paper. Firstly, six-dimensional Poincaré maps are established through choosing suitable Poincaré section and solving periodic solutions of vibro-impact system. Then, as the analytic expressions of all eigenvalues of Jacobi matrix of six-dimensional map are unavailable, the numerical calculations to search for the critical bifurcation values point by point is a laborious job based on the classical critical criterion described by the properties of eigenvalues. To overcome the difficulty from the classical bifurcation criteria, the explicit critical criterion without using eigenvalues calculation of high-dimensional map is applied to determine bifurcation points of Co-dimension-one bifurcations and Co-dimension-two bifurcations, and then local dynamical behaviors of these bifurcations are further analyzed. Finally, the existence of the grazing periodic solution of the vibro-impact system and grazing bifurcation point are analyzed, the discontinuous grazing bifurcation behavior is studied based on the compound normal form map near the grazing point, the discontinuous jumping phenomenon and the co-existing multiple solutions near the grazing bifurcation point are revealed.
Titan Balloon Convection Model, Phase I
National Aeronautics and Space Administration — This innovative research effort is directed at determining, quantitatively, the convective heat transfer coefficients applicable to a Montgolfiere balloon operating...
REVERSALS IN THE 6-CELLS CONVECTION DRIVEN
Directory of Open Access Journals (Sweden)
G.M. Vodinchar
2015-12-01
Full Text Available We describe the large-scale model geodynamo, which based on indirect data of inhomogeneities in the density of the Earth’s core. Convection structure is associated with spherical harmonic Y24 , which defines the basic poloidal component of velocity. Coriolis drift of this mode determines the toroidal component of velocity. Thus, 6 convective cells are formed. The model takes into account the feedback effect of the magnetic field on convection. It was ascertained that the model contains stable regimes of field generation. The velocity of convection and the dipole component of the magnetic field are close to the observed ones.
Scale analysis of convective clouds
Directory of Open Access Journals (Sweden)
Micha Gryschka
2008-12-01
Full Text Available The size distribution of cumulus clouds due to shallow and deep convection is analyzed using satellite pictures, LES model results and data from the German rain radar network. The size distributions found can be described by simple power laws as has also been proposed for other cloud data in the literature. As the observed precipitation at ground stations is finally determined by cloud numbers in an area and individual sizes and rain rates of single clouds, the cloud size distributions might be used for developing empirical precipitation forecasts or for validating results from cloud resolving models being introduced to routine weather forecasts.
Characterizing Convection in Stellar Atmospheres
International Nuclear Information System (INIS)
Tanner, Joel; Basu, Sarbani; Demarque, Pierre; Robinson, Frank
2011-01-01
We perform 3D radiative hydrodynamic simulations to study the properties of convection in the superadiabatic layer of stars. The simulations show differences in both the stratification and turbulent quantities for different types of stars. We extract turbulent pressure and eddy sizes, as well as the T-τ relation for different stars and find that they are sensitive to the energy flux and gravity. We also show that contrary to what is usually assumed in the field of stellar atmospheres, the structure and gas dynamics of simulations of turbulent atmospheres cannot be parameterized with T eff and log(g) alone.
Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus
Directory of Open Access Journals (Sweden)
Tao Dong
2012-01-01
Full Text Available By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti-virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.
Bifurcation and synchronization of synaptically coupled FHN models with time delay
International Nuclear Information System (INIS)
Wang Qingyun; Lu Qishao; Chen Guanrong; Feng Zhaosheng; Duan Lixia
2009-01-01
This paper presents an investigation of dynamics of the coupled nonidentical FHN models with synaptic connection, which can exhibit rich bifurcation behavior with variation of the coupling strength. With the time delay being introduced, the coupled neurons may display a transition from the original chaotic motions to periodic ones, which is accompanied by complex bifurcation scenario. At the same time, synchronization of the coupled neurons is studied in terms of their mean frequencies. We also find that the small time delay can induce new period windows with the coupling strength increasing. Moreover, it is found that synchronization of the coupled neurons can be achieved in some parameter ranges and related to their bifurcation transition. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behavior are clarified.
Local stability and Hopf bifurcation in small-world delayed networks
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong
2004-01-01
The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis
Local stability and Hopf bifurcation in small-world delayed networks
Energy Technology Data Exchange (ETDEWEB)
Li Chunguang E-mail: cgli@uestc.edu.cn; Chen Guanrong E-mail: gchen@ee.cityu.edu.hk
2004-04-01
The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis.
International Nuclear Information System (INIS)
Laney, D.F.
1996-01-01
On larger and/or more complex sites, remediation of soil and groundwater is sometimes bifurcated. This presents some unique advantages with respect to expedited cleanup of one medium, however, it requires skillful planning and significant forethought to ensure that initial remediation efforts do not preclude some long-term options, and/or unduly influence the subsequent selection of a technology for the other operable units and/or media. this paper examines how the decision to bifurcate should be approached, the various methods of bifurcation, the advantages and disadvantages of bifurcation, and the best methods to build flexibility into the design of initial remediation systems so as to allow for consideration of a fuller range of options for remediation of other operable units and/or media at a later time. Pollutants of concern include: metals; petroleum hydrocarbons; and chlorinated solvents
Hopf bifurcation in a environmental defensive expenditures model with time delay
International Nuclear Information System (INIS)
Russu, Paolo
2009-01-01
In this paper a three-dimensional environmental defensive expenditures model with delay is considered. The model is based on the interactions among visitors V, quality of ecosystem goods E, and capital K, intended as accommodation and entertainment facilities, in Protected Areas (PAs). The tourism user fees (TUFs) are used partly as a defensive expenditure and partly to increase the capital stock. The stability and existence of Hopf bifurcation are investigated. It is that stability switches and Hopf bifurcation occurs when the delay t passes through a sequence of critical values, τ 0 . It has been that the introduction of a delay is a destabilizing process, in the sense that increasing the delay could cause the bio-economics to fluctuate. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation are exhibited by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the results.
Phenomenological and ratio bifurcations of a class of discrete time stochastic processes
Diks, C.G.H.; Wagener, F.O.O.
2011-01-01
Zeeman proposed a classification of stochastic dynamical systems based on the Morse classification of their invariant probability densities; the associated bifurcations are the ‘phenomenological bifurcations’ of L. Arnold. The classification is however not invariant under diffeomorphisms of the
Small-bubble transport and splitting dynamics in a symmetric bifurcation
Qamar, Adnan; Warnez, Matthew; Valassis, Doug T.; Guetzko, Megan E.; Bull, Joseph L.
2017-01-01
Simulations of small bubbles traveling through symmetric bifurcations are conducted to garner information pertinent to gas embolotherapy, a potential cancer treatment. Gas embolotherapy procedures use intra-arterial bubbles to occlude tumor blood supply. As bubbles pass through bifurcations in the blood stream nonhomogeneous splitting and undesirable bioeffects may occur. To aid development of gas embolotherapy techniques, a volume of fluid method is used to model the splitting process of gas bubbles passing through artery and arteriole bifurcations. The model reproduces the variety of splitting behaviors observed experimentally, including the bubble reversal phenomenon. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Small bubbles, having initial length less than twice the vessel diameter, were found unlikely to split in the presence of gravitational asymmetry. Maximum shear stresses were found to decrease exponentially with increasing Reynolds number. Vortex-induced shearing near the bifurcation is identified as a possible mechanism for endothelial cell damage.
Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses
Directory of Open Access Journals (Sweden)
Chuandong Li
2014-01-01
Full Text Available We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.
Small-bubble transport and splitting dynamics in a symmetric bifurcation
Qamar, Adnan
2017-06-28
Simulations of small bubbles traveling through symmetric bifurcations are conducted to garner information pertinent to gas embolotherapy, a potential cancer treatment. Gas embolotherapy procedures use intra-arterial bubbles to occlude tumor blood supply. As bubbles pass through bifurcations in the blood stream nonhomogeneous splitting and undesirable bioeffects may occur. To aid development of gas embolotherapy techniques, a volume of fluid method is used to model the splitting process of gas bubbles passing through artery and arteriole bifurcations. The model reproduces the variety of splitting behaviors observed experimentally, including the bubble reversal phenomenon. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Small bubbles, having initial length less than twice the vessel diameter, were found unlikely to split in the presence of gravitational asymmetry. Maximum shear stresses were found to decrease exponentially with increasing Reynolds number. Vortex-induced shearing near the bifurcation is identified as a possible mechanism for endothelial cell damage.
Local and global bifurcations at infinity in models of glycolytic oscillations
DEFF Research Database (Denmark)
Sturis, Jeppe; Brøns, Morten
1997-01-01
We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity, giving rise to a second saddle and a stable node...... at infinity. Depending on model parameters, a stable limit cycle may blow up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable...... sink (not at infinity) or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior reports for one of the models...
Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion
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Shaban Aly
2016-01-01
Full Text Available The main goal of this paper is to continue the investigations of the important system of Fengqi et al. (2008. The occurrence of Turing and Hopf bifurcations in small homogeneous arrays of two coupled reactors via diffusion-linked mass transfer which described by a system of ordinary differential equations is considered. I study the conditions of the existence as well as stability properties of the equilibrium solutions and derive the precise conditions on the parameters to show that the Hopf bifurcation occurs. Analytically I show that a diffusion driven instability occurs at a certain critical value, when the system undergoes a Turing bifurcation, patterns emerge. The spatially homogeneous equilibrium loses its stability and two new spatially non-constant stable equilibria emerge which are asymptotically stable. Numerically, at a certain critical value of diffusion the periodic solution gets destabilized and two new spatially nonconstant periodic solutions arise by Turing bifurcation.
Step-by-step manual for planning and performing bifurcation PCI: a resource-tailored approach.
Milasinovic, Dejan; Wijns, William; Ntsekhe, Mpiko; Hellig, Farrel; Mohamed, Awad; Stankovic, Goran
2018-02-02
As bifurcation PCI can often be resource-demanding due to the use of multiple guidewires, balloons and stents, different technical options are sometimes being explored, in different local settings, to meet the need of optimally treating a patient with a bifurcation lesion, while being confronted with limited material resources. Therefore, it seems important to keep a proper balance between what is recognised as the contemporary state of the art, and what is known to be potentially harmful and to be discouraged. Ultimately, the resource-tailored approach to bifurcation PCI may be characterised by the notion of minimum technical requirements for each step of a successful procedure. Hence, this paper describes the logical sequence of steps when performing bifurcation PCI with provisional SB stenting, starting with basic anatomy assessment and ending with the optimisation of MB stenting and the evaluation of the potential need to stent the SB, suggesting, for each step, the minimum technical requirement for a successful intervention.
Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps
International Nuclear Information System (INIS)
Avrutin, V; Granados, A; Schanz, M
2011-01-01
Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined discontinuous systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with one boundary in state space and become virtual, and, in the one-dimensional case, the map becomes continuous. Depending on the properties of the map near the codimension-two bifurcation point, there exist different scenarios regarding how the infinite number of periodic orbits are born, mainly the so-called period adding and period incrementing. In our work we prove that, in order to undergo a big bang bifurcation of the period incrementing type, it is sufficient for a piecewise-defined one-dimensional map that the colliding fixed points are attractive and with associated eigenvalues of different signs
Delay-induced stochastic bifurcations in a bistable system under white noise
International Nuclear Information System (INIS)
Sun, Zhongkui; Fu, Jin; Xu, Wei; Xiao, Yuzhu
2015-01-01
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses
Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay
Dong, Tao; Xia, Linmao
2017-12-01
In this paper, a type of reaction-diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.
Beeftink, Martine M A; Spiering, Wilko; De Jong, Mark R; Doevendans, Pieter A; Blankestijn, Peter J; Elvan, Arif; Heeg, Jan-Evert; Bots, Michiel L; Voskuil, Michiel
2017-04-01
Renal denervation may be more effective if performed distal in the renal artery because of smaller distances between the lumen and perivascular nerves. The authors reviewed the angiographic results of 97 patients and compared blood pressure reduction in relation to the location of the denervation. No significant differences in blood pressure reduction or complications were found between patient groups divided according to their spatial distribution of the ablations (proximal to the bifurcation in both arteries, distal to the bifurcation in one artery and distal in the other artery, or distal to the bifurcation in both arteries), but systolic ambulatory blood pressure reduction was significantly related to the number of distal ablations. No differences in adverse events were observed. In conclusion, we found no reason to believe that renal denervation distal to the bifurcation poses additional risks over the currently advised approach of proximal denervation, but improved efficacy remains to be conclusively established. ©2017 Wiley Periodicals, Inc.
Hopf bifurcation and chaos from torus breakdown in voltage-mode controlled DC drive systems
International Nuclear Information System (INIS)
Dai Dong; Ma Xikui; Zhang Bo; Tse, Chi K.
2009-01-01
Period-doubling bifurcation and its route to chaos have been thoroughly investigated in voltage-mode and current-mode controlled DC motor drives under simple proportional control. In this paper, the phenomena of Hopf bifurcation and chaos from torus breakdown in a voltage-mode controlled DC drive system is reported. It has been shown that Hopf bifurcation may occur when the DC drive system adopts a more practical proportional-integral control. The phenomena of period-adding and phase-locking are also observed after the Hopf bifurcation. Furthermore, it is shown that the stable torus can breakdown and chaos emerges afterwards. The work presented in this paper provides more complete information about the dynamical behaviors of DC drive systems.
Bifurcation and complex dynamics of a discrete-time predator-prey system involving group defense
Directory of Open Access Journals (Sweden)
S. M. Sohel Rana
2015-09-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system involving group defense. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including phase portraits, period-7, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors.
Delay-induced stochastic bifurcations in a bistable system under white noise
Energy Technology Data Exchange (ETDEWEB)
Sun, Zhongkui, E-mail: sunzk@nwpu.edu.cn; Fu, Jin; Xu, Wei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); Xiao, Yuzhu [Department of Mathematics and Information Science, Chang' an University, Xi' an 710086 (China)
2015-08-15
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.
Small-bubble transport and splitting dynamics in a symmetric bifurcation.
Qamar, Adnan; Warnez, Matthew; Valassis, Doug T; Guetzko, Megan E; Bull, Joseph L
2017-08-01
Simulations of small bubbles traveling through symmetric bifurcations are conducted to garner information pertinent to gas embolotherapy, a potential cancer treatment. Gas embolotherapy procedures use intra-arterial bubbles to occlude tumor blood supply. As bubbles pass through bifurcations in the blood stream nonhomogeneous splitting and undesirable bioeffects may occur. To aid development of gas embolotherapy techniques, a volume of fluid method is used to model the splitting process of gas bubbles passing through artery and arteriole bifurcations. The model reproduces the variety of splitting behaviors observed experimentally, including the bubble reversal phenomenon. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Small bubbles, having initial length less than twice the vessel diameter, were found unlikely to split in the presence of gravitational asymmetry. Maximum shear stresses were found to decrease exponentially with increasing Reynolds number. Vortex-induced shearing near the bifurcation is identified as a possible mechanism for endothelial cell damage.
Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We first study the distribution of the zeros of a fourth-degree exponential polynomial. Then we apply the obtained results to a simplified bidirectional associated memory (BAM neural network with four neurons and multiple time delays. By taking the sum of the delays as the bifurcation parameter, it is shown that under certain assumptions the steady state is absolutely stable. Under another set of conditions, there are some critical values of the delay, when the delay crosses these critical values, the Hopf bifurcation occurs. Furthermore, some explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and center manifold reduction. Numerical simulations supporting the theoretical analysis are also included.
Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps
Avrutin, V.; Granados, A.; Schanz, M.
2011-09-01
Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined discontinuous systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with one boundary in state space and become virtual, and, in the one-dimensional case, the map becomes continuous. Depending on the properties of the map near the codimension-two bifurcation point, there exist different scenarios regarding how the infinite number of periodic orbits are born, mainly the so-called period adding and period incrementing. In our work we prove that, in order to undergo a big bang bifurcation of the period incrementing type, it is sufficient for a piecewise-defined one-dimensional map that the colliding fixed points are attractive and with associated eigenvalues of different signs.
International Nuclear Information System (INIS)
Li, Jinhui; Teng, Zhidong; Wang, Guangqing; Zhang, Long; Hu, Cheng
2017-01-01
In this paper, we introduce the saturated treatment and logistic growth rate into an SIR epidemic model with bilinear incidence. The treatment function is assumed to be a continuously differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large enough. Sufficient conditions for the existence and local stability of the disease-free and positive equilibria are established. And the existence of the stable limit cycles also is obtained. Moreover, by using the theory of bifurcations, it is shown that the model exhibits backward bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcations. Finally, the numerical examples are given to illustrate the theoretical results and obtain some additional interesting phenomena, involving double stable periodic solutions and stable limit cycles.
Classification of coronary artery bifurcation lesions and treatments: Time for a consensus!
DEFF Research Database (Denmark)
Louvard, Yves; Thomas, Martyn; Dzavik, Vladimir
2007-01-01
by intention to treat, it is necessary to clearly define which vessel is the distal main branch and which is (are) the side branche(s) and give each branch a distinct name. Each segment of the bifurcation has been named following the same pattern as the Medina classification. The classification......, heterogeneity, and inadequate description of techniques implemented. Methods: The aim is to propose a consensus established by the European Bifurcation Club (EBC), on the definition and classification of bifurcation lesions and treatments implemented with the purpose of allowing comparisons between techniques...... in various anatomical and clinical settings. Results: A bifurcation lesion is a coronary artery narrowing occurring adjacent to, and/or involving, the origin of a significant side branch. The simple lesion classification proposed by Medina has been adopted. To analyze the outcomes of different techniques...
Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model
Kö pf, Michael H; Thiele, Uwe
2014-01-01
© 2014 IOP Publishing Ltd & London Mathematical Society. We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first-order phase transition and is kept permanently out of equilibrium
Problems in Microgravity Fluid Mechanics: G-Jitter Convection
Homsy, G. M.
2005-01-01
This is the final report on our NASA grant, Problems in Microgravity Fluid Mechanics NAG3-2513: 12/14/2000 - 11/30/2003, extended through 11/30/2004. This grant was made to Stanford University and then transferred to the University of California at Santa Barbara when the PI relocated there in January 2001. Our main activity has been to conduct both experimental and theoretical studies of instabilities in fluids that are relevant to the microgravity environment, i.e. those that do not involve the action of buoyancy due to a steady gravitational field. Full details of the work accomplished under this grant are given below. Our work has focused on: (i) Theoretical and computational studies of the effect of g-jitter on instabilities of convective states where the convection is driven by forces other than buoyancy (ii) Experimental studies of instabilities during displacements of miscible fluid pairs in tubes, with a focus on the degree to which these mimic those found in immiscible fluids. (iii) Theoretical and experimental studies of the effect of time dependent electrohydrodynamic forces on chaotic advection in drops immersed in a second dielectric liquid. Our objectives are to acquire insight and understanding into microgravity fluid mechanics problems that bear on either fundamental issues or applications in fluid physics. We are interested in the response of fluids to either a fluctuating acceleration environment or to forces other than gravity that cause fluid mixing and convection. We have been active in several general areas.
Directory of Open Access Journals (Sweden)
Renata Weissmann Borges Mendonça
2008-12-01
Full Text Available O desempenho do Modelo Global do Centro de Previsão de Tempo e Estudos Climáticos (CPTEC em simular a energética modal para um composto de sete episódios de Zona de Convergência do Atlântico Sul (ZCAS é avaliado, enfatizando-se a influência da resolução espacial do modelo e de três diferentes parametrizações de convecção profunda: Kuo, Relaxed Arakawa-Schubert (RAS e Grell na partição vertical de energia entre os modos externos e internos, e as trocas de energia entre os modos horizontais de oscilação Rossby, Kelvin, Misto Rossby-Gravidade, Gravidade Oeste e Leste. Os resultados mostraram que as previsões utilizando os esquemas de convecção profunda Kuo, RAS e Grell foram semelhantes entre si e apresentaram uma boa concordância em relação aos padrões obtidos na parte observacional (Parte I deste artigo. O emprego de diferentes esquemas de convecção profunda não apresentou impactos significativos na partição e interação de energia entre os modos verticais e horizontais. Um impacto maior foi obtido com o aumento da resolução vertical das análises e do modelo, de 28 para 42 níveis, em que um maior número de modos internos apresenta um papel relevante nas trocas horizontais e verticais de energia.The performance of the CPTEC Global Model in simulating the modal energetics for a composite of seven South Atlantic Convergence Zone (SACZ episodes was evaluated, emphasizing the influence of the model resolution and the three different deep convection parameterizations: Kuo, Relaxed Arakawa-Schubert (RAS and Grell on the vertical energy partition between external and internal modes and on the energy interactions within and between various horizontal oscillation modes: Rossby, Kelvin, Mixed Rossby-Gravity and West and East Gravity. The results showed that the model predictions using the Kuo, RAS and Grell deep convection schemes were similar with each other, and had a good agreement with the patterns obtained in the
Two-dimensional turbulent convection
Mazzino, Andrea
2017-11-01
We present an overview of the most relevant, and sometimes contrasting, theoretical approaches to Rayleigh-Taylor and mean-gradient-forced Rayleigh-Bénard two-dimensional turbulence together with numerical and experimental evidences for their support. The main aim of this overview is to emphasize that, despite the different character of these two systems, especially in relation to their steadiness/unsteadiness, turbulent fluctuations are well described by the same scaling relationships originated from the Bolgiano balance. The latter states that inertial terms and buoyancy terms balance at small scales giving rise to an inverse kinetic energy cascade. The main difference with respect to the inverse energy cascade in hydrodynamic turbulence [R. H. Kraichnan, "Inertial ranges in two-dimensional turbulence," Phys. Fluids 10, 1417 (1967)] is that the rate of cascade of kinetic energy here is not constant along the inertial range of scales. Thanks to the absence of physical boundaries, the two systems here investigated turned out to be a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive "ultimate state of thermal convection" [R. H. Kraichnan, "Turbulent thermal convection at arbitrary Prandtl number," Phys. Fluids 5, 1374-1389 (1962)].
Li, Chengyuan; Deng, Licai; de Grijs, Richard; Jiang, Dengkai; Xin, Yu
2018-01-01
Bifurcated patterns of blue straggler stars in their color--magnitude diagrams have atracted significant attention. This type of special (but rare) pattern of two distinct blue straggler sequences is commonly interpreted as evidence of cluster core-collapse-driven stellar collisions as an efficient formation mechanism. Here, we report the detection of a bifurcated blue straggler distribution in a young Large MagellanicCloud cluster, NGC 2173. Because of the cluster's low central stellar numbe...
Si'lnikov chaos and Hopf bifurcation analysis of Rucklidge system
International Nuclear Information System (INIS)
Wang Xia
2009-01-01
A three-dimensional autonomous system - the Rucklidge system is considered. By the analytical method, Hopf bifurcation of Rucklidge system may occur when choosing an appropriate bifurcation parameter. Using the undetermined coefficient method, the existence of heteroclinic and homoclinic orbits in the Rucklidge system is proved, and the explicit and uniformly convergent algebraic expressions of Si'lnikov type orbits are given. As a result, the Si'lnikov criterion guarantees that there exists the Smale horseshoe chaos motion for the Rucklidge system.
On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields
Directory of Open Access Journals (Sweden)
Michail P. Markakis
2016-01-01
Full Text Available The restriction of an n-dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration.
Bifurcation analysis in delayed feedback Jerk systems and application of chaotic control
International Nuclear Information System (INIS)
Zheng Baodong; Zheng Huifeng
2009-01-01
Jerk systems with delayed feedback are considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associated characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, the stability and direction of the Hopf bifurcation are determined by applying the normal form method and center manifold theorem. Finally, the application to chaotic control is investigated, and some numerical simulations are carried out to illustrate the obtained results.
Hopf bifurcation of a ratio-dependent predator-prey system with time delay
International Nuclear Information System (INIS)
Celik, Canan
2009-01-01
In this paper, we consider a ratio dependent predator-prey system with time delay where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the system based on the normal form approach and the center manifold theory. Finally, we illustrate our theoretical results by numerical simulations.
Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices
International Nuclear Information System (INIS)
Testa, J.; Perez, J.; Jeffries, C.
1982-01-01
Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos
Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters
DEFF Research Database (Denmark)
Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik
2017-01-01
be modeled in terms of piecewise smooth maps with an extremely high number of switching manifolds. We have recently shown that models of this type can demonstrate a complicated bifurcation structure associated with the occurrence of border collisions. Considering the example of a PWM H-bridge single...... structure. We explain the observed bifurcation phenomena, show under which conditions they occur, and describe them quantitatively by means of an analytic approximation....
Hopf bifurcation in love dynamical models with nonlinear couples and time delays
International Nuclear Information System (INIS)
Liao Xiaofeng; Ran Jiouhong
2007-01-01
A love dynamical models with nonlinear couples and two delays is considered. Local stability of this model is studied by analyzing the associated characteristic transcendental equation. We find that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical example is given to illustrate our results
Bifurcation analysis on a delayed SIS epidemic model with stage structure
Directory of Open Access Journals (Sweden)
Kejun Zhuang
2007-05-01
Full Text Available In this paper, a delayed SIS (Susceptible Infectious Susceptible model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given.
Stability and Hopf bifurcation in a delayed competitive web sites model
International Nuclear Information System (INIS)
Xiao Min; Cao Jinde
2006-01-01
The delayed differential equations modeling competitive web sites, based on the Lotka-Volterra competition equations, are considered. Firstly, the linear stability is investigated. It is found that there is a stability switch for time delay, and Hopf bifurcation occurs when time delay crosses through a critical value. Then the direction and stability of the bifurcated periodic solutions are determined, using the normal form theory and the center manifold reduction. Finally, some numerical simulations are carried out to illustrate the results found
Liu, Ping; Shi, Junping
2018-01-01
The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.
Onset of Fast Magnetic Reconnection via Subcritical Bifurcation
Directory of Open Access Journals (Sweden)
ZHIBIN eGUO
2015-04-01
Full Text Available We report a phase transition model for the onset of fast magnetic reconnection. By investigating the joint dynamics of streaming instability(i.e., current driven ion acoustic in this paper and current gradient driven whistler wave {color{blue} {prior to the onset of fast reconnection}}, we show that the nonlinear evolution of current sheet(CS can be described by a Landau-Ginzburg equation. The phase transition from slow reconnection to fast reconnection occurs at a critical thickness, $Delta_csimeq frac{2}{sqrt{pi}}left|frac{v_{the}}{v_c}right|d_e$, where $v_{the}$ is electron thermal velocity and $v_c$ is the velocity threshold of the streaming instability. For current driven ion acoustic, $Delta_c$ is $leq10d_e$. If the thickness of the CS is narrower than $Delta_c$, the CS subcritically bifurcates into a rough state, which facilitates breakage of the CS, and consequently initiates fast reconnection.
Bifurcation of plasma balls and black holes to Lobed configurations
International Nuclear Information System (INIS)
Cardoso, Vitor; Dias, Oscar J.C.
2009-01-01
At high energy densities any quantum field theory is expected to have an effective hydrodynamic description. When combined with the gravity/gauge duality an unified picture emerges, where gravity itself can have a formal holographic hydrodynamic description. This provides a powerful tool to study black holes in a hydrodynamic setup. We study the stability of plasma balls, holographic duals of Scherck-Schwarz (SS) AdS black holes. We find that rotating plasma balls are unstable against m-lobed perturbations for rotation rates higher than a critical value. This unstable mode signals a bifurcation to a new branch of non-axisymmetric stationary solutions which resemble a 'peanut-like' rotating plasma. The gravitational dual of the rotating plasma ball must then be unstable and possibly decay to a non-axisymmetric long-lived SS AdS black hole. This instability provides therefore a mechanism that bounds the rotation of SS black holes. Our results are strictly valid for the SS AdS gravity theory dual to a SS gauge theory. The latter is particularly important because it shares common features with QCD, namely it is non-conformal, non-supersymmetric and has a confinement/deconfinement phase transition. We focus our analysis in 3-dimensional plasmas dual to SS AdS 5 black holes, but many of our results should extend to higher dimensions and to other gauge theory/gravity dualities with confined/deconfined phases and admitting a fluid description.
Automated Identification of MHD Mode Bifurcation and Locking in Tokamaks
Riquezes, J. D.; Sabbagh, S. A.; Park, Y. S.; Bell, R. E.; Morton, L. A.
2017-10-01
Disruption avoidance is critical in reactor-scale tokamaks such as ITER to maintain steady plasma operation and avoid damage to device components. A key physical event chain that leads to disruptions is the appearance of rotating MHD modes, their slowing by resonant field drag mechanisms, and their locking. An algorithm has been developed that automatically detects bifurcation of the mode toroidal rotation frequency due to loss of torque balance under resonant braking, and mode locking for a set of shots using spectral decomposition. The present research examines data from NSTX, NSTX-U and KSTAR plasmas which differ significantly in aspect ratio (ranging from A = 1.3 - 3.5). The research aims to examine and compare the effectiveness of different algorithms for toroidal mode number discrimination, such as phase matching and singular value decomposition approaches, and to examine potential differences related to machine aspect ratio (e.g. mode eigenfunction shape variation). Simple theoretical models will be compared to the dynamics found. Main goals are to detect or potentially forecast the event chain early during a discharge. This would serve as a cue to engage active mode control or a controlled plasma shutdown. Supported by US DOE Contracts DE-SC0016614 and DE-AC02-09CH11466.
Dansgaard–Oeschger events: bifurcation points in the climate system
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A. A. Cimatoribus
2013-02-01
Full Text Available Dansgaard–Oeschger events are a prominent mode of variability in the records of the last glacial cycle. Various prototype models have been proposed to explain these rapid climate fluctuations, and no agreement has emerged on which may be the more correct for describing the palaeoclimatic signal. In this work, we assess the bimodality of the system, reconstructing the topology of the multi-dimensional attractor over which the climate system evolves. We use high-resolution ice core isotope data to investigate the statistical properties of the climate fluctuations in the period before the onset of the abrupt change. We show that Dansgaard–Oeschger events have weak early warning signals if the ensemble of events is considered. We find that the statistics are consistent with the switches between two different climate equilibrium states in response to a changing external forcing (e.g. solar, ice sheets, either forcing directly the transition or pacing it through stochastic resonance. These findings are most consistent with a model that associates Dansgaard–Oeschger with changing boundary conditions, and with the presence of a bifurcation point.
Freeform inkjet printing of cellular structures with bifurcations.
Christensen, Kyle; Xu, Changxue; Chai, Wenxuan; Zhang, Zhengyi; Fu, Jianzhong; Huang, Yong
2015-05-01
Organ printing offers a great potential for the freeform layer-by-layer fabrication of three-dimensional (3D) living organs using cellular spheroids or bioinks as building blocks. Vascularization is often identified as a main technological barrier for building 3D organs. As such, the fabrication of 3D biological vascular trees is of great importance for the overall feasibility of the envisioned organ printing approach. In this study, vascular-like cellular structures are fabricated using a liquid support-based inkjet printing approach, which utilizes a calcium chloride solution as both a cross-linking agent and support material. This solution enables the freeform printing of spanning and overhang features by providing a buoyant force. A heuristic approach is implemented to compensate for the axially-varying deformation of horizontal tubular structures to achieve a uniform diameter along their axial directions. Vascular-like structures with both horizontal and vertical bifurcations have been successfully printed from sodium alginate only as well as mouse fibroblast-based alginate bioinks. The post-printing fibroblast cell viability of printed cellular tubes was found to be above 90% even after a 24 h incubation, considering the control effect. © 2014 Wiley Periodicals, Inc.
The origin of the bifurcating style in Asteraceae (Compositae).
Katinas, Liliana; Hernández, Marcelo P; Arambarri, Ana M; Funk, Vicki A
2016-05-01
The plant family Asteraceae (Compositae) exhibits remarkable morphological variation in the styles of its members. Lack of studies on the styles of the sister families to Asteraceae, Goodeniaceae and Calyceraceae, obscures our understanding of the origin and evolution of this reproductive feature in these groups. The aim of this work was to perform a comparative study of style morphology and to discuss the relevance of important features in the evolution of Asteraceae and its sister families. The histochemistry, venation and general morphology of the styles of members of Goodeniaceae, Calyceraceae and early branching lineages of Asteraceae were analysed and put in a phylogenetic framework to discuss the relevance of style features in the evolution of these families. The location of lipophilic substances allowed differentiation of receptive from non-receptive style papillae, and the style venation in Goodeniaceae and Calyceraceae proved to be distinctive. There were several stages of style evolution from Goodeniaceae to Asteraceae involving connation and elongation of veins, development of bilobation from an initially cup-shaped style, and a redistribution of the receptive and non-receptive papillae. These developments resulted in bifurcation in the styles of Asteraceae, with each branch face having a different function, and it is suggested here as a mechanism that promoted outcrossing, which in turn led to the great diversification in the family. © The Author 2016. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
European monetary union: limits to growth or bifurcation point
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Oleksandr Sharov
2014-02-01
Full Text Available The paper presents the background and process of the EU monetary union establishment with regard to historical experience of European countries involving previous attempts of currency integration between separate countries. The author also analyzes methods of solving various theoretical and practical problems arising during the process. In particular, it is pointed out that the majority of the problems were caused by neglecting monetary integration principles, the need for observing which had been clearly stated yet at the preliminary stages of the integration process. Special emphasis is made on reviewing current development stage of the monetary union, in particular, with regard to problems caused by the financial crisis in "peripheral countries" of the Union as well as by concurrent intensification of cooperation in the field of banking and fiscal issues. In this context, the trends of further European monetary integration development are also considered. As resulted from analysis, the author concludes that the European Monetary Union had exhausted its energy for development along previously assigned trajectory and reached the bifurcation point, whereas its further improvement or gradual preservation and decline depend upon the direction in which the point is passed.
Axisymmetric bifurcations of thick spherical shells under inflation and compression
deBotton, G.; Bustamante, R.; Dorfmann, A.
2013-01-01
Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before.© 2012 Published by Elsevier Ltd.
Bifurcation in epigenetics: Implications in development, proliferation, and diseases
Jost, Daniel
2014-01-01
Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of biochemical marks on chromatin. Here, we develop a stochastic model that describes the dynamics of epigenetic marks along a given DNA region. Through mathematical analysis, we show the emergence of bistable and persistent epigenetic states from the cooperative recruitment of modifying enzymes. We also find that the dynamical system exhibits a critical point and displays, in the presence of asymmetries in recruitment, a bifurcation diagram with hysteresis. These results have deep implications for our understanding of epigenetic regulation. In particular, our study allows one to reconcile within the same formalism the robust maintenance of epigenetic identity observed in differentiated cells, the epigenetic plasticity of pluripotent cells during differentiation, and the effects of epigenetic misregulation in diseases. Moreover, it suggests a possible mechanism for developmental transitions where the system is shifted close to the critical point to benefit from high susceptibility to developmental cues.
Topological chaos, braiding and bifurcation of almost-cyclic sets.
Grover, Piyush; Ross, Shane D; Stremler, Mark A; Kumar, Pankaj
2012-12-01
In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or "ghost rods" around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence, we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.
A model of competing species that exhibits zip bifurcation
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Luis F. Echeverri
2017-01-01
Full Text Available El objetivo de este trabajo es presentar un modelo concreto d e poblaciones de especies en competición que exhibe la bifurc ación Zip. La bifurcación zip fue introducida por Farkas en 1984 para un si stema tridi- mensional de ecuaciones diferenciales ordinarias que desc ribe un quimiostato. Estudiaremos un sistema tridimensional de ecuaciones dife renciales ordinarias que modela la competición de dos poblaciones distintas de pr edadores por una única población presa. El sistema usa funciones trigonomét ricas concretas pa- ra representar la tasa de crecimiento de la presa y la respues ta funcional del predador. El modelo exhibe diferentes clases de comportami entos y muestra ejemplos de los llamados principio de exclusión competitiva y la competición de un r-estratega contra un k-estratega . Adicionalmente, para ilustrar la bi- furcacion zip, presentaremos algunas simulaciones numéri cas.
International Nuclear Information System (INIS)
Hajihosseini, Amirhossein; Maleki, Farzaneh; Rokni Lamooki, Gholam Reza
2011-01-01
Highlights: → We construct a recurrent neural network by generalizing a specific n-neuron network. → Several codimension 1 and 2 bifurcations take place in the newly constructed network. → The newly constructed network has higher capabilities to learn periodic signals. → The normal form theorem is applied to investigate dynamics of the network. → A series of bifurcation diagrams is given to support theoretical results. - Abstract: A class of recurrent neural networks is constructed by generalizing a specific class of n-neuron networks. It is shown that the newly constructed network experiences generic pitchfork and Hopf codimension one bifurcations. It is also proved that the emergence of generic Bogdanov-Takens, pitchfork-Hopf and Hopf-Hopf codimension two, and the degenerate Bogdanov-Takens bifurcation points in the parameter space is possible due to the intersections of codimension one bifurcation curves. The occurrence of bifurcations of higher codimensions significantly increases the capability of the newly constructed recurrent neural network to learn broader families of periodic signals.
Bifurcating fronts for the Taylor-Couette problem in infinite cylinders
Hărăguş-Courcelle, M.; Schneider, G.
We show the existence of bifurcating fronts for the weakly unstable Taylor-Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices, with the trivial ground state, here the Couette flow. In order to show the existence result we improve a method which was already used in establishing the existence of bifurcating fronts for the Swift-Hohenberg equation by Collet and Eckmann, 1986, and by Eckmann and Wayne, 1991. The existence proof is based on spatial dynamics and center manifold theory. One of the difficulties in applying center manifold theory comes from an infinite number of eigenvalues on the imaginary axis for vanishing bifurcation parameter. But nevertheless, a finite dimensional reduction is possible, since the eigenvalues leave the imaginary axis with different velocities, if the bifurcation parameter is increased. In contrast to previous work we have to use normalform methods and a non-standard cut-off function to obtain a center manifold which is large enough to contain the bifurcating fronts.
Gaudreault, Mathieu; Drolet, François; Viñals, Jorge
2010-11-01
Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for a nonlinear stochastic differential delay equation with feedback. Our results assume that the delay time τ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average , where x(t) is the dynamical variable. This conditional probability incorporates the combined effect of fluctuation correlations and delayed feedback. We also find a Hopf bifurcation line which is obtained by a multiple scale expansion around the oscillatory solution near threshold. We solve the Fokker-Planck equation associated with the slowly varying amplitudes and use it to determine the threshold location. In both cases, the predicted bifurcation lines are in excellent agreement with a direct numerical integration of the governing equations. Contrary to the known case involving no delayed feedback, we show that the stochastic bifurcation lines are shifted relative to the deterministic limit and hence that the interaction between fluctuation correlations and delay affect the stability of the solutions of the model equation studied.
Anatomy and function relation in the coronary tree: from bifurcations to myocardial flow and mass.
Kassab, Ghassan S; Finet, Gerard
2015-01-01
The study of the structure-function relation of coronary bifurcations is necessary not only to understand the design of the vasculature but also to use this understanding to restore structure and hence function. The objective of this review is to provide quantitative relations between bifurcation anatomy or geometry, flow distribution in the bifurcation and degree of perfused myocardial mass in order to establish practical rules to guide optimal treatment of bifurcations including side branches (SB). We use the scaling law between flow and diameter, conservation of mass and the scaling law between myocardial mass and diameter to provide geometric relations between the segment diameters of a bifurcation, flow fraction distribution in the SB, and the percentage of myocardial mass perfused by the SB. We demonstrate that the assessment of the functional significance of an SB for intervention should not only be based on the diameter of the SB but also on the diameter of the mother vessel as well as the diameter of the proximal main artery, as these dictate the flow fraction distribution and perfused myocardial mass, respectively. The geometric and flow rules for a bifurcation are extended to a trifurcation to ensure optimal therapy scaling rules for any branching pattern.
International Nuclear Information System (INIS)
Agliari, Anna
2006-01-01
In this paper we study some global bifurcations arising in the Puu's oligopoly model when we assume that the producers do not adjust to the best reply but use an adaptive process to obtain at each step the new production. Such bifurcations cause the appearance of a pair of closed invariant curves, one attracting and one repelling, this latter being involved in the subcritical Neimark bifurcation of the Cournot equilibrium point. The aim of the paper is to highlight the relationship between the global bifurcations causing the appearance/disappearance of two invariant closed curves and the homoclinic connections of some saddle cycle, already conjectured in [Agliari A, Gardini L, Puu T. Some global bifurcations related to the appearance of closed invariant curves. Comput Math Simul 2005;68:201-19]. We refine the results obtained in such a paper, showing that the appearance/disappearance of closed invariant curves is not necessarily related to the existence of an attracting cycle. The characterization of the periodicity tongues (i.e. a region of the parameter space in which an attracting cycle exists) associated with a subcritical Neimark bifurcation is also discussed
Multistability and gluing bifurcation to butterflies in coupled networks with non-monotonic feedback
International Nuclear Information System (INIS)
Ma Jianfu; Wu Jianhong
2009-01-01
Neural networks with a non-monotonic activation function have been proposed to increase their capacity for memory storage and retrieval, but there is still a lack of rigorous mathematical analysis and detailed discussions of the impact of time lag. Here we consider a two-neuron recurrent network. We first show how supercritical pitchfork bifurcations and a saddle-node bifurcation lead to the coexistence of multiple stable equilibria (multistability) in the instantaneous updating network. We then study the effect of time delay on the local stability of these equilibria and show that four equilibria lose their stability at a certain critical value of time delay, and Hopf bifurcations of these equilibria occur simultaneously, leading to multiple coexisting periodic orbits. We apply centre manifold theory and normal form theory to determine the direction of these Hopf bifurcations and the stability of bifurcated periodic orbits. Numerical simulations show very interesting global patterns of periodic solutions as the time delay is varied. In particular, we observe that these four periodic solutions are glued together along the stable and unstable manifolds of saddle points to develop a butterfly structure through a complicated process of gluing bifurcations of periodic solutions
Dynamics and Physiological Roles of Stochastic Firing Patterns Near Bifurcation Points
Jia, Bing; Gu, Huaguang
2017-06-01
Different stochastic neural firing patterns or rhythms that appeared near polarization or depolarization resting states were observed in biological experiments on three nervous systems, and closely matched those simulated near bifurcation points between stable equilibrium point and limit cycle in a theoretical model with noise. The distinct dynamics of spike trains and interspike interval histogram (ISIH) of these stochastic rhythms were identified and found to build a relationship to the coexisting behaviors or fixed firing frequency of four different types of bifurcations. Furthermore, noise evokes coherence resonances near bifurcation points and plays important roles in enhancing information. The stochastic rhythms corresponding to Hopf bifurcation points with fixed firing frequency exhibited stronger coherence degree and a sharper peak in the power spectrum of the spike trains than those corresponding to saddle-node bifurcation points without fixed firing frequency. Moreover, the stochastic firing patterns changed to a depolarization resting state as the extracellular potassium concentration increased for the injured nerve fiber related to pathological pain or static blood pressure level increased for aortic depressor nerve fiber, and firing frequency decreased, which were different from the physiological viewpoint that firing frequency increased with increasing pressure level or potassium concentration. This shows that rhythms or firing patterns can reflect pressure or ion concentration information related to pathological pain information. Our results present the dynamics of stochastic firing patterns near bifurcation points, which are helpful for the identification of both dynamics and physiological roles of complex neural firing patterns or rhythms, and the roles of noise.
Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model
Köpf, Michael H
2014-10-07
© 2014 IOP Publishing Ltd & London Mathematical Society. We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first-order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model, e.g., for the deposition of stripe patterns of different phases of surfactant molecules through Langmuir-Blodgett transfer. Employing continuation techniques the bifurcation structure is numerically investigated using the non-dimensional transfer velocity as the main control parameter. It is found that the snaking structure of steady front states is intertwined with a large number of branches of time-periodic solutions that emerge from Hopf or period-doubling bifurcations and end in global bifurcations (sniper and homoclinic). Overall the bifurcation diagram has a harp-like appearance. This is complemented by a two-parameter study in non-dimensional transfer velocity and domain size (as a measure of the distance to the phase transition threshold) that elucidates through which local and global codimension 2 bifurcations the entire harp-like structure emerges.
A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag
Directory of Open Access Journals (Sweden)
Yu Xiaodan
2014-01-01
Full Text Available One type of bifurcation named oscillation emergence bifurcation (OEB found in time-delayed linear time invariant (abbr. LTI systems is fully studied. The definition of OEB is initially put forward according to the eigenvalue variation. It is revealed that a real eigenvalue splits into a pair of conjugated complex eigenvalues when an OEB occurs, which means the number of the system eigenvalues will increase by one and a new oscillation mode will emerge. Next, a method to determine OEB bifurcation in the time-delayed LTI system with single lag is developed based on Lambert W function. A one-dimensional (1-dim time-delayed system is firstly employed to explain the mechanism of OEB bifurcation. Then, methods to determine the OEB bifurcation in 1-dim, 2-dim, and high-dimension time-delayed LTI systems are derived. Finally, simulation results validate the correctness and effectiveness of the presented method. Since OEB bifurcation occurs with a new oscillation mode emerging, work of this paper is useful to explore the complex phenomena and the stability of time-delayed dynamic systems.
Nonresonant Double Hopf Bifurcation in Toxic Phytoplankton-Zooplankton Model with Delay
Yuan, Rui; Jiang, Weihua; Wang, Yong
This paper investigates a toxic phytoplankton-zooplankton model with Michaelis-Menten type phytoplankton harvesting. The model has rich dynamical behaviors. It undergoes transcritical, saddle-node, fold, Hopf, fold-Hopf and double Hopf bifurcation, when the parameters change and go through some of the critical values, the dynamical properties of the system will change also, such as the stability, equilibrium points and the periodic orbit. We first study the stability of the equilibria, and analyze the critical conditions for the above bifurcations at each equilibrium. In addition, the stability and direction of local Hopf bifurcations, and the completion bifurcation set by calculating the universal unfoldings near the double Hopf bifurcation point are given by the normal form theory and center manifold theorem. We obtained that the stable coexistent equilibrium point and stable periodic orbit alternate regularly when the digestion time delay is within some finite value. That is, we derived the pattern for the occurrence, and disappearance of a stable periodic orbit. Furthermore, we calculated the approximation expression of the critical bifurcation curve using the digestion time delay and the harvesting rate as parameters, and determined a large range in terms of the harvesting rate for the phytoplankton and zooplankton to coexist in a long term.
RADLAC II high current electron beam propagation experiment
International Nuclear Information System (INIS)
Frost, C.A.; Shope, S.L.; Mazarakis, M.G.; Poukey, J.W.; Wagner, J.S.; Turman, B.N.; Crist, C.E.; Welch, D.R.; Struve, K.W.
1993-01-01
The resistive hose instability of an electron beam was observed to be convective in recent RADLAC II experiments for higher current shots. The effects of air scattering for these shots were minimal. These experiments and theory suggest low-frequency hose motion which does not appear convective may be due to rapid expansion and subsequent drifting of the beam nose
Benard convection in gaps and cavities
International Nuclear Information System (INIS)
Mueller, U.
1981-04-01
The article contains two parts. In the first part a condensed review of the most striking phenomena in Benard convection in laterally confined fluid layers is given. In the second part recent experimental and theoretical work on Benard convection in gaps is presented an analysed. (orig.) [de
Convective mixing and accretion in white dwarfs
International Nuclear Information System (INIS)
Koester, D.
1976-01-01
The evolution of convection zones in cooling white dwarfs with helium envelopes and outer hydrogen layers is calculated with a complete stellar evolution code. It is shown that white dwarfs of spectral type DB cannot be formed from DA stars by convective mixing. However, for cooler temperatures (Tsub(e) [de
Southern Ocean Convection and tropical telleconnections
Marinov, I.; Cabre, A.; Gnanadesikan, A.
2014-12-01
We show that Southern Ocean (SO) temperatures in the latest generation of Earth System Models exhibit two major modes of variation, one driven by deep convection, the other by tropical variability. We perform a CMIP5 model intercomparison to understand why different climate models represent SO variability so differently in long, control simulations. We show that multiyear variability in Southern Ocean sea surface temperatures (SSTs) can in turn influence oceanic and atmospheric conditions in the tropics on short (atmospheric) time-scales. We argue that the strength and pattern of SO-tropical teleconnections depends on the intensity of SO deep convection. Periodic convection in the SO is a feature of most CMIP5 models under preindustrial forcing (deLavergne et al., 2014). Models show a wide distribution in the spatial extent, periodicity and intensity of their SO convection, with some models convecting most of the time, and some showing very little convection. In a highly convective coupled model, we find that multidecadal variability in SO and global SSTs, as well as SO heat storage are driven by Weddell Sea convective variability, with convective decades relatively warm due to the heat released from the deep southern ocean and non-convective decades cold due to the subsurface storage of heat. Furthermore, pulses of SO convection drive SST and sea ice variations, influencing absorbed shortwave and emitted longwave radiation, wind, cloud and precipitation patterns, with climatic implications for the low latitudes via fast atmospheric teleconnections. We suggest that these high-low latitude teleconnection mechanisms are relevant for understanding hiatus decades. Additionally, Southern Ocean deep convection varied significantly during past, natural climate changes such as during the last deglaciation. Weddell Sea open convection was recently weakened, likely as a consequence of anthropogenic forcing and the resulting surface freshening. Our study opens up the
Hydrodynamical simulation of the core helium flash with two-dimensional convection
International Nuclear Information System (INIS)
Cole, P.W.
1981-01-01
The thermonuclear runaway of helium reactions under the condition of electron degeneracy in the hot, dense central regions of a low mass Population II red giant is investigated. A two-dimensional finite difference approach to time dependent convection has been applied to a peak energy production model of this phenomenon called the core helium flash. The dynamical conservation equations are integrated in two spatial dimensions and time which allow the horizontal variations of the dynamical variables to be followed explicitly. The unbalanced bouyancy forces in convectively unstable regions lead to mass flow (i.e., convective energy transport) by calculation of the velocity flow patterns produced by the conservation laws of mass, momentum, and energy without recourse to any phenomenological theory of convection. The initial phase of this hydrodynamical simulation is characterized by a thermal readjustment via downward convective energy transport into the neutrino cooled core in a series of convection modulated thermal pulses. Each of these pulses is driven by the thermal runaway and quenched by the convective energy transport when the actual temperature gradient in the flash region becomes sufficiently superadiabatic. These convection modulated thermal pulses are observed throughout 95% of the calculation, the duration of which is approximately 570,000 cycles or nearly 96,000 seconds of evolution. After this initial thermal restructuring, there ensues in the simulation a dynamic phase in which the thermonuclear runaway becomes violent. The degree of violence, the final composition, and the peak temperature depend sensitively on the nuclear energy generation rates of those reactions involving alpha particle captures
Topology Optimisation for Coupled Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
This thesis deals with topology optimisation for coupled convection problems. The aim is to extend and apply topology optimisation to steady-state conjugate heat transfer problems, where the heat conduction equation governs the heat transfer in a solid and is coupled to thermal transport...... in a surrounding uid, governed by a convection-diffusion equation, where the convective velocity field is found from solving the isothermal incompressible steady-state Navier-Stokes equations. Topology optimisation is also applied to steady-state natural convection problems. The modelling is done using stabilised...... finite elements, the formulation and implementation of which was done partly during a special course as prepatory work for this thesis. The formulation is extended with a Brinkman friction term in order to facilitate the topology optimisation of fluid flow and convective cooling problems. The derived...
Convective penetration in a young sun
Pratt, Jane; Baraffe, Isabelle; Goffrey, Tom; MUSIC developers group
2018-01-01
To interpret the high-quality data produced from recent space-missions it is necessary to study convection under realistic stellar conditions. We describe the multi-dimensional, time implicit, fully compressible, hydrodynamic, implicit large eddy simulation code MUSIC. We use MUSIC to study convection during an early stage in the evolution of our sun where the convection zone covers approximately half of the solar radius. This model of the young sun possesses a realistic stratification in density, temperature, and luminosity. We approach convection in a stellar context using extreme value theory and derive a new model for convective penetration, targeted for one-dimensional stellar evolution calculations. This model provides a scenario that can explain the observed lithium abundance in the sun and in solar-like stars at a range of ages.